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**Analysis of Coplanar Intermediate Coils for EV Charging**

**Introduction**

Developing high power charging systems for EVs has several challenges since the vehicle manufacturers want the vehicle pad to be as small as possible but also want the system to operate over a large air gap at high eﬃciency. Despite these requirements, the output power from IPT systems with two coils are still fundamentally bound by the following equation derived in Section 2.3.1:

Since *ω* is fixed by regulatory committees and *Q*_{LOAD} is ideally limited to around 10 to limit the system sensitivity to parameter variations as well as the VA and losses on the secondary, the only other parameters that a system designer can adjust are the primary vars (*ωL*_{P}*I*_{LP}2) or the coupling factor (*k*). Given that the air gap size between the primary and secondary pads cannot be reduced, the usual approach to achieve improved coupling is to increase the size of the pads. Alternatively, one or more intermediate coupler coils that sit in the air gap between the primary and secondary can be used to eﬀectively increase the transmitting range without having to increase the size of the primary and secondary pads [146,166,168,187–198] and it is this eﬀectiveness of this approach which is investigated in this chapter. Intermediate coupler coils are normally independently tuned near the operating frequency of the system and increase the transmitting range since they produce extra flux within the air gap. Several systems with intermediate couplers have been built including an experiment [188] where six intermediate coupler coils were used to increase the transmitting range to 2*.*1 m while delivering 18 W with a maximum eﬃciency of 60.4%.

Integrating intermediate coupler coils within an EV charging system is impractical in most cases since the intermediate coil would have to be floating in mid air. An alternative approach is proposed in [146] where an independently tuned coplanar intermediate coil was placed within the ground pad structure as shown in Fig. 3.2. The results from this study have shown an increase in system eﬃciency which was attributed to an increase in the apparent coupling factor from 0.191 to 0.408 when compared to a system without the intermediate coil.

While the results presented in 3.2 were interesting, the work did not present a fair comparison of both systems since the system without the intermediate coil had less copper (and hence current carrying turns) within the ground pad assembly. Other similar studies also have made assumptions in order to simplify the analysis such as assuming ideal tuning [166], ignoring the coupling from the primary to the secondary coils [166,168,198], assuming that the coupling factor from both the primary and intermediate coupler coils to the secondary coils is equal [187], or combining several coupling factors into one fixed value [146]. However, these assumptions are not valid for all the possible intermediate coil configurations.

To fully evaluate the benefits of having a coplanar intermediate coupler, a study com-paring a traditional system comprised of only one primary and one secondary coil (referred to as the two coil system) to a system with an intermediate coupler (referred to as a three coil system) was carried out. For this study a mathematical model was developed that allows any three coil system to be converted to an equivalent two coil system so that they can be compared. The mathematical model considers all of the variables in the system so it can be applied independent of the tuning topology. The initial results from this work were presented at the ECCE 2014 conference [199] and then expanded to a journal paper [200].

**Mathematical model development**

In this section the mathematical model required for the rest of this chapter will be derived. The model allows three coil systems to be transformed into an equivalent two coil system for comparison as required. Initially the model is derived for just parallel-parallel (PP) tuned systems and then it is adapted for series-series (SS) tuned systems. Models for analysing other tuning topologies such as parallel-series or series-parallel can be derived following a similar approach.

**Comparing two coil and three coil systems**

Basic two coil and three coil IPT systems are shown in Fig. 3.3(a) and (b) respectively. The primary, intermediate and secondary coils *L*_{P}, *L*_{I} and *L*_{S} are tuned by the tuning capacitors *C*_{P}, *C*_{I} and *C*_{S} respectively. Since the power supplies are parallel tuned, they are driven by a current source *I*_{AC} however, most equations will be expressed in terms of the primary coil current *I*_{LP}. The coupling between the coils is given by *k* for the two coil system and *k*_{PI}, *k*_{PS} and *k*_{IS} for the three coil system.

The output power of a two coil system (as discussed in Section 2.3.1) can be given (3.1). The term *ωL*_{P}*I*_{LP}2 is the primary coil vars assuming that the reflected impedances are low. Using (3.1), two coil systems can be compared by keeping *Q*_{LOAD} fixed and driving both pads with the same amount of input vars. The system with the highest output power will be the system with the highest coupling and hence the highest eﬃciency after optimisation.

In a similar way, the *V*_{OC} and *I*_{SC} of a three coil system can be given by:

The first two terms of (3.4) are functions of the primary and intermediate coil vars √similar to (3.1) but the third term 2*k*_{PS}*k*_{IS} *L*_{P}*L*_{I}*I*_{LP}*I*_{LI} is not. This means that three coil systems cannot be compared to two coil systems by just keeping the input vars constant. The simplest way of comparing two coil systems to three coil systems is therefore to compare the system eﬃciencies when delivering a fixed output power.

**A two coil equivalent model**

To have a fair comparison between two coil and three coil systems, both structures must have the same layout and volume of copper in the primary and secondary sides. This separates the benefits of adding extra copper to the primary pad from the benefits of having an independently tuned intermediate coupler. A three coil system can be converted to a two coil system by driving the primary and intermediate coil in series as shown in Fig. 3.4 (a). The resulting equivalent two coil system shown in Fig. 3.4(b) has a primary coil inductance of *L*_{P−2} and the coupling between the primary and secondary is *k*_{PS−2}. The ‘-2’ notation in the subscript denotes a two coil equivalent variable.

Since *L*_{P} and *L*_{I} are simply two mutually coupled inductors in series, *L*_{P−2} is simply defined as:

The equivalent two coil system coupling factor can be found by equating the open-circuit voltage of the three coil system with the open-circuit voltage of the two coil equiv-alent system as shown:

This equation can be rearranged to give:

**Steady-state model for parallel-parallel systems**

A three coil system can now be compared with its two coil equivalent system by com-paring the eﬃciencies of the two systems. Here, the pad and source losses must both be considered because the pad losses tend to be the highest loss in a parallel-parallel tuned IPT system, whereas the source losses also start to become more significant when con-sidering series-series systems. Capacitor losses on the other hand are significantly lower since the tuning capacitors tend to have quality factors in excess of 2000. As such these capacitor losses are neglected in the following analysis for simplicity. This subsection will show the development of a mathematical model which considers pad losses for a parallel-parallel system. In Section 3.2.4 the model will be modified to allow for the modelling of series-series tuned systems while the source losses will be accounted for in Section 3.2.5.

The three coil and the two coil equivalent systems which will be modelled are shown in Fig. 3.5(a) and (b) respectively. Here, *r*_{P−2} in the two coil model is the sum of *r*_{P} and *r*_{I}. For this evaluation, the primary tuning capacitance* C*_{P} and* C*_{P−2} in both systems is assumed to automatically adjust itself so that the impedance seen by the supply *I*_{AC} is always purely resistive. In practice, this can be achieved by using a self-tuning converter such as that discussed in Chapter 4. Here *L*_{I} and *C*_{I} are tuned to frequency *f*_{I} (angular frequency *ω*_{I}) while *L*_{S} and *C*_{S} are tuned to frequency *f*_{S} (angular frequency *ω*_{S}). The power supply is assumed to operate at a constant driving frequency *f* (angular frequency) and the eﬀects of bifurcation are ignored due to operation at low secondary *Q*_{LOAD} All the results presented in this paper have *f* fixed at 85 kHz.

By applying Kirchoﬀ’s voltage law to each tuned coil in Fig. 3.5(a), the following equations can be derived:

The currents in (3.11) and (3.12) are expressed in terms of *I*_{LP} and *I*_{LP−2} respectively, instead of in terms of *V*_{AC} for convenience. The expressions for *S*_{I}, *S*_{S} and *S*_{S−2} are not used but are included for completeness. Furthermore, (3.8)-(3.12) are applicable to any three coil IPT system, regardless of the location of the intermediate coil, and not just the coplanar intermediate coil structures studied later in this chapter. The output power of each system can be calculated using:

**A modified model for series-series systems**

Several studies have used intermediate couplers with series–series tuned systems. To ensure a more comprehensive analysis, the model in Section 3.2.3 will be modified here to accommodate series–series tuned systems shown in Fig. 3.6.

**Modelling Source Losses**

The source losses are the losses that occur in the components that generate the AC current in the power supply. In a practical system they would be the losses within the high frequency inverter and they can be modelled by a resistor. The source loss is important to consider for series LC tuned power supplies since the inverter has to provide the vars to drive the track. This can be seen in Fig. 3.7(a) where the primary coil current *I*_{LP} flows through the source *V*_{AC} resulting in noticeable source losses. However with a parallel tuned primary system, the large track current is created by the resonant LC tank as shown in Fig. 3.7(b). The source loss has much less impact here given the power supply only provides the real power necessary to drive the load and overcome other losses. As a result, there is a lower source current *I*_{src} and therefore lower source losses compared to a series tuned power supply.

For this study it is assumed that the inverter is an H-bridge is driven by an ideal DC source with ideal gate driving circuitry. The main losses in an H-bridge are the conduction losses and the switching losses. The conduction losses in an H-bridge are given by:

where *R*_{ON} is the on state resistance of one switch.

In this analysis switching losses can be assumed to be negligible compared to the conduction losses. This is because the circuit is eﬀectively zero current switched since the inductor and its reflected impedances are perfectly tuned using *C*_{P} and *C*_{P−2}. In practice this is verified by a previous study which used a similar converter and found that the switching losses were only 20% of the total H-bridge losses [175]. Even if the primary coil was slightly mistuned, as is normally done to avoid the eﬀects of bifurcation in series tuned primary coils, the maximum switching loss of a power MOSFET can be approximated to within 30% [201] by:

where *I*_{D} and *V*_{D} are the drain current and drain voltage of the switch at the moment of switching, *t*_{ON} and *t*_{OFF} are the turn on and turn oﬀ times of the MOSFET and *f* is the switching frequency. This suggests that the switching loss is proportional to the power being delivered by the H-bridge. In this study, the output power is always held constant at 1 kW in all the situations explored so any switching losses will be approximately constant and hence can be ignored in the comparisons.

The source resistance can therefore be approximated as:

Since *R*_{ON} is dependent on the quality of the MOSFETs used, simulations will be run at *r*_{src} = 0, 0.08 and 0*.*2 Ω. This allows the system to be evaluated with no source resistance, as well as allowing the trend of varying source losses to be observed.

The source current for a parallel-parallel tuned system is given by:

**Model Validation with LTSpice**

To validate the mathematical model, the circuit shown in Fig. 3.5(a) was simulated in LTspice with the parameters listed in Table 3.1.

Table 3.1: Parameters used to validate mathematical model based on experimental data The values for key parameters were solved with the mathematical model as well as with the LTspice model and the results are presented in Table 3.2. The measurements from the LTspice model were collected at steady state. It can be seen that there is very little diﬀerence between the mathematical model and the LTspice simulation at steady state.

**Magnetic Modelling**

With the complexity of (3.22) and the equations leading to it, a simplification is very diﬃcult to carry out without making some assumptions. However, since the aim of this study is to consider various intermediate coupler designs, it is not possible to make an assumption that applies to all scenarios. Instead, a wide range of three coil system designs which may be of interest will be considered.

For this study, a 420 mm circular pad which was optimised in [117] was used as the base pad for both the primary and secondary pads. The dimensions of this pad are listed in Appendix A. The original primary coil was removed and a variety of diﬀerent primary and intermediate coupler winding designs have been investigated. In all the simulated designs a total of 12 turns of 4 mm diameter copper wire were used to construct both the primary and intermediate coupler windings. The secondary pad was not changed. The primary and secondary pads were aligned at their centres and separated with a pad to pad air gap of 100 mm between them.

In total 62 models were simulated in JMAG with various combinations of primary and intermediate coil locations as shown in the general configuration in Fig. 3.8. Primary coils with 1, 4, 6, 8 and 11 turns were simulated while maintaining a total of 12 turns for both the primary and intermediate coupler coils. Simulations with the primary coil placed either inside or outside the intermediate coupler coil were also carried out.

The inductance of each winding and the coupling between them were measured from the JMAG simulations. Since it is diﬃcult to simulate the AC losses within the pad, the ESR of each winding was simply assumed to be 0*.*0146 Ω for every meter of litz wire used. This is the average resistance per meter when the wire was placed on top of the ferrite and aluminium shielding as measured with an Agilent E4980A LCR meter set to 85 kHz. This represents both the AC resistance of the winding as well as the losses in the ferrite. It is also assumed that the ferrite does not saturate under all operating conditions tested.

In this study five cases of particular interest are discussed as described in the following sections. The structures of the primary pads are shown in Fig. 3.9 with the measured parameters presented in Table 3.3 and the parameters for the rest of the cases that were simulated can be found in Appendix B. The magenta coloured coil in Fig. 3.8 and Fig. 3.9 is the primary coil (*L*_{P}) while the yellow coloured coil is the intermediate coupler winding (*L*_{I}).

**Contents**

**Abstract **

**Acknowledgements **

**Nomenclature **

**1 Introduction**

1.1 Introduction

1.2 Electric vehicles

1.3 Inductive Power Transfer

1.4 Inductive Power Transfer for EV charging

1.5 Thesis objectives and outline

**2 Fundamentals of Inductive Power Transfer Systems **

2.1 Introduction

2.2 IPT system topologies

2.3 Basic IPT system analysis techniques

2.4 IPT Pad topologies

2.5 IPT Power supply topologies

2.6 IPT Secondary side topologies

2.7 System modelling tools

2.8 Conclusions

**3 Analysis of Coplanar Intermediate Coils for EV Charging **

3.1 Introduction

3.2 Mathematical model development

3.3 Magnetic Modelling

3.4 Tuning intermediate coupler and secondary coils

3.5 Efficiency comparisons between cases using the parallel-parallel tuning topology

3.6 Analysis with series-series tuned topologies

3.7 Practical considerations

3.8 Experimental results

3.9 Conclusions

**4 Self-Tuning Push-pull Power Supply **

4.1 Introduction

4.2 Push-pull converter operation

4.3 Steady state model

4.4 Switchable capacitor bank .

4.5 Experimental results

4.6 Discussions

4.7 Conclusions

**5 Mistuning Tolerant Push-pull Power Supply **

5.1 Introduction

5.2 Proposed Topology

5.3 Mathematical Model

5.4 Constant current control

5.5 Experimental results and discussions

5.6 Conclusion

**6 EV Detection Scheme for Dynamic Highway Charging **

6.1 Introduction

6.2 Detection of secondary pad

6.3 Implementation with multiple electronic topologies

6.4 Simulation of a highway charging system

6.5 Experimental results

6.6 Considerations for large scale system implementations

6.7 Conclusion

**7 Development of a general system model for future comparisons **

7.1 Introduction

7.2 Points of interest when approaching a general comparison

7.3 Different modelling approaches

7.4 Development of the model

7.5 Evaluation of proposed model

7.6 Discussion for future work using the presented model

7.7 Conclusions

**8 Conclusion and Future Work **

8.1 Conclusions

8.2 Future Work

8.3 Thesis outputs

Bibliography

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Development of Intermediate Controllers for Inductive Charging Systems in Dynamic Roadway Systems