WPW 2022 - Mini Assignment

## IEEE Wireless Power Week 
# Mini Assignment 
### Specifications & Guidelines

.TitleAuthor[Duleepa J Thrimawithana & Grant A Covic]

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.logo-slide[]
.footer[[Duleepa J Thrimawithana](https://www.linkedin.com/in/duleepajt) & [Grant A Covic](), Department of Electrical, Computer and Software Engineering (2022)]

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# The Application

.left-column-s[
- Autonomous robots are increasing used in hospitals for various applications
- These robots need to be charged in-between shifts
- Wireless charging in an ideal solution for this application
- Due to low ground clearance, these robots are typically charged through a wall mounted charger
 - It also simplifies the design, since this ensures little change in air-gap and y-axis alignment 
- In this assignment we will develop the magnetic couplers and the electronics for a 1kW wireless charging station for robots
]

.right-column-s[
.center[
<img src="img/wpt.jpg" width="380">
.credits[Wireless charging station for robots [[1]](https://industrytoday.com/wireless-charging-for-industry-4-0s-mobile-robots/)]
]
]

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# Key Design Specifications

<table class="tg" style="undefined;table-layout: fixed; width: 747px; margin-left:auto; margin-right:auto;">
  <colgroup>
  <col style="width: 433px">
  <col style="width: 314px">
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  <thead>
    <tr>
      <th class="tg-dzaw"><span style="color:white">Parameter</span></th>
      <th class="tg-dzaw"><span style="color:white">Value</span></th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="tg-jayl">Input DC Voltage</td>
      <td class="tg-jayl"> 450V</td>
    </tr>
    <tr>
      <td class="tg-sabo">Output DC Voltage</td>
      <td class="tg-sabo">52V</td>
    </tr>
    <tr>
      <td class="tg-ig71">Power Rating</td>
      <td class="tg-ig71">1kW</td>
    </tr>
    <tr>
      <td class="tg-sabo">Operating Frequency</td>
      <td class="tg-sabo">85kHz</td>
    </tr>
    <tr>
      <td class="tg-ig71">Operating Air Gap</td>
      <td class="tg-ig71">100mm</td>
    </tr>
    <tr>
      <td class="tg-sabo">X-Axis Misalignment</td>
      <td class="tg-sabo">± 40mm</td>
    </tr>
    <tr>
      <td class="tg-ig71">Y-Axis Misalignment</td>
      <td class="tg-ig71">0mm</td>
    </tr>
    <tr>
      <td class="tg-sabo">Maximum Coil Current Density</td>
      <td class="tg-sabo">4A/mm<sup>2</sup></td>
    </tr>
    <tr>
      <td class="tg-ig71">Maximum Ferrite Flux Density</td>
      <td class="tg-ig71">100mT</td>
    </tr>
    <tr>
      <td class="tg-sabo">Recommended Primary Compensation Topology</td>
      <td class="tg-sabo">LCL or LCCL</td>
    </tr>
    <tr>
      <td class="tg-ig71">Recommended Secondary Compensation Topology</td>
      <td class="tg-ig71">Parallel</td>
    </tr>
  </tbody>
</table>

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# The Design Process
### Recommendations & Guidelines

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.logo-slide[]
.footer[[Duleepa J Thrimawithana](https://www.linkedin.com/in/duleepajt) & [Grant A Covic](), Department of Electrical, Computer and Software Engineering (2022)]

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name: S3

# Step 1: FEM Model of the Couplers (PI)

.left-column[
- An Ansys Maxwell model, which has a unipolar square primary coupler design, is provided to you 
 - The coil of the primary coupler is sized to be 300mm x 300mm
 - The ferrite base is sized to be 350mm x 350mm
 - Initially, a 10mm thick ferrite base and a conductor diameter of 5mm is assumed
 - An inner to outer diameter ratio of 40% is used for the coil
- Modify the Ansys Maxwell model to add a secondary coupler that is identical to the primary
- Place the secondary coupler such that the air gap is 100mm and it is center aligned
]

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name: S4

# Step 1: FEM Model of the Couplers (PII)

.center[<iframe width="800" height="450" src="https://www.youtube.com/embed/8_JAxLc0OhM" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>]

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name: S5

# Step 2: Worst Case Coupling (PI)

- Move the secondary coupler such that it is misaligned in the x-direction by 40mm
 - This is because we want to simulate the worst case situation for coupling 
- Worst case coupling dictates the circuit parameters since the design will employ LCL compensation in the primary and parallel compensation in the secondary
 - As coupling increases, power converters are modulated to regulate power

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name: S6

# Step 2: Worst Case Coupling (PII)

.center[<iframe width="800" height="450" src="https://www.youtube.com/embed/cL3elc9B_XI" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>]

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name: S7

# Step 3: Highest Primary & Secondary VA

- Knowing the worst case coupling, we can now start to determine the highest VA we primary and secondary should be driven at since
\\[P\_{o} = k \sqrt{\mathit{VA}\_{pt}\mathit{VA}\_{st}} \sin(\theta) \\]
- As we have not specified any restrictions, we can assume the both the primary and secondary couplers can be designed to have similar Qs
 - Thus, to achieve best efficiency, `\( \mathit{VA}_{pt} = \mathit{VA}_{st} \)`
- Lets also assume that we are going to compensate the system such that `\( \sin(\theta) \approx 1 \)` under worst case k 
- We can now determine `\( \mathit{VA}_{pt} \)` and `\( \mathit{VA}_{st} \)`, and in our example since `\( k = 0.313 \)`
\\[P\_{o} = k \mathit{VA}\_{pt} = k \mathit{VA}\_{st} \quad \Rightarrow \quad \mathit{VA}\_{pt} = \mathit{VA}\_{st} = \frac { 1000} {0.313} \approx 3.2kVA \\]

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name: S8

# Step 4: Coupler Inductances

- So far we simulated the couplers assuming only a single turn in the primary as well as secondary coils
- To determine the number of turns, we need to first know the inductance we aim for in each coupler
 - Inductance required depends on the compensation strategy we aim to employ
- Lets assume we plan to use LCL compensation in the primary and parallel compensation in the secondary
\\[I\_{pt(RMS)} \approx \frac {2 \sqrt{2} V\_{in}} {\pi \omega L\_{pi}} = \frac {2 \sqrt{2} V\_{in}} {\pi \omega L\_{pt}} \quad \text{and} \quad  I\_{st(RMS)} \approx \frac {\pi V\_{out}} {2 \sqrt{2} \omega L\_{st}} \\]
- Since we know `\( \mathit{VA}_{pt} \)` and `\( \mathit{VA}_{st} \)` as well as `\( V_{in} \)` and `\( V_{out} \)`
\\[L\_{pt} \leqslant \frac { 8V\_{in}^2 } {\pi^2 \omega \mathit{VA}\_{pt}}  \quad \text{and} \quad L\_{st} \leqslant \frac { \pi^2 V\_{out}^2 } {8 \omega \mathit{VA}\_{st}} \\]
- Based on the design specifications, we can calculate `\( L_{pt} \leqslant 96 \mu H \)` and `\( L_{st} \leqslant 1.95 \mu H\)`

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name: S9

# Step 5: Final Coupler Specifications (PI)

- From the initial Ansys Maxwell simulations, per-turn inductance of the primary coil, `\( \mathit{AL}_{pt} \)`, and the secondary coil `\( \mathit{AL}_{st} \)` were similar due to their identical geometries and was,
\\[\mathit{AL}\_{pt} = \mathit{AL}\_{st} = 0.48 \mu H \text{ per turns squared} \\]
- Therefore, we can calculate the turns needed in the primary coil, `\( N_{pt} \)`, as 14 and the turns needed in the secondary coil, `\( N_{st} \)`, as 2, which theoretically result in 
\\[ L\_{pt} = 0.48 \times 14^2 =  94 \mu H \quad \text{and} \quad L\_{st} = 0.48 \times 2^2 =  1.92 \mu H  \\]
- The current in each coupler can be now found as 
\\[ I\_{pt} = \sqrt{ \mathit{VA}\_{pt} / \omega L\_{pt} } \approx 8A\_{rms} \quad \text{and} \quad I\_{st} = \sqrt{ \mathit{VA}\_{st} / \omega L\_{st} } \approx 56A\_{rms} \\]
- Refine the Ansys Maxwell model to reflect these coupler specifications and simulate to obtain the final `\( k \)`, `\( L_{pt} \)` and `\( L_{st} \)` values both at X = 0mm and X = 40mm

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name: S10

# Step 5: Final Coupler Specifications (PII)

.center[<iframe width="800" height="450" src="https://www.youtube.com/embed/Hf0AmImIqLw" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>]

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name: S11

# Step 6: Designing Compensation & Simulate (PI)

- From the latest Ansys Maxwell simulation results we know expected `\( k \)`, `\( L_{pt} \)` and `\( L_{st} \)` values both at X = 0mm and X = 40mm
- Using these values we can determine the parallel tuning capacitors needed in the primary and secondary 
 - We can for example design the system to be tuned at X = 40mm
 \\[ C\_{pt} = \frac {1} {\omega^2 L\_{pt} } \quad \text{and} \quad C\_{st} = \frac {1} {\omega^2 L\_{st} } \\]
- In a practical system, the LCL compensation network is required to have a series blocking capacitor to avoid DC circulating currents in case the primary inverter output voltage has a DC average
 - We can for example, add a series capacitor `\( C_{pi} \)` in series with `\( L_{pi} \)` such that
\\[ \omega L\_{pt} = \omega L\_{pi} - \frac {1} {\omega C\_{pi}} \\]
- We can now simulate this wireless charger in, for example, LTspice to investigate its performance

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name: S12

# Step 6: Designing Compensation & Simulate (PII)

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name: S13

# Step 7: Designing Controller (PI)

- A short-circuit controller can be used in the secondary to control the power delivered to the battery in the robot 
- In this case both the primary inverter and the secondary short-circuit controller can be controlled to achieve best performance
 - This however leads to a quite challenging controller design
- Since the variation of `\( k \)` in this design is quite small we can choose to only use the short-circuit controller and maintain the primary always at its maximum duty-cycle 
- As the final step of this project, develop a slow-switching short-circuit controller to regulate the output voltage of the secondary to 52V
 - Modify the LTspice model to validate the design 
 - Model the battery of the robot as a load resistor that has a value between 2.7Ω and 5.4Ω 
- After concluding the project prepare a small presentation highlighting your findings

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name: S14

# Step 7: Designing Controller (PII)

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name: S15

# Optional Further Improvements

- You may wish to improve your design further and these improvements can be to the magnetic design, compensation topology, power electronics and/or control
- In case of the magnetics, in a practical application the weight of the secondary needs to be minimized 
 - You can investigate DD couplers and try to make the secondary coupler smaller than the primary by redistributing the VAs
- In case of the compensation, in a practical design, having just 2 turns in the secondary can lead to poor `\( k \)`
 - We didnt observe this as the winding was modeled as a plate in Ansys Maxwell
 - One option can be to have a higher inductance in the secondary and use series compensation 
 - Also when selecting the compensation components you can consider zero voltage switching conditions
- In case of the power electronics, we should model the losses and ensure devices selected are suitable
 - You can improve the LTSpice model using device models provided by for example Wolfspeed and investigate losses in both the primary and the secondary converter

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# The End