# Efficient Wireless Drone Charging Pad for Any Landing Position and Orientation

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## Abstract

**:**

## 1. Introduction

- −
- Full integration in the landing gear of the receiving coil, meaning that no extra weight and no reduction in payloads occur;
- −
- High tolerance of misalignment conditions through the adoption of an array of planar transmitting coils in the ground base station;
- −
- High charging power and good electrical efficiency for every possible drone landing position and orientation in the ground base station.

## 2. WPT Equivalent Circuit

_{1}and L

_{2}and by the mutual inductance M [3]; and the ohmic losses are modeled by the resistances R

_{1}and R

_{2}for the transmitting (primary) and receiving (secondary) coils, respectively. The series-parallel (SP) compensation topology is adopted, since this topology allows greater efficiency when the number of turns of the secondary coil is small, as described in [10,11]. The capacitor C

_{1}is connected in series with the transmitting coil, while the capacitor C

_{2}is connected in parallel with the receiving coil. The values of C

_{1}and C

_{2}are adequately chosen to obtain the resonance condition at the same operational angular frequency ω

_{0}= 2πf

_{0}as:

_{s}; in reality, the feeding block includes converters (i.e., a rectifier and an inverter). A similar simplification is adopted for the load, here modeled by a simple resistance R

_{L}at resonance while in real world it includes an AC/DC converter (i.e., a rectifier), a charging regulator and a battery, as shown in Figure 2. From the battery specification, it is possible to approximately calculate the value of the equivalent resistance R

_{dc}. This value depends on the voltage and current waveforms in the receiving coil, but for the sake of simplicity and without introducing a large approximation, the load resistance R

_{L}before the rectifier is assumed to be

_{dc}and I

_{dc}are the voltage and current after the rectifier, respectively, when neglecting the losses in the AC/DC converter.

_{L}is the real power on the resistive load R

_{L}(i.e., port 22’ in Figure 1), given by:

_{1}is the real power at the input port 11’ of the transmitting circuit given by

_{1}and I

_{1}the voltage and current at the input port (i.e., port 11’ in Figure 1).

_{1}modeling the ohmic losses on the primary coils, are directly obtained from the Litz wire datasheet. The inductances L

_{1}and L

_{2}and M are calculated by post-processing the magnetic field distribution in the considered domain, which can be obtained through the numerical solution of the time-harmonic magneto-quasi-static (MQS) field equations, using the finite element method (FEM). The simulations are performed in this work using the commercial software COMSOL for solving the magnetic field equations:

**B**is the magnetic flux density,

**J**is the external current density,

_{e}**A**is the magnetic vector potential and V is the electric potential. Magnetic insulation is imposed at the external boundaries of the computational domain, far from the source. The coils are modelled as 1D loops, where the currents are imposed using the Edge Currents tool. In the presence of thin conductive material, the Transition Boundary Conditions (TBCs) can be applied to reduce the computational cost as they avoid the discretization of the conductive regions. The theory of TBC can be found in [24,25].

_{in}at the input port 11’ for the SP compensation is given by [26]:

_{0}= 2π f

_{0}, by replacing the capacitors C

_{1}and C

_{2}given by (1) in (8), the input impedance becomes:

## 3. System Configuration

- A.
- WPT Design Specifications

_{bat}= 14.4 V. It can be assumed that the battery capacity is 5 Ah, so that the total energy is E

_{bat}= 72 Wh.

_{wpt}requested from the charging system can be expressed in relation to the desired charging time T

_{ch}, expressed in hours as

_{ch}= 1 h is adopted here, which corresponds to a charging power of P

_{wpt}= 72 W. The equivalent resistance is approximately R

_{L}= 2.9 Ω.

- B.
- WPT Coil Design

_{1}= 30 cm, d

_{2}= 20 cm, d

_{3}= 25 cm, d

_{4}= 10 cm and d

_{5}= 15 cm, as shown in Figure 3b. It should be noted that the size of the landing gear is significantly smaller than the wavelength at 300 kHz, that is, about 1000 m. The electrical parameters of the landing gear in terms of self-inductance and self-resistance are obtained by calculation and measurement. The external inductance was calculated by a MQS field analysis while the AC resistance of the landing gear was measured by an RLC meter at the considered frequency [17]. The obtained values were L

_{2}= 1.33 μH and R

_{2}= 33 mΩ.

^{2}. It is clear that with such a large charging area demand, a single primary coil, much larger than the secondary coil, leads to very poor coupling factor k and electrical efficiency η. To avoid this inconvenience, an array of square transmitting coils is proposed, with the goal of assuring an efficiency in the landing area η ≥ 75% for any possible landing position and orientation of the drone in the ground pad.

- detecting the maximum size of the single transmitting coil suitable to meet the efficiency target for the admissible lateral offset;
- defining the array in terms of number, size and position of the coils.

_{rx}) and the y-axis (t

_{ry}). The allowable length of the s side of the transmitting coil is set in the range 0.3–0.6 m. A smaller size for s is not considered as the transmitting coil would be smaller than the receiving coil (i.e., landing gear). Conversely, a larger transmitting coil would produce too large a magnetic flux leakage. The maximum lateral offset is set at t

_{rmax}= 0.3 m in both the x- and y-axis directions.

_{rx}and t

_{ry}for different values of transmitting coil side s are shown in Figure 5. For each configuration considered, the electrical efficiency η was also calculated from the analysis of the equivalent electrical circuit, considering N

_{1}= 10 turns of the primary coil and R

_{L}= 2.9 Ω, as shown in Figure 6. For all the calculations, the input voltage was adjusted to obtain a fixed output power P

_{2}= 72 W. The efficiency, defined by (3), was calculated through the analysis of the equivalent circuit of Figure 1. The design target for the efficiency was set at η ≥ 75%. A minimum efficiency of 75% is assumed to be very good for this type of application, considering the high variability of the drone’s landing position. Furthermore, this efficiency value does not degrade the wireless charging process. However, the efficiency target is an input design parameter and can be varied.

_{rx}≤ 50 cm and t

_{ry}≤ 50 cm (landing area 1 m

^{2}), an array of multiple transmitting coils was adopted. With four transmitting coils, arranged as a 2 × 2 matrix, it was possible to obtain η ≥ 75% for any lateral offset t

_{rx}≤ 54 cm and t

_{ry}≤ 54 cm. The four planar coils were partially overlapped for a distance O

_{p}= s/2–t

_{rmax}= 3 cm, to avoid areas (from t

_{rmax}–s/2) where the efficiency was below the efficiency target. It should be noted that t

_{rmax}for the considered case of square coils is assumed to be the same on both x and y axis. The conductors of the transmitting coils were insulated with a thin layer of plastic to avoid electrical contact between them.

_{in}in (9) is strongly dependent on the mutual inductance M, which is proportional to the coupling factor k. A graph of the input impedance Z

_{in}vs. k is shown in Figure 9. A higher value of the coupling factor k, or mutual inductance M, generally leads to an increase in electrical efficiency [4], as can also be seen from (10). The procedure for choosing the coil in the landing pad to be activated is as follows: after the drone has landed, the electronic unit powers one transmitting coil at a time to evaluate its input impedance Z

_{in}and memorize this value. In this way, Z

_{in}is evaluated for all five landing pad coils. At the end of polling, the coil that features the highest Z

_{in}input impedance is selected as the transmitting coil to be activated. The input impedance Z

_{in}is calculated by measuring the input voltage V

_{1}, the input current I

_{1}and the phase between them. A block diagram summarizing the selection of the transmission coil, in which there is a five-port switch controlled by the control unit to select the best transmitting coil, is presented in Figure 10.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Coil configuration with a single transmitting coil (in green) and a 3D receiving coil (in red) (

**a**). Top view of the coil configuration with lateral offsets t

_{rx}, t

_{ry}and rotation θ of the receiving coil (

**b**).

**Figure 5.**Coupling factor k vs. lateral misalignments t

_{rr}(

**a**) and t

_{ry}(

**b**) for variable side length s of the transmitting coil.

**Figure 6.**Efficiency η vs. lateral misalignment (offset) t

_{rx}(

**a**) and t

_{ry}(

**b**) for variable side length s of the transmitting coil.

**Figure 12.**Transmitting coil activation at any point of the landing area using the same colors for the coils as in Figure 8.

**Table 1.**Electrical quantities in the equivalent circuit for different values of the coupling factor k.

k | I_{1} (A) | I_{s} (A) | V_{1} (V) | V_{2} (V) | η |
---|---|---|---|---|---|

0.06 | 8.03 | 8.10 | 11.75 | 14.48 | 0.77 |

0.10 | 4.51 | 8.11 | 19.62 | 14.47 | 0.81 |

0.15 | 2.99 | 8.15 | 26.71 | 14.48 | 0.89 |

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**MDPI and ACS Style**

Campi, T.; Cruciani, S.; Maradei, F.; Feliziani, M. Efficient Wireless Drone Charging Pad for Any Landing Position and Orientation. *Energies* **2021**, *14*, 8188.
https://doi.org/10.3390/en14238188

**AMA Style**

Campi T, Cruciani S, Maradei F, Feliziani M. Efficient Wireless Drone Charging Pad for Any Landing Position and Orientation. *Energies*. 2021; 14(23):8188.
https://doi.org/10.3390/en14238188

**Chicago/Turabian Style**

Campi, Tommaso, Silvano Cruciani, Francesca Maradei, and Mauro Feliziani. 2021. "Efficient Wireless Drone Charging Pad for Any Landing Position and Orientation" *Energies* 14, no. 23: 8188.
https://doi.org/10.3390/en14238188