1. Introduction
Implantable medical devices (IMDs) are used for monitoring physiological signs, therapeutic functions, and the treatment of chronic diseases [
1,
2,
3,
4]. According to [
3,
4], in 2019, about 10-million people worldwide depended on implantable cardiac pacemakers, and this number has grown by about 15% per year. Most IMDs use built-in batteries for their operation, and for fully IMDs, the battery replacement is performed through a surgical procedure [
1,
2,
3,
4]. Battery replacement through a surgical procedure has the potential for infection and generates patient anxiety, and during battery replacement, the IMD must be turned off [
1]. Based on these prerogatives, a wireless power transfer system (WPT) becomes very interesting for charging implantable devices; after all, this would significantly reduce the number of surgical procedures for replacing batteries, increasing the lifespan of the device and allowing operation during battery recharging [
3,
4,
5]. Currently, wireless power transfer is being used in IMDs through a near-field resonant inductive coupling (NRIC) [
4]. Some examples would be cochlear implants, whose function is to restore hearing in patients with hearing loss, ocular and retinal implants, whose function is to restore vision in patients with visual impairment, and neurostimulator implants, used to restore motor and sensory function [
4,
6].
Basically, in an application of WPT in IMDs, the primary transmitting coil is positioned close to the patient’s skin. From the circulation of a time-varying current, a magnetic field is induced in the receiving coil, implanted next to the load, and in this way, current is produced to charge the device [
7]. However, applying WPT to IMDs brings with it some concerns. A serious restriction, related to biocompatibility, concerns the exposure of living beings to the electromagnetic field and the specific absorption rate (SAR) of tissues [
4,
8]. In addition to biological factors, it is essential to ensure operational stability and acceptable efficiency to make the application safe and viable.
In general terms, WPT classical compensation topologies are named series–series (SS), series–parallel (SP), parallel–series (PS), and parallel–parallel (PP). The main advantages of these topologies are the reduced number of elements and the consequent implementation simplicity. However, despite the reduced number of parameters, in order to achieve a good performance with classical topologies, a rigorous selection of the elements that will compose the circuits is essential. Based on this selection, the efficiency can be maximized and situations of instability can be avoided [
9].
The inductive power transfer applied to battery charging has two stages, which are the constant current charging process followed by constant voltage charging. Charging starts in constant current mode while the battery voltage gradually increases; once the battery voltage reaches its maximum charging voltage value, charging switches to constant voltage mode, so the current decreases considerably. Charging ends when the current in the battery reaches a specific value. Since batteries are considered to have a variable load during the charging process, there is a significant fluctuation in the output voltage; therefore, a converter is needed to regulate its output precisely in order to implement charging [
10,
11,
12].
In this paper, the authors intended to demonstrate that classical topologies with an input current source are more stable in the face of variations in the load, due to the charging process, as well as the coupling factor variation, and also vary little in terms of output power and input current. A first step is to carry out an in-depth review of the four classical topologies of inductive resonant coupling. After clarifying all the advantages and disadvantages of each, it is possible to justify the application of the PS topology in IMDs.
Commencing with the primary and secondary inductances, the choice of resonant components is influenced by multi-criteria decision-making processes. Consequently, a subsequent phase of this study involved the implementation of an algorithm based on Differential Evolution (as referenced in [
13]). This algorithm is aimed at determining inductances and capacitances that are viable both technically and practically.
Presently, a diverse array of bio-inspired optimization techniques are utilized across various engineering disciplines, including power flow analysis. Notable among these are the Artificial Hummingbird [
14], Prairie Dog [
15], Marine Predators [
16], and Slime Mold Algorithms [
17], along with the Differential Evolution algorithm. Although each of these methods demonstrates commendable accuracy and convergence speed, the Differential Evolution (DE) algorithm has been specifically selected for this research. This choice is attributable to DE’s rapid convergence, high precision, straightforward implementation process, and proficient handling of constraints.
With a focus on experimental validation, other practical considerations must be taken into account. Topologies with series compensation on the primary have the great advantage of being able to operate from a voltage source at the input, avoiding the need for other stages, which could compromise the overall performance of the system. On the other hand, with parallel compensation in the primary, the circuit must be powered by a current source, which, in a way, makes the execution of the project difficult and can compromise the overall performance if an intermediate stage is necessary [
18]. However, although parallel compensation in the primary brings with it the mentioned disadvantage, other technical advantages may justify the application of this topology.
In this paper, in order to circumvent the limitation of primary parallel compensation, it was decided to feed the chosen circuit through a Class-E amplifier. The Class-E amplifier stands out for its topological simplicity and for its good performance at MHz or GHz frequencies [
19]. An aggravating factor of this application lies in the fact that the Class-E amplifier is highly sensitive to parametric variations, that is small variations in the resonant elements or in the load can impair its operation [
20].
The results revealed that the Differential Evolution algorithm employed in this study precisely selected parameters that enabled the system to operate with an efficiency exceeding 94%. This efficiency level demonstrated notable stability against variations in frequency and coil coupling. Additionally, considering the incorporation of a Class-E power amplifier for generating alternating current, the system’s overall efficiency was maintained above 86%.
3. Differential Evolution-Based Parameter Selection
Aiming at the selection of optimal parameters for the classical wireless energy transfer topologies, an algorithm developed from the Differential Evolution (DE) algorithm was used. DE is a meta-heuristic based on the process of species evolution, which consists of generating an initial random population, mutating, crossing characteristics between individuals, and selecting the best individuals at the end of each generation [
13]. For the proposed application, some changes were made in the pseudocode of the presented algorithm.
First, an initial population is defined, composed of NP vectors of randomly chosen parameters,
pop(i, 1) and
pop(i, 2), in the interval between the minimum of 0.01
H and the maximum of 100
H, which correspond to the values of the primary and secondary inductances. The population is created from a uniform probability distribution and follows a natural evolution with the number of individuals fixed during the optimization process. It is noteworthy that the population must meet the non-bifurcation criteria. That is, if the generated population presents bifurcation, it will be discarded, and a new population will be formed. As shown in
Figure 11, the generation of the initial population is illustrated.
In one generation, three individuals are selected,
X(1),
X(2), and
X(3), obtained from a randomly established population, in an interval from 1 to NP. Another vector, named the target vector
pop(
i,
j), is also selected randomly. In the first generation, therefore, the target vector and the vectors
X(1),
X(2) and
X(3) are selected to be part of the mutation, crossover, and selection steps. The four individuals must be distinct from each other, meeting the condition that
, as illustrated in
Figure 12.
In the context of evolutionary computation, mutation can be defined as a change or perturbation with a random element [
23]. From the random selection of three individuals of a generation G,
X(1),
X(2), and
X(3), a vector of mutated parameters (
V) is obtained. The differential mutation operation is performed according to (1).
In accordance with the operation,
X(2)
X(1) is defined as the difference between the parameter vectors. Let
F be a real constant
[0, 2], called the mutation factor. This factor is responsible for controlling the size of the step to be performed, that is orienting the vector amplitude. The weighted vector difference is added to the third individual
X(3) as illustrated in
Figure 13.
The mutated vector
V is combined with the target vector,
pop(
i,
j), i.e., an arbitrarily chosen target vector, and the combination results in the trial vector. This process is called crossover, increasing the diversity of mutated individuals. The algorithm performs the combination respecting the real crossover constant
cr [0, 1]. Let rand be a random scalar
[0, 1]; if rand is less than the
cr, the muted vector parameters are selected; otherwise, the target vector is selected. The crossover operation is exemplified in
Figure 14. It is noteworthy that, in this paper, the mutation and crossover operations were performed concurrently.
After the mutation and crossover of the individuals, the selection of the best individuals is carried out. Initially, the value of the characteristics was analyzed, and it was verified if the value was within the range of 0.01 H to 100 H. If it was within the range, the characteristic was maintained; otherwise, it was replaced by the characteristic of the previous individual. Subsequently, the bifurcation criterion was analyzed. If the values obtained presented the bifurcation phenomenon when implemented, they would be replaced by the characteristics of the individual of the previous generation; otherwise, they would be maintained.
Finally, the fitness function, in this case, the overall efficiency, was analyzed. Therefore, it was verified whether the value obtained with the new characteristics was higher or lower than the value obtained with the past characteristics. If it was superior, the new individual would keep its characteristics. Otherwise, the new individual would assume the characteristics of the individual of the previous generation. In this iterative framework, the mutation, crossover, and selection processes generate a new population in each cycle, continuing until the generation count aligns with the pre-set maximum or another stop criterion is achieved. The DE algorithm’s flowchart, as applied in the study, is showcased in
Figure 15. Importantly, for a deeper, more-technical insight into the Differential Evolution algorithm proposed, the pseudocode is presented and detailed in Algorithm 1.
Algorithm 1 Differential Evolution algorithm. |
- 1:
Randomly generate the initial population following the bifurcation criteria. - 2:
for each generation k do - 3:
for each individual i do - 4:
Randomly select three different individuals X(1), X(2), X(3) - 5:
for each dimension j do - 6:
if rand(0,1) < cr then - 7:
Trial(j) = X(3) + F(X(2) X(1)) - 8:
else - 9:
Trial(j) = pop(i, j) - 10:
end if - 11:
end for - 12:
if f(Trial) > f(pop(i)) and the Trial meets the bifurcation criteria then - 13:
pop(i) = Trial - 14:
end if - 15:
end for - 16:
Perform replacements - 17:
end for
|
5. Simulation Results and Discussion
A Differential Evolution algorithm is proposed to obtain the best values for the primary and secondary inductances, aiming to maximize the efficiency of the system. In
Figure 17c, the curve of the efficiency of the best individual in relation to the number of generations of the Differential Evolution is presented. Note that the algorithm showed rapid convergence to the global maximum of 94.79% for the PS WPT stage efficiency.
The initial population was generated within a predefined range.
Figure 17a shows the distribution of the initial individuals. As expected, the position of the individuals was dispersed, since the population was randomly generated.
Figure 17b shows the individual distribution after performing all iterative processes. Note that the position of all individuals converged to the global maximum, where
L2 was equal to 430.2 nH. Since the efficiency dependency of
L1 was neglected, the
L1 values were distributed throughout the defined range.
As mentioned before, the WPT circuit parameters were sized considering an output power of 1 W. However, aiming to evaluate the practical non-idealities and the effective losses in each stage depicted in
Figure 16, a 1 W input power was imposed for the Class-E amplifier. Thus, the currents and voltages across the circuit elements, as well as the output power were expected to be lower than those previously calculated. Before analyzing the PS WPT circuit, it is reasonable to check the operation of the Class-E circuit. Looking at
Figure 18, the input current
IIN is depicted in (a). As observed, its value was slightly superior to 80 mA, draining about 1 W from the DC power source. In
Figure 18b,c, the
Ie and
Cm currents prove the resonance at 13.56 MHz; however, a small DC level was present, which denotes some mismatch caused by the values’ divergences and dissipative elements; this behavior did not make the circuit operation unfeasible; however, it increased the switch losses due to the current peaks, a consequence of the remanent voltage noticed in
Figure 18e.
Figure 18d shows the
Ce voltage, and it is important to note its peak value, which can reach almost 150 V, being important data for a practical design.
Carrying out the analysis of the circuit for the WPT part, it can be concluded that the current in the primary inductor added to the current in the primary capacitor resulted in the input current
I1.
Figure 19a,b illustrate the respective primary inductor and capacitor currents over time. The RMS currents in
L1 and
C1 were 311 mA and 306 mA, respectively. The current across all secondary elements (
I2) is presented in
Figure 19c. Due to the losses, the RMS value for
I2 was slightly inferior to the expected one, about 256 mA, and the RMS voltage over
RL was 3.3 V (
Figure 19d). Subsequently, the voltage stresses over the capacitances
C1 and
C2 can be noticed in
Figure 19e,f, respectively. The expected RMS voltages for the respective primary and secondary capacitances were close to 16.4 V and 9.4 V.
Figure 20 shows the active power drained in different parts of the circuit. In
Figure 20a, the DC source input power is presented. As can be noticed, its value corresponded to 1.0 W.
Figure 20b shows the power delivered to the PS WPT stage, which resulted in being about 0.91 W. Finally, the output power is depicted in
Figure 20c, reaching 0.86 W. Based on the obtained values, it is possible to conclude that the Class-E part operated with an efficiency of 91%; the PS WPT part reached about 94%; the overall efficiency was near 86%. It is worth mentioning the Class-E efficiency was sufficiently good in comparison with the other current source circuits, and the PS WPT efficiency was close to that expected in the preliminary results presented in
Table 4. In summary, the overall expected efficiency was significantly satisfactory for this range of power.
Based on the comprehensive analysis of the simulation results, we can assertively conclude that the system’s overall performance met, if not exceeded, the anticipated standards set forth for this project. The recorded values of the currents and voltages across the inductances and capacitances played a pivotal role in the system’s behavior. It is imperative to understand that these measurements are not just mere numerical results; they offer valuable insights that are instrumental for the judicious selection of components. By ensuring the components align with these values, we can guarantee optimal performance and reliability, fortifying the system’s robustness against potential anomalies or discrepancies in real-world applications.
6. Conclusions and Future Works
The present study provided a comprehensive assessment of a Differential-Evolution-assisted optimization of classical compensation topologies for 1 W current-fed IMD wireless charging systems with a biocompatible operating frequency of 13.56 MHz. This innovative approach aimed to indicate that the parallel–series compensation topology fed through a Class-E power amplifier was more stable in the face of coupling factor variation and also tended to reduce the input current despite a frequency oscillation of up to 10%. The system was optimized using a Differential Evolution algorithm in order to select optimal parameters that must provide non-bifurcation criteria, along with higher efficiency.
A wide review of the four classical topologies of inductive resonant coupling was made by evaluating their behavior in terms of frequency and coupling factor variations. Once having clarified all the advantages and disadvantages of each, the PS topology was selected. The Differential Evolution algorithm showed rapid convergence to the global maximum of 94.79% for the PS WPT stage efficiency. The values of the primary and secondary inductances obtained for L2 were equal to 430.2 nH; as the efficiency had no dependency on L1, the L1 value remained as previously selected, equal to 610 nH. The main results proved the good stability with an efficiency of around 94% of the PS WPT part. The Class-E PA developed achieved 91% efficiency, with the whole system standing above 86%.
The proposed system presents a potential path as a consistent energy supply for implantable medical devices, reducing the number of surgical procedures, also increasing the lifespan of the batteries and allowing operation during recharging. The results highlight the valuable role of the wireless charging systems in medical applications, considering biological factors so as to guarantee operational stability and appropriate efficiency, making the application safe and viable.
Future work will rely on evaluating the challenges of transitioning our idealized circuit to practical applications. It is paramount to consider the constraints posed by high-frequency operations. The high-frequency system necessitates sourcing suitable electronic components. GaN field-effect transistors emerge as a viable choice for Switch RDS
, due to their capability to handle high switching frequencies and compatibility with the project’s current requirements. Subsequently, a low-side ultra-fast gate driver optimized for switching GaN FETs in high-speed scenarios is indispensable. A clock oscillator with a frequency of 13.56 MHz will also be required. Designing inductors for high-frequency operation presents its unique challenges. The advantage of high-frequency operation is that it necessitates significantly lower inductance values. This makes air–core designs, which eliminate core losses at high frequencies, attractive [
29]. Planar inductors on printed circuit boards (PCBs) stand out as they support higher operational frequencies and offer the added benefits of reduced weight and size—factors critical for biomedical applications [
30]. High-frequency winding losses in PCB planar inductors are substantially influenced by skin and proximity effects, given the specific geometry of the PCB planar winding conductors [
30]. This can lead to increased high-frequency losses. Therefore, an inductor design that holistically considers winding losses, overall performance, and thermal issues becomes crucial [
31]. Furthermore, accurate temperature predictions and management of the coupling inductors are vital, not just for the electrical attributes, but also for the overall reliability and performance of the WPT system—integral for any IMD application.