A misalignment-adaptive wireless power transfer system using PSO-based frequency tracking

a Department of Mechatronics Engineering, Faculty of Engineering, Balıkesir University, Balıkesir, Turkey b Department of Electrical & Energy, Uzunçiftlik Nuh Çimento Vocational School, Kocaeli University, Kocaeli, Turkey c Department of Electrical & Electronics Engineering, Faculty of Engineering, Balıkesir University, Balıkesir, Turkey fuatkilic@balikesir.edu.tr, serkan.sezen@kocaeli.edu.tr, seyit.sis@balikesir.edu.tr


Introduction
Magnetic coupling based wireless power transfer (WPT) systems have been comprehensively investigated in recent years. The WPT finds its use in various applications such as mobile electronic devices [1], electric vehicles (EVs) [2,3], robots [4,5] and medical devices [6,7]. Magnetically coupled coils, or so called couplers, are the major components in these systems determining the efficiency and power level delivered to the load. The WPT systems need to operate at one of the system's resonance frequencies for transferring the power in an efficient manner. However, temperature dependent variations in component values and load variations shift the resonance frequencies of the system. In this case, for guaranteeing maximum power delivery or maximum efficiency, a frequency tracking mechanism should be incorporated into the system. Another important issue in WPT systems is so called frequency splitting phenomenon. Frequency splitting occurs when system operates at strongly coupled regime. In this regime, two more resonance frequencies emerge at lower and upper side of the isolated couplers' resonance frequency, making total of three resonance frequencies for the coupled system. The power values are maximum, same and independent of the coupling coefficient at these emerging split resonance frequencies; however, these frequencies are strongly-A misalignment-adaptive wireless power transfer system using PSO-based frequency tracking 207 dependent on the coupling variations. Furthermore, any small difference between the isolated resonance frequencies of the primary and secondary coils results in different peak power and efficiency values at these frequencies. Hence, a local and a global maximum for the delivered power levels are observed. Operating the system at a global maximum is important for reducing charging time, utilizing electrical power efficiently, reducing the losses in power electronic components and reactive power. Therefore, the WPT system should adopt itself to achieve maximum power delivery when resonance frequencies shift due to coupling coefficient variations. Numerous works have been reported on realizing adaptive WPT systems. In [8], an impedance matching network is utilized to maximize power transfer by compensating the efficiency reduction due to coupling variations. This method necessitates changing the position of coils, making the system less practical for the implementation. In [9,10], authors again utilize matching circuits at both primary and secondary side; however, large number of passive elements increases the loss and the complexity of the system. In another work, zero crossing detector based phase angle is obtained by reading the voltage and current at the primary side to maximize the power transfer [11]. However, this method may become unstable if there is no resonance in the system. In another work [12], which is published by the authors of this manuscript, a fluxpipe coupler structure with three movable sub-coils is exploited for realizing an adaptive WPT system. The inductance value of the coupler is tuned by moving the position of the sub-coils to get back the system's resonance frequency shifted by the coupling variations. This solution, however, requires a complex mechanical mover and a dual side control [12]. In [13], authors propose a frequency tracking method based on simulated annealing algorithm for achieving maximum power transfer, but this algorithm is time inefficient and computationally dense [14]. Impedance matching and Perturb and Observe (PO) algorithm are implemented together in [15] for maximum power delivery to the load. In [16], power reduction due to resonance frequency shift caused by misalignment between primary and secondary coils is compensated by tracking the system's resonance frequency using again a PO algorithm. A drawback in PO algorithm, however, is that the algorithm may stuck at a local maximum rather than converging to the global maximum point. Ant Colony algorithm is also utilized for achieving maximum power transfer in [17]. Low converging speed and possibility of convergence to local maximum in large searching space are the main disadvantages in this algorithm [18]. In [19], derivation of power response is calculated and then the direction of frequency search is determined based on the sign of the derivation. As in PO algorithm, derivation method based algorithm may also stick to a local maximum rather than converging to the global maximum power point.
Particle Swarm Optimization (PSO) algorithm is another technique used in several adaptive WPT systems [20,21]. In [20], a software-defined, near-field WPT system is proposed where a particle swarm optimizer (PSO) is used to optimize the power transfer efficiency of the system. Matching network of the transmit and receive chain is controlled through the PSO algorithm to compensate for the efficiency reductions due to coupling variations [20]. However, the tuning range of the tunable components in matching circuits is limited and these components increase loss and complexity of the system. In [21], PSO algorithm is utilized in a frequency tracking controller to improve the power transfer efficiency of the WPT system. PSO algorithm's iterations are seems to be offline and does not consider the effect of dynamic variations on the system. In both [20] and [21], WPT systems operate in MHz range with a sinusoidal RF signal source and a power amplifier. MHz range WPT systems are not suitable for high power applications such as electric vehicle (EV) chargers. In this paper, the Particle Swarm Optimization algorithm is implemented in a frequency tracking controller for use in misalignment adaptive WPT systems suitable for high power applications. The implemented frequency tracking system accurately finds the global maximum point without sticking to a local maximum under varying conditions. Therefore, the WPT system becomes insensitive to frequency splitting phenomenon caused by coupling variations. The algorithm needs only voltage and current measurement data at the resonant primary side coupler, making the proposed tracking system a simple primary side controller. The algorithm iteratively changes the switching frequency of the inverter. At each iteration, the controller calculates the power level at the input of the primary side resonant coupler. Iterations are online so that the algorithm does not stop and track the right frequency as long as the system is powered. The paper is organized as follows: section 2 presents the frequency splitting phenomenon by analyzing a circuit model for a series-series (SS) compensated WPT system. Subsequently, PSO based frequency tracking algorithm is described in section 3. Finally, experimental setup and measurement results are presented in detail in section 4. Measurements are performed under three different scenarios with different misalignments and resonance conditions. For each scenario, a power vs frequency graph as an oscilloscope screenshot is obtained experimentally to show the frequency splitting phenomenon. Finally, accuracy of the PSO algorithm is proven by comparing the tracked frequency with the maximum power points shown in these graphs.

WPT system and mathematical model for maximum power delivery
In quite a few modern WPT applications (e.g electric vehicle chargers), separation between these primary 208 F. Kılıç, S. Sezen, S.A. Sis / IJOCTA, Vol. 10, No.1, pp.206-217 (2020) and secondary side couplers needs to be large enough (loosely coupled) and the system should be suitable for lateral and vertical misalignments between the couplers to some extent. One needs to compensate for this loose coupling by connecting compensation capacitors to both primary and secondary side couplers. Except recently introduced hybrid compensation schemes, there are four basic compensation topologies: seriesseries (SS), series-parallel (SP), parallel-series (PS) and parallel-parallel (PP). In this work, voltage-source inverter is utilized as a high power source hence series compensation is chosen for the primary side. Parallel compensation at the secondary side results in a kdependent compensation capacitor at the primary side [24]. Therefore, series compensation scheme is chosen at the secondary side as well. Figure 1 shows a circuit model for a WPT system with an SS compensation topology. The components, L1,2 and R1,2 represent the self-inductances and loss resistances of the primary and secondary side couplers, respectively. C1 and C2 are the series connected compensation capacitors at primary and secondary sides, respectively. Vs and M are the RMS voltage level of the inverter and the mutual inductance between the couplers, respectively.
The input impedance of the coupled system seen towards the resonant primary coupler ( Figure 1) is as follows: Usually, WPT systems are realized with identical primary and secondary side couplers. In this case, one can simplify the model by assuming as L1=L2=L, C1=C2=C and R1=R2 = R. The resonance in a coupled system occurs at frequencies where imaginary part of Zin becomes zero as given Eq. (3).
Solving Eq. (3) results in only one or three roots for ω for given conditions as shown in (4). As seen in (4), when the first condition (ωM ≤ R + RL) is satisfied, then the coupled system only exhibits a single resonance frequency of ω0, which is equal to the isolated resonance frequency of the couplers, and the system is said to be operating at the weakly-coupled regime. When the second condition (ωM > R + RL) is satisfied, then two more resonance frequencies ω1, ω2 emerge along with the ω0. This phenomenon is called as frequency splitting, and the system is said to be operating at strongly-coupled regime. Maximum power to the load is delivered at system's resonance frequencies.
By plugging Eq. (4) into Eq. (1), the output power (PL) at ω0, ω1 and ω2 is simplified as follows: As seen in Eq. (5), the output power at ω0 is quite dependent on the mutual inductance (M) between the couplers. That is, when a misalignment occurs between the primary and secondary side couplers, or the distance between them changes, PL also changes. One needs to vary the inverter's voltage level to stabilize output power against varying coupling level. However, if system operates at the other resonance frequencies, ω1 or ω2, the output power is independent of M (as given in Eq. (6)), making the system insensitive to the coupling variations.  It should be remembered that the ω1 or ω2 exist only at the strongly coupled regime and their values are dependent on M when the second condition in Eq. (4) is satisfied. Figure 2 shows simulated output power (PL) using Eq. (1) as a function of f and M. Frequency splitting phenomenon is clearly observed in Figure 2.
As seen in these graphs, any variation of M and RL significantly changes the output power transferred to the load. Therefore, for a large power delivery to the load, system's frequency should be tuned to either ω1 or ω2 by applying a frequency tracking algorithm.

Basics of PSO Algorithm
Particle Swarm Optimization (PSO) algorithm is inspired from the behaviors of swarm animals such as birds and fishes. Each individual animal in the swarm is called as particle and have the potential of exhibiting a solution to the problem to be solved. The particle looks for the best location in a three dimensional (3D) space [26]. A major advantage of PSO is its easier applicability to various different applications such as power systems, thermodynamics, image processing, proportional-integral-derivative (PID) control and machine learning as compared to other algorithms [27,28]. PSO algorithm has several topologies and one of the most utilized topologies is a so called Von Neumann topology. In this topology, the particles are connected to one another in such a way that they communicate with each other from one point to the opposite point in a square pattern [29]. As in other topologies, Von Neumann topology based PSO algorithm is established on two principles; learning the previous knowledge and providing communication between the particles in the swarm. The Von Neumann topology consists of N element particles in a D dimensional space [30]. Each particle should achieve the best performance and all the particles should move towards the particle with the best performance [31]. Each particle has its own speed, and this speed is updated based on previous performance of the particle and the swarm. The algorithm initially produces random solutions and recursively update the locations of particles and search for the global maximum within the search space. By evaluating each individual particle, the best performance (Pbest) and the particle associated with the best performance are stored in the memory. The inputs of the algorithm are varied until some of the goals are satisfied. Figure 3 shows the vectorial movement of frequencybased particles in the PSO algorithm. The direction of particles depends on the best frequency per particle, the frequency at which maximum power is achieved in the whole swarm, previous frequency, current frequency and up-to-date frequency. Figure 4 shows algorithm's flow chart for frequency tracking to maximum power. This flow chart is elaborated under four main steps as follows:

The application of PSO algorithm to frequency tracking in a WPT System
Step I (Start): In this first step, optimization is launched by establishing an initial population. A frequency solution vector with Np elements is setup as given in Eq. (7). The initial vector is built on randomly chosen frequencies. The constants, γ1 and γ2, given in Eq. (8) and (9) are then determined based on c1 and c2 which satisfy the conditions given in Eq. (10) and (11).
The fwpt, fact, Pwpt, and Pact variables shown in the flow chart are the stored frequency, up-to-date frequency, calculated power and up-to-date power, respectively.
Step II (Acquiring Measurement Data): Current and voltage values at the input of the WPT system are measured using hall effect based sensors as will be discussed in the next section. These measured data are acquired into the microcontroller and utilized as an input to the microcontroller. Subsequently, the power is calculated using measured voltage and current data. Once the condition in Eq. (14) is satisfied, the algorithm utilizes the best individual particle location to update the frequency as given in Eq. (15).
From the start of the algorithm, the best frequency (fPbest) for jth iteration and ith particle is stored in the memory. The best global frequency is also stored in the memory as fGbest.
The i, t, fi,j, fi,j(t+1) and δi,j (t+1) are particle number, iteration number, current particle frequency, updated particle frequency and updated correction term.
Step According to flow chart, once initial values are assigned, initial frequency value is sent to pulse width modulation (PWM) unit and then time based period is formed. The full-bridge inverter is driven by 50 % duty cycled PWM signal at a given frequency. The algorithm is run real-time and the frequency is recursively updated until it converges to the frequency at which power is maximized. The frequency range over which the algorithm make searching is from 10 kHz to 40 kHz.

Experimental setup and measurement results
An experimental WPT system is setup using a DC to AC high frequency inverter, flux-pipe couplers, seriesconnected capacitors and a heater load resistance (RL).  Two series connected 2200 µF/450V DC capacitors and a 1µF/1200V snubber capacitor, which is parallel to these two 2200 µF capacitors, are utilized at the DC bus node. The flux-pipe coupler utilized in this experiment is basically a helical structure with three sub-coils wound around a common ferrite core ( Figure  5 (b)). The detailed simulation and measurement results of this coupler structure are out of scope of this paper and are reported elsewhere [12]. The list of component values and other details for the experimental setup are shown Table 1.
The proposed frequency tracking method is experimentally verified under three scenarios. In the first scenario, the couplers are perfectly aligned and separated with 100 mm vertical gap (dz = 100 mm). In the second scenario, the coupling coefficient between couplers is reduced by applying a 150 mm lateral misalignment along the coupler's longer side (dy = 150 mm). In the third scenario, the sub-coil separation (dsub), which is originally 60 mm for each coupler, is changed in secondary side coupler until the selfinductance of the secondary side coupler increases to 185 µH from its original value of 170 µH. This final scenario results in moving the maximum power point from lower resonance frequency to the higher one. The difference between the power levels becomes also larger in this last scenario. A PO algorithm is also run in the last scenario and compared to the PSO algorithm. All three scenarios are sketched in Figure 6 and are summarized in Table 2.

Scenario I
In scenario I, the couplers are perfectly aligned and separated with 100 mm vertical gap (dz = 100 mm). Before running PSO based frequency tracking algorithm, input power to the primary side resonant coupler and the inverter's switching frequency are scanned simultaneously in time to make sure that the system exhibits frequency splitting phenomenon. The switching frequency of the inverter is linearly increased from 10 kHz to 40 kHz with approximately 100 Hz increase at each time step. Figure 7 (a) shows oscilloscope screenshot of this scan. The data shown with cyan-colored line is the scanned input power and exhibits two peaks at approximately 24 kHz and 33 kHz, respectively. The data with maize-colored line is the scanned frequency. The PSO based frequency tracking algorithm is then utilized in microcontroller to drive the gates of IGBTs. Figure 7 (b) shows the oscilloscope screenshot of the PSO algorithm's performance for tracking the frequency of maximum power. In this graph (Figure 7

33kHz 24kHz
Power 75W/div Frequency 10 kHz/div Current 3,5A/div Frequency 10 kHz/div Current 10 A/div Voltage 20V/div Current 10 A/div Voltage 20V/div One can read the searched frequency and input current level as well as the time using given kHz/div, A/div and s/div (on the top left of the graph) scales on the graphs. As seen in Figure 7 (b), the PSO algorithm finds the resonance frequency for maximum power as 24 kHz in approximately 25 seconds. The tracked 24 kHz agrees with the initial scanning results shown in Figure 7 (a), verifying the accuracy of PSO algorithm. The measured voltage and currents at the input and at the load resistance (RL), when inverter operates at tracked 24 kHz, are shown as oscilloscope screenshots in Figure 8.

Scenario II
In this scenario, the coupling coefficient between couplers is reduced by applying a 150 mm lateral misalignment along the coupler's longer side (dy = 150 mm). As in scenario 1, first, input power to the primary side resonant coupler and the inverter's switching frequency are scanned simultaneously in time. Figure 9 (a) shows oscilloscope screenshot of this scan. The data shown with cyan-colored line is the scanned input power and exhibits two peaks at approximately 25.5 kHz and 31.5 kHz, respectively. The data with maizecolored line is the scanned frequency.   As seen in Figure 9 (a), the resonance frequencies approach to one another when 150 mm misalignment is applied along the longer side of the couplers. This change in the resonance frequencies can be attributed to the decrease in the mutual inductance between the couplers. Figure 9 (b) shows the oscilloscope screenshot of the PSO algorithm's performance for tracking the frequency of maximum power. In this graph, the instantaneous frequency searched by the PSO algorithm and the corresponding input current are shown with maize and cyan colored lines, respectively. The PSO algorithm finds the resonance frequency for maximum power as 25.5 kHz in approximately 15 seconds. The tracked 25.5 kHz agrees with the frequency of global maximum power shown in Figure  9 (a)), verifying the accuracy of PSO algorithm. The measured voltage and currents at the input and at the load resistance (RL), when inverter operates at tracked 25.5 kHz, are shown as oscilloscope screenshots in Figure 10.

Scenario III
In the third scenario, the sub-coil separation (dsub), which is originally 60 mm for each coupler, is changed in secondary side coupler until the self-inductance of the secondary side coupler increases to 185 µH. Such a change results in switching the global power maximum from lower resonance frequency to the higher one as shown in Figure 11 (a).  The data shown in Figure 11 (a) with cyan-colored line is the scanned input power and exhibits two peaks at approximately 24 kHz and 33 kHz, respectively. The data with maize-colored line is the scanned frequency. As seen in Figure 11 (b), algorithm converges in less than 20 seconds and finds the 33 kHz resonance frequency as the global maximum power point which agrees with Figure 11 (a). A major advantage of PSO algorithm is that it always converges to the global maximum and never stuck in a local maximum. To make a comparison, a PO algorithm is also run in the last scenario (scenario III). Figure 12 shows the oscilloscope screenshot of the PO algorithm's performance for tracking the frequency of maximum power.  In Figure 12, within approximately ten seconds, the PO algorithm stucks in 24 kHz which is not the maximum power point. Although the PO algorithm converges faster than the PSO algorithm, the converged frequency does not guarantee the maximum power point. Figure  13 shows the oscilloscope screenshots of measured voltage and current waveforms on the load resistance (RL) for both PSO and PO algorithms. Performance data obtained for 3 different scenarios discussed in this article are summarized in Table 3. Comparison between PO and PSO algorithm has also been made for Scenario 3 to show incapability of PO algorithm tracking global maximum power point frequency . Although the PO algorithm converges faster than PSO algorihm, it stuck with the local maximum where input power (300 W) is much less than the global maximum (500 W) tracked by the PSO algorithm.

Conclusion
In this paper, a frequency tracking WPT system based on a PSO algorithm is presented. With the use of a PSO algorithm, inverter's frequency is tuned to a resonance frequency where maximum power is delivered to the load without sticking to a local maximum. An experimental WPT system is implemented under three different scenarios covering various misalignment and resonance conditions and compared with PO algorithm in misalignment scenario 3. The proposed PSO algorithm always converges to the resonance frequency of global maximum power in case frequency splitting. Furthermore, the proposed frequency tracking control method utilizes the current and voltage data at the primary side of the WPT system, making it a less complex single-sided controller. Therefore, no additional communication link between primary and secondary side is needed for maximizing the delivered power level. A potential future direction would be incorporating missing secondary side electronics such as a rectifier, a DC-DC converter, a battery management circuit and a battery to realize a complete WPT charger targeting a certain application such as an electric vehicle charger.