Dynamic Bifurcation Phenomena Study of Wireless Power Transfer System

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Chapter 3 Variable Frequency Primary Side Power Flow Controller with Pre-defined Upper Boundary

Introduction

A power flow controller can be developed at the primary side of an IPT system to regulate the power flow to a heart pump at the secondary side. The controller should maintain the output voltage at a constant level despite the presence of variations in magnetic coupling level and load resistance. Patient movement or tissue regrowth after implantation can cause direct distance, lateral or angular displacements between the TET coils. Variations in coil displacements will change the magnetic coupling and affect the system power transfer capability. The equivalent load resistance may change when blood flow and pressure vary under different patient physiological states, which also requires the controller to regulate the power flow.
Implanted heart pumps currently in use are powered by percutaneous drivelines, which are a major source of infection [21]. Wireless power transfer [96-98] for heart pump applications is known as transcutaneous energy transfer (TET), which can deliver power without the percutaneous driveline and its associated risks. As previously mentioned (in Chapter 1), Si et al. have proposed a variable resonant frequency method for power regulation [35] by changing the effective capacitance of the primary through switching in and out parallel capacitors to the primary MOSFETs. Dissanayake et al. [34] successfully implemented this frequency control in a TET system for powering heart pumps. This approach requires the system to have more switching devices and resonant capacitors.
Thrimawithana et al. [99-103] have proposed and analysed a split capacitor push-pull parallel resonant converter (SC-PPRC) in three different operational modes – namely buck, normal and boost modes. The SC-PPRC changes its frequency and duty cycle simultaneously to achieve the ZVS condition at a range of operational frequencies, and the SC-PPRC can regulate power flow by varying the switching frequency directly. The boost version of SC-PPRC is so named because, as the operating frequency reduces, the peak resonant voltage increases.
In this study, a new frequency controller operating solely via a slow feedback loop is proposed for TET systems to deliver rated power for implanted heart pumps. The switching frequency regulation range was chosen to ensure a monotonic relationship between frequency and power flow; this allows the use of simple proportional and integral control to vary the system switching frequency. The switching frequency range is set below the system’s lowest resonant tank zero voltage switching frequency, leading to resonant tank shorting (but no instant resonant capacitor shorting), and ZVS operation during MOSFET commutation without the need of fast detection circuitry. This controller also offers the advantage of reduced switching components and capacitors compared to the variable frequency circuit of Dissanayake et al. [34], and leads to a saving of about 25% in physical space as shown by Figure 3–1. The systems of Thrimawithana et al. operate in open-loop without feedback and output regulation. The system of Dissanayake et al. requires feedback from the primary resonant waveform which is oscillating at approximately 180kHz to derive gate driving signals. Here, the proposed system only need to feed back the dc output voltage and is therefore a slow feedback system.

System Overview

Figure 3–2 shows the proposed TET system with a proportional and integral (PI) controller. The system includes a push-pull parallel tuned resonant converter to invert a dc input voltage into a high frequency current flowing through a primary coil. A secondary pickup coil (with a quality factor Q of about 165) is coupled to the primary coil (with a quality factor Q of about 205) by magnetic induction. Then the pickup coil is parallel tuned and the induced voltage rectified to output a dc voltage to drive the load. The quality factors here are unloaded Qu of the coils given by (3.1), where the resistance is the equivalent series resistance of the coil (ESR).
The load voltage is detected and sent back to the controller via a radio frequency (RF) channel, which makes use of the already available RF channel used for physiological sensors in an implantable heart pump application. The proposed controller compares the received feedback information with a pre-set reference Vref, and the difference is regulated by the PI controller to generate a dc signal, which is fed into a voltage controlled oscillator (VCO) to generate gate drive signals G’A and G’B (inversion of G’A) at a certain frequency.
The controller can operate in two separate gate drive modes by a manual selection switch: the basic mode and enhanced mode. In the basic mode, G’A and G’B are used to drive the two MOSFETs directly at 50% duty cycle after a gate drive circuit. One of the body diodes of the two MOSFETs would be conducting if the resonant tank needed to be shorted, as will be discussed later. The basic mode is based solely on a slow feedback PI loop, and does not require any fast detection, which simplifies the speed and timing requirement of the feedback channel and its components. Alternatively, in the enhanced mode, both MOSFETs would be ON during resonant tank shorting periods to reduce the voltage drop of the body diodes so as to improve the power efficiency. However, the enhanced mode requires an additional logic circuit that would require fast detection for resonant tank voltage as shown in Figure 3–2.
Figure 3–3 illustrates the ideal circuit waveforms of the proposed system. VAB is the differential resonant tank waveform measured across the resonant capacitor; VA and VB are comparator results of MOSFET drain to source voltages (V’A and V’B) with respect to ground. The primary MOSFETs QA and QB can be driven either by the basic mode, G’A and G’B, which are simply the VCO outputs or by the enhanced mode, GA and GB.
In the basic gate driving mode, the MOSFET body diodes will take turns to conduct during consecutive resonant tank shorting periods (Tsh); note that Tsh occurs twice every switching period (Tsw), Tzc is the zero crossing period, which is the duration in between two Tsh. In enhanced gate drive mode, the MOSFETs’ body diodes will cease to conduct as both MOSFETs are ON simultaneously during all Tsh. The circuit operation and current flow for basic mode and enhanced mode are shown in Figure 3–4 and Figure 3–5 respectively.
Instant capacitor shorting must be avoided to prevent damage to the capacitor and switching components. It will occur whenever MOSFETs are switched ON where there is a voltage present across the resonant capacitor leading to an unwanted high shorting current.
Instant capacitor shorting must not be confused with resonant tank shorting in the proposed controller. Resonant tank shorting occurs when MOSFETs are driven with a system switching frequency (fsw) that is below the lowest system ZVS frequency, which means the resonant tank will resonate and then be shorted for a short period by a current loop formed by the two MOSFETs including their body diodes, if basic mode control is employed.

Determination of Switching Frequency Regulation Range

Finding System ZVS Frequency

It is necessary to solve (2.8) to find the zero voltage switching frequency (fzvs) points of the system, in order to determine an operating frequency range that avoids instant capacitor shorting. At a fzvs point, the circuit inductive and capacitive elements cancel each other, making the impedance purely resistive. The number of fzvs points as well as their actual values are influenced by system parameters; for TET, important parameters are the load resistance and coupling levels. Under certain conditions, the system will have more than one zero voltage switching frequency, causing it to bifurcate. Similar bifurcation phenomena have also been found and studied in resonant converters in other wireless power transfer systems [71, 72, 91, 95, 104].
Figure 3–6 ignores all equivalent series resistances (ESR) of inductances and capacitances for simplicity. By employing the same approach discussed in Section 2.2.1 – equating the complex components of Zp to zero and finding the phase plot zero crossings
– (3.2) can be solved to give the approximate system fzvs points. Stroboscopic mapping method can be used to attain a more accurate ZVS bifurcation plot [71]. The resistance, R in (3.2) is the effective load resistance seen by the resonant tank. For a full bridge rectifier, the relationship between R and the load resistance is given by (3.3).
There are two graphical approaches to find fzvs. Firstly and more conveniently LTspice can frequency sweep the circuit in Figure 3–6 to give phase plots of Zp. The induced voltages from primary to secondary and vice versa need not be included during LTspice simulations as they are integral part of Lp and Ls. To represent the system more accurately, primary and secondary ESR of capacitances and inductances are included. Secondly, MATLAB can plot fzvs bifurcation trends while stepping load resistance or coupling coefficients.
To differentiate between non-bifurcated and bifurcated system operating conditions, Figure 3–7 shows a single phase plot zero crossing, meaning one fzvs point, while Figure 3–8 shows three phase plot zero crossings indicating fzvs bifurcation with three fzvs points.

Switching Frequency Regulation Range

Instant capacitor shorting is to be avoided. It occurs at negative resonant tank impedance phase angles, and thus the system must be constrained to operate in a fsw regulation range with positive phase angles. The system can operate either in non-bifurcated or in bifurcated conditions. Figure 3–7 shows the load power, phase angle and impedance magnitude plot for a non-bifurcated condition. The phase angle is positive when fsw is below fzvs and is negative when fsw is above fzvs. During a bifurcated condition as shown by Figure 3–8, there are three fzvs points, with positive phase angles when fsw falls below fzvs1 or in between fzvs2 and fzvs3. The frequency range between fzvs2 and fzvs3 may be utilised in theory since it has positive phase angles and will avoid instant capacitor shorting, but this frequency range is variable under different loading and coupling conditions, and it is difficult to track its bounds, operating inside that range was avoided. Therefore, in both non-bifurcated and bifurcated conditions, the fsw regulation range must be less than or equal to the lowest fzvs.
The PI action operates on a monotonic and positive load power over frequency slope. Under steady state operation and ignoring the effect of harmonics, the primary resonant tank is driven by a sinusoidal voltage source, this means for impedance analysis, the primary side resonant capacitance can be ignored making the resonant tank 3rd order; a frequency sweep in LTspice gives Figure 3–7 and Figure 3–8, which shows there is only one peak for the load power while two peaks emerge in impedance magnitude upon bifurcation. With the load power peak greater than fzvs1, the load power over frequency slope remains positive and monotonic, so the upper frequency boundary should remain at fzvs1. Here, the magnitude of the load power peaks are indicative only – actual peaks should be acquired through physical measurements.
The lower boundary of the fsw regulation range will be affected by a resonant tank voltage boosting effect in the converter as fsw range decreases. Despite the differences between the proposed controller and SC-PPRC, the analysis done by Thrimawithana et al. [102, 103] for boost mode SC-PPRC can be used to explain the boosting effect. Varying fsw has two effects on power flow. The dominating effect in the proposed controller is frequency tuning and detuning as fsw moves toward and away from fzvs1; the lesser effect is change in resonant tank peak voltage (Vpk) and resonant tank RMS voltage (Vrms) with fsw. An increase in the switching period (Tsw) will lead to an increase in Vrms as shown in (3.4), leading to increased power transfer.
In addition, because fsw reduces as Tsw increases, the system will become increasingly detuned with a dropping power flow. However Vrms will be increasing to raise the power flow, and these two power flow effects will superpose. There will be a crossover point when the magnitude boosting effect overrides the frequency tuning effect, and this point shall be the theoretical lower fsw boundary to maintain the monotonic relationship between power flow and fsw.
The quality factor (Q) of the system will affect the frequency regulation range. If Q is increased, it means the magnitude is more sensitive to changes in frequency, and then to maintain the same variation in magnitude, the frequency range would be narrower. Conversely, if Q is decreased, the frequency range would need to be wider.

Phase Plot Trends and Bifurcation Plots

At increased loading or coupling level, bifurcation results when the number of phase zero crossing points increases from one to three. A series of phase plots can be summarised within a bifurcation trend plot, which shows fzvs points while a system parameter is being stepped, usually coupling level or load resistance. When the primary and secondary resonant tanks are tuned to pre-set nominal frequency (f0) (given by (3.5) and (3.6)), with increased loading or coupling level leading to fzvs bifurcation, two additional fzvs emerge on either side of original fzvs. These two points will depart from the original fzvs, with one rising and the other falling in frequency. Figure 3–9 shows the bifurcation plot for the proposed system while stepping the coupling coefficient – coupling level increase spreads bifurcated fzvs points apart with a decreasing lower ZVS branch. In this case the system parameters are not exactly tuned to the nominal frequency, and on bifurcation the two additional fzvs appear below the original fzvs. When the primary and secondary resonant tanks are tuned to (3.7) and (3.8) respectively, the three possible ZVS branch locations upon bifurcation are expressed in (3.9).

Controller Design

Finding the Switching Frequency Regulation Range

The highest coupling level and highest load resistance need to be considered to find the switching frequency regulation range, as this will give the worst case scenario giving the lowest expected ZVS point on bifurcation. The system will be constrained to work below this worst case ZVS point and above the switching frequency when magnitude boosting effect overrides frequency tuning effect.
The practical TET coils used for primary and secondary are encased in silicone with the same diameter of 50mm, but the primary is double layered and the secondary is single layered. The maximum coupling coefficient is 0.5 when the TET coils are flat against each other without lateral displacement. Such a best coupling condition is used to find the upper frequency boundary of the controller. The nominal load of the heart pump is equivalent to 10Ω, which translates to a loaded quality factor of 5.63 and 1.41 at primary (Qp) and secondary (Qs) circuits respectively. The parallel-tuned loaded quality factors are represented in (3.10) and (3.11) respectively. To find Qp, one need to first find the reflected inductance and resistances, then find the net inductances and resistances. The resistance of Qs is the effective load resistance seen by the resonant tank.
The thesis also investigates a load variation up to 20Ω in order to study a severe bifurcated situation. Figure 3–8 shows the load power, phase and magnitude sweep of the system with a coupling coefficient of 0.5 and a load resistance of 20Ω. Other system parameters are Lp (11.3µH), Cp (47nF), Ls (3.31µH) and Cs (168nF). The inductances and capacitances are selected so that the primary and secondary resonate at a nominal frequency. The equivalent mutual inductance at the highest coupling level is M (3.06 µH).
By applying (3.2), the six roots are ±178.60, ±245.85 and ±302.07. However, only positive frequencies are practically possible, so the system ZVS points are 178.60kHz (fzvs1), 245.85kHz (fzvs2) and 302.07kHz (fzvs3), which are shown in Figure 3–9. The lowest ZVS point being 178.60kHz or fzvs1 is set as the upper fsw boundary. As shown by Figure 3–8, at fzvs1 the maximum load power potential (11.92W) is greater than the rated 10W power, and the frequency controller then regulates the excess power by detuning and decreasing the switching frequency. When coupling decreases, frequency then increases to regain the previously detuned power flow.
As a practical verification of the calculated upper frequency boundary for power flow regulation, let the proposed controller run in open loop with a desirable dc input voltage (VIN), and the highest expected coupling level and load resistance. Then, start at a switching frequency lower than the theoretical fzvs1 and tune the fsw upwards toward a ZVS point by avoiding instant capacitor shorting. This practical ZVS point can be used as the upper frequency boundary. The location of theoretical fzvs1 approximates the practical; the process used to attain the theoretical calculations assumes the resonant tank to be fed with perfect sinusoidal waveforms of different frequencies, whereas practical waveforms are distorted by differing load resistance, coupling level, practical component drifts, parasitic elements, the resonant tank shorting period and its associated magnitude boosting effect. These factors can offset the practical results from the theoretical and change the location of fzvs1.
When the coupling is weak and the system is not bifurcated, for example with a coupling coefficient of 0.2 and load of 10Ω as shown by Figure 3–7. From (3.2) the six roots are – 212.19±j31.84, 212.19±j31.84, ±225.08. Clearly only 225.08kHz is a valid frequency; this frequency is the one and only unique fzvs point for the system to operate under. Note that this fzvs is 46kHz higher than the upper boundary operating frequency corresponding to the closest coupling and bifurcated situation. With these parameters, the system fails to regulate load power at 10W as its maximum power potential is only 7.35W. This means the power flow controller has insufficient power to regulate with through frequency tuning, so this particular operational point is outside the frequency regulation range. In order to supply rated power, the system parameters must be re-designed, which can include coil size, make and geometry, operating frequency and so forth.
When accounting for component variations and other factors, a frequency margin is needed in practical design to ensure the system can work properly. This may affect the system’s full power capability and the power efficiency slightly.
The lower fsw boundary can be found empirically by operating the controller in open loop. The fsw should be decreased away from the fully tuned state. The fsw boundary will be when output voltage reaches a minimum and begin to rise. The lower boundary need not be at its theoretical minimum and can be set sufficiently low to allow enough room to regulate power flow downwards. In addition, as frequency lowers the magnitude boosting effects cause higher voltage rating requirements for primary MOSFETs.

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PI Controller Parameters

The PI controller achieves regulation when VLOAD equals Vref. Important parameters that influence this process include the fsw regulation range, VIN, coupling level and the load resistance. To maximise the regulated coil separation range, the upper frequency boundary (fzvs1) is first determined according to prior analysis, then under close loop, the TET coils are pushed flat against each other for the highest coupling level, then VIN is increased so that PI action starts to regulate VLOAD to Vref by decreasing the frequency downwards. Stop increasing VIN just before VLOAD starts to increase beyond Vref. This condition shows the signs of failing regulation and can be set as the lower boundary. This procedure is simplified in Figure 3–10 and ensures that the system is capable of regulating voltage down to Vref under highest coupling level, and as the coupling level drops by separating the TET coils, PI action will increase fsw to deliver more power, until the system reaches fzvs1 and the separation distance becomes too great to maintain Vref at the load.

Controller Hardware Design

The new controller as shown in Figure 3–11 has a PI to vary frequency and regulate the output power flow. This controller was built with discrete analogue components using OPAMPs, VCO and NAND gates. The OPAMPs achieve the needed buffering, differencing, summing, offsetting, proportional gain and integral gain functions of the PI controller; the PI output is stepped down through a potentiometer and an offset voltage is added to complete the necessary frequency range level shifting. The resulting dc voltage level is processed by a VCO into a square wave, which is not 50% duty cycle, so a ripple counter can be used to halve the frequency of the VCO output in order to produce a 50% duty cycle waveform. NAND gates are used to realise the required NOT gate function in order to produce the complement of the VCO output resulting in G’A and G’B, which are two complementary 50% duty cycle basic mode gate driving signals. To generate MOSFET overlap conducting enhanced mode gate drive signals, GA and GB, the falling edge of VA is used to set a SR latch while a falling edge of G’A resets that SR latch producing GA. Similarly a falling edge of VB sets a second SR latch while a falling edge of G’B resets the second SR latch producing GB. The enhanced mode waveforms will step in after VLOAD is above a threshold as it relies on the readiness of basic mode waveforms, G’A and G’B, as well as the comparator waveforms VA and VB. This design has used only discrete components to realise all the necessary elements of the power flow controller. However microcontrollers or FPGA can also be used to realise the controller. The output dc inductor normally conducts continuously to smooth the load current, while discontinuous operation reduces the smoothness of output voltage.

Simulation and Experimental Results

PLECS has been used to simulate the proposed controller and its PI action used to regulate the output voltage to 10V. The system switching frequency regulation range has been calculated according to the previous analysis and set to 140kHz to 180.26kHz. The simulated VIN range for which regulation is achievable is between 23V and 28V for a load of 10Ω and a 0.2 coupling coefficient.
Similarly, a simulation study was undertaken using PLECS under different coupling and load variations. In all cases the calculated fsw regulation range was used and VIN set at 25V, the coupling regulation range was between 0.19 to 0.23 for a load of 10Ω, while the simulated load regulation range between 7Ω and 50Ω for a 0.2 coupling coefficient. If the fsw regulation range is to increase by lowering the fsw lower boundary, the simulated VIN, coupling and load regulation ranges would also increase, leading to a larger fsw regulation range and increased controller regulation capability. Note that the simulated regulation ranges are useful for guiding system design; they may not be exactly the same as the actual system operating ranges. Further details of this PLECS simulation can be found in Appendix B.
Practical TET systems require a regulated power of typically 10W at the heart pump; the power flow controller must overcome variations in TET coil separation and misalignment due to patient movement, which corresponds to variations in coupling level between primary and secondary. A 10Ω load is used to model a working heart pump approximately. The practical switching frequency regulation range is between 149.3kHz to 182.2 kHz. The proposed controller has demonstrated good power regulation of 10W to the load with a TET coil separation ranging from 4 mm to 10mm. Note that the minimum distance of 4mm in fact corresponds to the best coupling situation with the two coils touching – the distance is caused by the silicone casing. The 10mm distance is the lowest coupling level for maintaining the rated power delivery. Normally the system operates in a non-bifurcated condition; however when the TET coils are less than about 5mm from each other, the system may bifurcate. Under both non-bifurcated and bifurcated conditions the practical system continues to work well below the fzvs1 within its fsw regulation range, and avoids instant capacitor shorting.
The PLECS simulation circuit waveforms are shown in Figure 3–12, the practical measurement setup is shown in Figure 3–13, and the practical circuit waveforms of three different TET coil separation distances are shown in Figure 3–14, Figure 3–15 and Figure 3–16 under an input dc voltage of 14V. Note that in all cases the system was able to maintain 10V at the load side. It is clear that the practical measurement waveforms correspond well to the simulation circuit waveforms and to the ideal circuit waveforms illustrated in Figure 3–3. In all three practical circuit waveform figures, the top waveform is the differential resonant tank voltage, VAB, the second waveform is the VCO output or basic mode gate driving waveform, G’A. The next waveform is the enhanced mode gate driving waveforms, GA and the last waveform is the load voltage, VLOAD. The circuit currently operates in enhanced mode. Operation under basic gate driving mode will give similar results, but due to body diode conduction during resonant tank shorting period, the efficiency drops slightly.
The basic mode achieved an end-to-end efficiency of 77.97% compared to 79.65% for the enhanced mode when delivering 10W at TET coil separation of 10mm. Figure 3–17 shows the end-to-end efficiencies for enhanced mode operation under different direct separation distances, where the system is operating with close loop feedback to regulate VLOAD at 10V. Here only the regulated separation range of up to 10mm is shown – larger separation is irrelevant as load regulation would fail. When TET coils are closer, frequency is lower to detune the excess power, which introduces more resonant shorting period. This is associated with increased coil current and losses. Therefore, efficiency would be lower at lesser coil separation, and as coil separation increases, frequency will increase to tune more power flow to compensate for the lesser magnetic coupling. This means less resonant shorting period, coil current and losses – efficiency would improve. This positive relationship between efficiency and coil separation would not continue indefinitely – load regulation fails with coil separation greater than 10mm, which means lower output power and efficiency. Figure 3–18 shows end-to-end efficiencies for enhanced mode under different VLOAD by operating the system in open loop and varying the operating frequency. These efficiencies do not include controller power losses as the controller components are fed by separate ±15V and ±5V supplies. The end-to-end efficiency with controller loss is estimated to be above 70%.
A demonstration system based on the proposed power flow controller has been made as shown in Figure 3–19, and it transfers wireless power from the primary to the secondary via a plastic human figure. The power received is used to drive a marine bilge pump to extract and pump blood coloured water from a fish tank around the human figure, imitating a human blood circulation system. The water is pumped through a series of transparent pipes and plastic tubes. The water eventually returns to the fish tank forming a complete circulation loop.

Table of Contents
Abstract
Acknowledgements
List of Figures
List of Tables
Nomenclature
Chapter 1 Introduction
1.1. Background
1.2. Challenges for Transcutaneous Energy Transfer
1.3. Current State of the Art for TET
1.4. The Objectives and Scope of this Thesis
Chapter 2 Dynamic Bifurcation Phenomena Study of Wireless Power Transfer System
2.1. Introduction
2.2. System ZVS Frequencies and Peak Power
2.3. Operation via ZVS Detection
2.4. Waveform Investigation between ZVS Transition
2.5. Conclusions
Chapter 3 Variable Frequency Primary Side Power Flow Controller with Pre-defined Upper Boundary
3.1. Introduction
3.2. System Overview
3.3. Determination of Switching Frequency Regulation Range
3.4. Controller Design
3.5. Simulation and Experimental Results
3.6. Conclusions
Chapter 4 Improved Primary Variable Frequency Power Flow Controller with Shorting Period Detection
4.1. Introduction
4.2. System Overview
4.3. Operating Principle of the Proposed Controller
4.4. Controller Design
4.5. Simulation and Experimental Results
4.6. Conclusions
Chapter 5 Maintaining Middle ZVS Operation of TET System under Bifurcation
5.1. Introduction
5.2. Primary Side ZVS Follower with Blocking Diode
5.3. Primary Side Control without Blocking Diodes
5.4. Conclusions
Chapter 6 Synchronous Rectification Combined with Secondary Power Flow Control 127
6.1. Introduction
6.2. Synchronous Rectifier
6.3. Synchronous Rectifier with Combined Power Flow Control
6.4. Conclusions
Chapter 7 Conclusions and Suggestion for Further Work
7.1. General Conclusions
7.2. Contributions Made by this Thesis
7.3. Suggestions for Future Work
Appendices
References
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