High frequency magnetic components
for EV-charging resonant converters
Author: Andrea Stratta
Supervisors:
Prof. Paolo Bolognesi, DESTEC, University of Pisa
Dr.-Ing. Veronica Biagini, ABB Forschungszentrum, Ladenburg Ing. Matthias Biskoping, ABB Forschungszentrum, Ladenburg
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BSTRACT
This work is a part of a research activity concerning electric vehicle charging conducted at the ABB research centre in Ladenburg, Germany. Battery chargers play a key role in the diffusion of electric vehicles (EV), which represent the best solution for dramatically reducing emissions in urban contexts and pollutants on a global scale. In fact, they are intended to provide controlled power for recharging the batteries, balancing at best different key aspects such as battery life preservation, recharge duration, low power losses, minimal distortion and high power factor at the mains size, while also ensuring electrical insulation from the grid for safety purposes. Cost effectiveness, small dimensions and light weight are also important features for such application, especially when on-board chargers are considered. A review of the most innovative EV charging techniques is conducted, highlighting the key role of resonant converters.
In Chapter 2 the LLC resonant converter is analysed with different variations of the First Harmonic Analyses (FHA). Zero voltage switching (ZVS) and a robust voltage control are the main features of this topology. The most important operative conditions are studied, focusing on which ones allow to achieve ZVS. A design methodology for the resonant tank is proposed, taking into account the battery voltage range and the micro-controller frequency resolution. As application example, a 10 kW LLC converter operating at 100 kHz rated frequency is considered as case study, assuming a secondary voltage range 320-420 Vac and a primary bus
voltage of 800 Vdc. For the case study a resonant tanks design is proposed and a PLECS® model
is implemented. Analysis and simulations show that the correct operation of the converter is related to the passive elements. As a result, in order to achieve high efficiency, an oriented design of the transformer and of the resonant inductors is needed.
The design of the transformer is addressed first, beginning with the explanation of some preliminary choices according to the converter specifications: such as the operative frequency and output power. Once the preliminary choices have been made, a step-by-step design procedure for the high-frequency transformer is proposed in Chapter 4. Differently from standard procedures, a set of libraries is supposed to be get ready, containing the most significant data related to soft magnetic materials, cores shape and size, copper and alloy conductor materials, and multi-strand Litz wires. In this way, the optimal design of the component consists in the most suited combination of library elements according to the design goals, with null customisation of the standard parts. After the parameter selection, analytic formulas, packed into a Matlab® function, are used to calculate total losses and efficiency. The
analytic function also provides a raw estimation of the materials cost and the average temperature of the device, which the designer has to take into account as well. The most effective solution for each set of design specifications is found by varying the combination of library components and the windings arrangement. Finally, for the cited above case study four candidate designs are selected, featuring different combinations of magnetic materials, core shape and dimensions, and number of turns for the winding.
In Chapter 5, the four transformers are analysed with a finite element software, ANSYS-Maxwell®. In this way is possible to validate the analytical results by means of 3D FEM models.
When the values of the equivalent leakage and magnetising inductances is not included as design specifications, as initially assumed, external inductors could be included in the converter design to adjust at best the converter behaviour. A design for the series and parallel inductors is proposed to estimate overall size, weight, cost and losses of the magnetic components.
In order to reduce costs and dimensions of the overall converter, the possibility of a magnetically integrated transformer is investigated. One can consider adjusting the transformer structure and design to meet also the inductance requirements, thus basically achieving the integration of the external components inside the transformer itself. To such purpose, several different possibilities are examined. Finally, a comparison between the “external inductors solution” and the “magnetically integrated solution” is performed.
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NDEX
Chapter 1. EV-Charging Topologies ... 5 1.1 EV-Charging classification ... 5 1.1.1 Power levels ... 5 1.1.2 Power Flow Direction ... 6 1.1.3 Connection type ... 6 1.2 Literature Review ... 7 1.2.1 Integrated non-isolated battery charger ... 8 1.2.2 Bidirectional isolated battery charger ... 9 1.2.3 Battery charger based on LLC resonant converter ... 10 1.2.4 Flash Charger ... 11 1.2.5 Wireless dynamic inductive charger ... 12 1.3 Conclusions ... 13 Chapter 2. Resonant Converters ... 14 2.1 Resonant converters classification ... 14 2.1.1 Series Resonant Converter ... 14 2.1.2 Parallel Resonant Converter ... 16 2.1.3 LCC Resonant Converter ... 17 2.1.4 LLC Resonant Converter ... 18 2.2 LLC resonant converter: FHA analysis ... 19 2.2.1 Traditional FHA ... 19 2.2.2 Effect of splitting the leakage inductance (split-FHA) ... 21 2.2.3 Effect of discontinuous current (DCM-FHA) ... 22 2.2.4 FHA overview ... 25 2.3 LLC resonant converter: operative modes ... 27 2.3.1 Resonant Stages ... 27 2.3.2 Operative Modes ... 27 2.4 LLC resonant converter: Resonant tank design ... 29 2.4.1 Case Study ... 31 2.5 LLC resonant converter: PLECS® simulation ... 32 2.5.1 PLECS® model ... 32 2.5.2 Case Study ... 34 2.6 Conclusions ... 36 Chapter 3. High Frequency Transformer: Preliminary Choices ... 38 3.1 Core Material ... 38 3.1.1 Supermalloy ... 39 3.1.2 Amorphous metals ... 40 3.1.3 Nanocrystalline materials ... 41 3.1.4 Liqualloy ... 42 3.1.5 Ferrites ... 433.1.6 Conclusions ... 45 3.2 Core Shape ... 45 3.3 Windings ... 46 3.3.1 Litz wire ... 48 Chapter 4. High Frequency Transformer: Analytical Design ... 50 4.1 Libraries creation ... 50 4.2 Geometric calculation ... 51 4.2.1 2E core ... 51 4.2.2 Pot core ... 52 4.3 Core Losses calculation ... 53 4.3.1 Steinmetz equation ... 53 4.3.2 iGSE ... 53 4.4 Copper Losses calculation ... 55 4.4.1 Copper losses in Litz wires: the Sullivan method ... 55 4.4.2 Copper losses in Litz wires: the Tourkhani method ... 57 4.5 Thermal Model ... 60 4.6 Case Study Results ... 62 4.6.1 2E cores in ferrite 3C94 ... 63 4.6.2 2E cores in ferrite 3C97 ... 64 4.6.3 4C cores in nanocrystalline materials ... 65 4.6.4 Pot Cores in ferrite 3C94 ... 66 4.6.5 Pot Cores in ferrite 3C97 ... 67 4.6.6 Conclusions ... 68 Chapter 5. High Frequency Transformer: Finite Element Analysis ... 70 5.1 ANSYS Maxwell®: Core Loss Model ... 70 5.2 ANSYS Maxwell®: Litz wire Loss Model ... 73 5.3 Modelling and Simulation ... 74 5.4 Results and analytic model validation ... 75 5.4.1 Core E71/33/32 in ferrite 3C94 ... 75 5.4.2 Core E71/33/32 in 3C97 ... 77 5.4.3 Core PM74/59 in ferrite 3C94 ... 78 5.4.4 Core PM74/59 in 3C97 ... 79 5.4.5 Analytical model validation ... 80 Chapter 6. High Frequency Transformer: Magnetic Integration ... 81 6.1 External Inductors Design ... 81 6.2 Magnetically integrated solutions ... 84 6.2.1 2E-core with non-concentric windings ... 85 6.2.2 2E-core with non-concentric windings and gaps ... 86 6.2.3 2E-core with an additional C core ... 88 6.3 Final comparison and conclusions ... 89 Chapter 7. Conclusions ... 91
Chapter 1. EV-Charging Topologies
In the last years the research activity focused on Electric Vehicle (EV) Charging was intense. A large number of different topologies was proposed resulting in a large literature and several applications. In this chapter, a method to classify EV-Charging applications is given, and some innovative solutions are presented.
1.1 EV-Charging classification
In order to properly analyse the different applications a classification is needed. In [1] battery chargers are classified on the basis of the following criteria:
- Power level: This classification is related to the voltage level, resulting in expected power and charging time.
- Power flow direction: In the past battery chargers have always been unidirectional, the power was flowing just grid-to-vehicle (G2V). Today electric vehicles with their energy storage are indicated as a possible source of ancillary services, resulting in the need of a bidirectional interface which allows the vehicle-to-grid (V2G) power flow.
- Type of connection: Most of the solutions available on the market present a conductive connection, but the inductive wireless connection has been studied as well because of its advantages, especially for public transportation vehicles.
1.1.1 Power levels
Level 1 Charging: In Europe, it uses the standard single phase 230 V/10 A grounded outlet. It
is the slowest charger: 11-36 hours to charge EVs with a storage of 15-50 kWh. This charger is usually integrated on the vehicle, without the need of additional infrastructures. It is suitable for home or business sites. In [2] and [3] an approximate overall cost between $500–$880 is indicated.
Level 2 Charging: In Europe, it uses the standard three phase 400 V allowing to reach power
from 4 kW up to 19.2 kW. The charging time is reduced: using an 8 kW charger it is possible to achieve a full charge of a 15-50 kWh storage in 2-6 hours. Not all the vehicles are equipped on board with this level charger, resulting in an additional infrastructure. In [4] the installed system cost is estimated to be in between $1000 and $3000. The Tesla Roadster charger cost is around $3000.
Level 3 Charging: The voltage level is from 400 V up to 600 V. This charger can be both AC
or DC. This solution is always off board, and is suitable for commercial applications. It can be installed in highway’s rest areas or in city refuelling points, as an analogous of gas stations. With a 50 kW charger, an EV with 15-50 kWh storage can be fully charged in 0.3-1 hour. Three different electric vehicles charging characteristics are listed in Table 1.
Table 1: Charging Characteristics of some EVs and HEVs Energy Storage Pure electric range
Level 1 Level 2 Level 3
Power Time Power Time Power Time
Toyota Prius (Hybrid) Li-Ion 4.4 kWh 22.5 km 1.4 kW 3 hours 3.8 kW 2.5
hours n.a. n.a.
Nissan Leaf (Electric) Li-Ion 24 kWh 160 km 1.8 kW 14 hours 3.3 kW 6-8 hours 50 kW 15-30 min Tesla Roadster (Electric) Li-Ion 50 kWh 390 km 1.8 kW 30 hours 16.8 kW 4
hours n.a. n.a.
1.1.2 Power Flow Direction
Unidirectional Chargers: They typically present a diode bridge with a passive filter on the grid
side, and a DC-DC converter. Their simplicity in control and their cost effectiveness make them suitable for level 1 home chargers and level 3 chargers for commercial applications.
Bidirectional Chargers: In the next years, the number of electric vehicles is forecasted to largely
increase, resulting in a massive presence of batteries connected to the grid. If these batteries are able to exchange power to the grid, EVs will be a possible solution to the problem of grid stability. To this end the charger must be a bidirectional interface. It has two stages: an active front end to control the power factor, and a bidirectional DC-DC converter to regulate the current to the battery.
Bidirectional chargers are more flexible, and they do not affect the grid with a high harmonic distortion. On the other hand, they are more expensive and they force the battery to a higher number of cycles, resulting in a shorter life.
1.1.3 Connection type
Conductive Charging: They use a direct cable connection between the electrical outlet and the
EV connector. This kind of charger is largely used by car manufacturers. The main drawback of conductive charging is that the driver needs to plug in the cable, exposing himself to possible faults.
Inductive Charging: This is a more complex and less efficient solution, but that could play a
the need of fast charging infrastructures. A resonant compensation circuit is always needed in order to maximize the active power transfer. There are two main ways to implement this solution:
1) Static Inductive Charging: The inductive coupler can be used as a high frequency transformer inside the DC-DC converter. It consists in two similar coils, a receiver and a transmitter. The main advantage of this solution is the possibility to use a large number of turns for the coils, resulting in a higher magnetizing inductance and hence minimize the magnetizing current that the converter needs to supply. The air gap can vary between 1 mm to 150 mm.
2) Dynamic Inductive Charging: In this case the receiver is still a circular or rectangular coil while the transmitter is a track or loop embedded below the pavement surface. This solution allows the vehicle to charge the battery both when it is still and when is moving on the track. This solution is particularly used for public transportation vehicles, which must follow an established path. The main advantage of this solution is the reduction of the energy storage capability due to the possibility of frequent recharges. The disadvantages include the position errors, resulting in a larger uncertainty of the transformer parameters.
Some operative inductive power transfer applications are listed in Table 2.
Table 2 : WPT operative applications Application Nominal
Power
Transmitter
frequency efficiency Demos
KAIST e-BUS 100 kW 60 kHz 85 %
Kaist campus, Gumi (2009)
WAVE e-shuttle 25 kW 20 kHz 90 % Logan Utah (2012)
IPT Technology e-BUS 60 kW 15-20 kHz 90 % Turin, Genoa (2002) Utrecht (2010) Bombardier
PRIMOVE e-BUS 200 kW n.a. n.a.
Urbino, Mannheim
(2013)
1.2 Literature Review
- Grid side filter: Usually it is an LC or LCL filter. It reduces the harmonic distortion to the grid.
- AC-DC converter: It rectifies the grid voltages, resulting in DC values suitable for the DC-DC converter. It can use diodes or active switches. In case active switches are used, it is defined Active Front End (AFE).
- DC-DC converter: It controls the current to the battery. It can be unidirectional or bidirectional, isolated or non-isolated.
Since the safety standards impose the galvanic isolation, if the DC-DC converter is non-isolated then the galvanic isolation stage must be before the charger. A common solution is to use a line frequency transformer before the filter.
Some examples of EV-charger topologies and structures are presented in the next sections. For each example, the topology is described, and advantages and disadvantages are discussed.
1.2.1 Integrated non-isolated battery charger
In this topology, the electric motor windings are used as a filter and the motor drive inverter is used as a bidirectional AC-DC converter. This integration can be done just if traction and charging are not simultaneous. There are different converter classes related to the number of motors and inverter used. The topology presented in [5] has two inverters and two motors, see Figure 2. During the charging time, the two inverters behave like an active front end, and in this case the DC-DC converter is a buck-boost. The overall topology allows the bidirectional power flow.
The main advantage of this topology is the possibility to reach high power, level 2 and level 3, Figure 2 : Integrated battery charger
1.2.2 Bidirectional isolated battery charger
In [6] and [7] the authors propose the topology shown in Figure 3. The aim of this topology is to be completely bidirectional and flexible in term of control.
The grid side filter is a LCL, and the AFE is a three-phase full bridge with IGBTs. This combination of filter and AC-DC converter allows to implement an optimum control of the power factor and the harmonic content.
The DC-DC converter is a bidirectional isolated converter, Dual Active Bridge (DAB). The couple IGBT-diode integrated with a snubber capacitor composes the switches. The snubber capacitor imposes a voltage transient across the IGBT, resulting in a dead time between closing and opening of the two switches in the same leg. The switch which is about to close will wait until its capacitor is completely discharged, and as a consequence the voltage is zero.
One of the main feature of this topology is that the DC-DC converter can achieve Zero Voltage Switching (ZVS). The first requirements to have ZVS is that the current must lag the voltage. To this end, it is sufficient to keep the equivalent load inductive. In addition, since there are the snubber capacitors, the value of the current must be high enough to charge/discharge them before the end of the dead time. Because of these requirements, ZVS cannot be achieved in all the operative condition. However, it has been demonstrated that this topology can operate in ZVS for a broad area inside the operative region, resulting in 96 % of average efficiency. In addition to the ZVS operation, the DC-DC bidirectional converter is able to provide the control of the active power flow to the battery. In particular controlling the phase shifting between the primary and secondary voltage square waves is possible to regulate the active power flow:
𝑃 =𝑉HI𝑉HJ
𝜔 𝐿MN 𝛿 − 𝛿J
𝜋 (1.1 )
where ω is the angular switching frequency, VD1 andVD2 are the amplitudes of the square waves,
δ is their phase shifting, and Leq is the sum of the leakage inductance of the transformer and the
additional inductance.
1.2.3 Battery charger based on LLC resonant converter
In [8] the LLC topology is implemented as shown in Figure 4 (a). The MOSFET bridge generates a voltage square wave with a 50% duty cycle at the switching frequency, fs. The square wave voltage is applied to the LLC resonant tank: Lr is the sum of the leakage inductance
of the transformer and an additional inductance, while Lm is the magnetizing inductance of the
transformer.
Since it can increase the efficiency and reduce the EMI, soft switching is the most desirable advantage of a resonant converter. The LLC resonant converter can work in an operative mode that results in ZVS for the input MOSFET inverter and ZCS for the output diode rectifier. ZVS in the input inverter occurs when the equivalent impedance of the resonant tank is inductive. Using the First Harmonic Approximation (FHA) is possible to calculate the transfer function of the resonant tank, Figure 4 (b). In order to keep the input impedance inductive, the transfer function must be decreasing in the desired frequency interval.
With this DC-DC converter is possible to implement a battery voltage control exploiting the natural droop of the resonant tank. Since the relation between output voltage and frequency is monotonic, it is possible to regulate the battery voltage changing the switching frequency.
Figure 4: LLC resonant converter topology (a), and FHA transfer function (b)
a)
1.2.4 Flash Charger
Since 2013 is operative in Geneva an electric powered articulated bus, named TOSA after the four-member partnership between TPG (Geneva’s public transport company), OPI (the Office for the Promotion of Industries and Technologies), SIG (the Geneva power utility) and ABB. TOSA main objective is to avoid catenary supply, thanks to flash charges at each bus stop. With
flash charge ABB means a power of 400 kW transferred in 15-20 seconds. In addition to these
charges, the batteries are charged at the final stop for 3-4 minutes. The block scheme of both charging station and on-board system is shown in Figure 5, [9].A line frequency transformer, an AFE and an ultra-capacitors bank compose the charging station. The ultra-capacitors play a key role in the flash charge. During the charging of the bus, the power of 400 kW is fully provided by the ultra-capacitors, not affecting the grid with a pulse power demand. When no bus is connected they are slowly charged by the AFE. Thanks to this fact the AFE can be rated for a nominal power level lower than the charging system nominal power. On board a 3-phase buck interleaved is used to control the current profile. Since rapid recharging is very demanding for batteries, lithium titanate (LTO) batteries are used, because they have the maximum limit of charging current available on the market. Nevertheless, the Battery Managing System (BMS) must carefully manage the power to the battery, in order to prevent potential damage to the energy storage. A robotic arm that makes contact with the overhead charger in station stops composes the roof mounted charging equipment.
1.2.5 Wireless dynamic inductive charger
In Figure 6 is shown the project developed at KAIST research university, [10]. It is an example of dynamic inductive charger. The off-board system is composed by a line transformer, a CSC rectifier and an IGBTs H-bridge. The CSC rectifier operates at 20 kHz and must provide the power for the whole rail. The H-bridge is the first half of a resonant converter; it transforms the DC voltage in an alternate waveform suitable for the IPT transmitter operation.
The transmitter consists in a rail embedded below the road floor. Along the way several segments are available for the charging. A control system supplies power just to the segments where a vehicle is approaching.
The on-board architecture is the receiver coil and diode rectifier. The receiver coil is made with Litz wires, multi strands wire that reduce parasitic effects due to high frequency. A large number of turns is used in order to increase the magnetizing inductance. The H diode bridge is the second half of the resonant converter. A unidirectional converter is used in this case because the V2G operation is considered useless in this case.
An application of this system for E-bus is operative both in KAIST campus and in Gumi, South Korea. The power provided by the rail is 100 kW and the overall charging efficiency can reach 85%.
Figure 6: IPT topology (a), general schematic of the dynamic inductive system (b)
a)
1.3 Conclusions
The integrated battery charger, section 1.2.1, allows a reduction in the number of components, but it introduces relays and it needs a grid frequency transformer.
TOSA, section 1.2.4, is one of the most innovative solutions. The flash recharge is so effective that even stops of few seconds are useful to manage the battery state of charge. The drawback is an expansive and bulky infrastructure, reasonable just for public transports.
The dynamic inductive power transfer developed at KAIST research center is an alternative to ultra-fast charge. Thanks to the possibility of charging while the vehicle is moving, the battery pack can be smaller.
The fact that must be highlighted is that both TOSA and KAIST solutions are suitable for electric buses in the context of public transportation. However, if the target is the private electric cars then the objective is to achieve the highest efficiency with a cost-effective and compact solution. The topologies presented in section 1.2.2 and 1.2.3 are both capable to achieve high efficiency and be compact. However, the LLC resonant converter is able to operate in soft switching at higher switching frequency compared to the bidirectional DC-DC converter, resulting in higher efficiency and smaller dimensions.
For these reasons, the resonant converter has been chosen as the most promising topology to investigate in this thesis. In Chapter 2 different kinds of resonant converter are analyzed in order to understand the possibility and the limits of this solution.
Chapter 2. Resonant Converters
In Chapter 1 has been concluded that the LLC resonant converter is one of the most promising DC-DC stage for EV-chargers. In order to understand better the positive features of this topology, in section 2.1 the other types of load resonant converter are briefly analysed. In the other sections, the focus is on the LLC resonant converter and its behaviour. In particular, three different variations of First Harmonic Analysis (FHA) are proposed, and the most considerable operative modes are described. For a case study, a design methodology of the resonant tank is described and a PLECS® model is implemented.
2.1 Resonant converters classification
Load resonant converters can be divided in:- Series resonant converter (SRC); - Parallel resonant converters (PRC) - LCC resonant converter
- LLC resonant converter.
A common way to analyze load resonant converters is through their transfer function which is usually derived using the First Harmonic Analysis (FHA). Despite of its simplifying assumptions, that will be discussed in section (2.2), this approach is largely used in literature because it is a good compromise between accuracy and simplicity.
2.1.1 Series Resonant Converter
The scheme of the SRC is shown in Figure 7. The inverter and the rectifier could be different from the solution presented in the scheme. However, for EV charging application a full bridge is the more appropriate choice due to its high-power rating.
The resonant tank consists of a series connection of a capacitor, Cr, and an inductor, Lr. Here
The SRC transfer function, M=nV0/Vin, for different load condition, is presented in Figure 8.
In the region below the resonance frequency, the equivalent input impedance appears capacitive, that allows to achieve ZCS in the inverter bridge, but as a side effect it results in the presence of sub-harmonics. Above the resonance frequency, the behavior is inductive allowing to achieve ZVS.
A positive feature of resonant converter, which designers want to exploit, is the intrinsic relation between voltage and frequency. This natural droop can be used in order to implement a robust voltage control varying the switching frequency. In this case, see Figure 8, the voltage/frequency characteristic is monotonic decreasing just above the resonance frequency, compromising the stability of the control. In addition, lower is the load flatter is the curve, ideally the curve is horizontal in no load condition. As a result, the SRC not capable to operate voltage regulation in no load condition.
Figure 7: Series Resonant Converter topology [13]
2.1.2 Parallel Resonant Converter
In this case, the resonant components are connected in parallel; in particular, Cr is in parallel
with the equivalent load (see Figure 9). The approximate transfer function, Figure 10, shows that the peak gain is load dependent: if the load is increased, its values is getting smaller, and its position shifts to lower frequency. Since to achieve ZVS the resonant converter must work in the frequency region above the peak, ZVS cannot be achieved in every load condition. The slope of the characteristic is higher for lighter load, resulting in smaller variation of frequency for the voltage regulation. The drawback of PRC is the circulating current. Due to high conduction loss it presents and poor efficiency for light load condition.
2.1.3 LCC Resonant Converter
Three resonant components are used for this topology, see Figure 11, one inductor and two capacitors. This solution is a hybrid between the SRC and PRC, Cr and Lr are connected in
series, while Cp is connected in parallel to the equivalent load. This connection results in two
different resonant frequencies, see Figure 12:
- Short Circuit resonant frequency, 𝑓g = 1/2𝜋 𝐿i𝐶i: similarly, to the SRC this point is load-independent, and the gain is equal to 1.
- Open Circuit resonant frequency, 𝑓k = 1/2𝜋 𝐿i(𝐶i||𝐶m): this is considered the nominal frequency of the converter.
In order to achieve ZVS and to perform a robust voltage control the converter must operate above the frequency corresponding to the peak.
Figure 11: LCC resonant converter topology [13]
2.1.4 LLC Resonant Converter
In the LLC topology, Lm substitutes Cp in parallel to the load, see Figure 13. Lr and Lm could be
the leakage inductance and the magnetizing inductance of the transformer or additional external inductances. Like the LCC, this topology has two resonant frequencies, see Figure 14:
- Short Circuit resonant frequency, 𝑓g = 1/2𝜋 𝐿i𝐶i: this point is load-independent, and the gain is equal to 1. This is considered the nominal frequency
- Open Circuit resonant frequency, 𝑓k= 1/2𝜋 (𝐿i+ 𝐿o)𝐶i: this value is always smaller than f0.
Since the gain peak occurs always below the nominal frequency, it is possible to achieve ZVS in a broad interval of frequency.
2.2 LLC resonant converter: FHA analysis
2.2.1 Traditional FHA
In order to apply the fundamental harmonic analysis (FHA), it must be taken into account that the following assumptions are made:
- Just the fundamental harmonic is taken into account, all the other harmonics are considered negligible;
- The FHA analyzes a steady state operation;
- Discontinuous conduction mode (DCM) is not taken into account; - No ripple on the output voltage;
- The transformer model used considers a single lumped leakage inductance at the primary side.
With FHA, the circuit shown in Figure 13 is approximated with the circuit in Figure 15.
Vin is the fundamental harmonic of the square wave generated by the MOSFET full bridge. Cr
is the series capacitor, Lr is the lumped inductor (sum of the transformer leakage inductance and
the possible external inductor), Lm can be the magnetizing inductance of the transformer or an
additional inductor, n is the ideal transformer ratio, Rac is the equivalent of a DC resistive load
brought to the primary side of the ideal transformer.
The output voltage is considered to be constant, equal to Vo. Therefore, the voltage across Rac
is a square wave, of which the fundamental amplitude is qp 𝑛 𝑉s. The load current, Io, is the
average value on half period of the rectifier input current. Since the rectifier input current is supposed to be a continuous sinusoidal signal, its amplitude, referred to the primary side, is
q
Jt𝐼s. From these considerations, the value of Rac is: 𝑅wx = p q 𝑛 𝑉s𝑠𝑖𝑛 𝜔 𝑡 q Jt𝐼s𝑠𝑖𝑛 𝜔 𝑡 =8𝑛J 𝜋J 𝑅s = 8𝑛J 𝜋J 𝑉sJ 𝑃s (2.1 ) Figure 15 : LLC simplified equivalent circuit for FHA
The input current to the resonant tank is: 𝐼 }t = 𝑉}t I ~•€•+ 𝑗𝜔𝐿i+ (𝑅wx||𝑗𝜔𝐿o) (2.2 )
Consequently, the output voltage is:
𝑛𝑉 s = 𝐼}t(𝑅wx||𝑗𝜔𝐿o) = 𝑉}t I ~•€•+ 𝑗𝜔𝐿i+ (𝑅wx||𝑗𝜔𝐿o) (𝑅wx||𝑗𝜔𝐿o) (2.3 ) The voltage transfer function is:
𝑀 =𝑛𝑉s 𝑉}t = 1 [ I ~•€•+ 𝑗𝜔𝐿i+ (𝑅wx||𝑗𝜔𝐿o)] /(𝑅wx| 𝑗𝜔𝐿o = 1 1 +~•„•~•€•…I ~•€• (†‡ˆ…~•„‰) †‡ˆ ~•„‰ = 1 1 +•Š„•€•~•„‰‹•Š„•€•†‡ˆ…~•„‰…†‡ˆ ~•€•†‡ˆ ~•„‰ = 1 1 +~•„• †‡ˆ + „• „‰+ I ~•€•†‡ˆ− I •Š„ ‰€• (2.4 ) Defining the following parameters, the final expression of the normalized gain M is given:
Quality factor: 𝑄 = „• €• 𝑅wx Inductance ratio: 𝜆 = 𝐿i Figure 16: rectifier continuous conduction mode with sinusoidal waveforms [13]
Normalized frequency: 𝑓t = 𝑓 𝑓i = 𝑓 2𝜋 𝐿i𝐶i 𝑀 𝜆, 𝑄, 𝑓t = 𝑛𝑉𝑜 𝑉}t = 1 1 + 𝜆 −“’ ”Š+ 𝑗𝑄(𝑓t− I “”) (2.5 )
2.2.2 Effect of splitting the leakage inductance (split-FHA)
When the primary and secondary leakage inductances of the transformer are not considered as a unique lumped inductor, the analytical expression of the voltage gain changes, [11]. Later in the report, this method will be called split-FHA.
Since the secondary leakage inductance is not in series with the primary leakage inductance, the input current to the resonant tank is:
𝐼 }t = 𝑉}t I ~•€•+ 𝑗𝜔𝐿w+ ((𝑅wx + 𝑗𝜔𝐿•)||𝑗𝜔𝐿o) (2.6 )
Consequently, the output voltage is: 𝑛𝑉s = 𝐼}t 𝑗𝜔𝐿o 𝑅wx + 𝑗𝜔𝐿•+ 𝑗𝜔𝐿o = I 𝑉}t ~•€•+ 𝑗𝜔𝐿w + ((𝑅wx + 𝑗𝜔𝐿•)||𝑗𝜔𝐿o) 𝑗𝜔𝐿o 𝑅wx + 𝑗𝜔𝐿•+ 𝑗𝜔𝐿o (2.7 )
The voltage transfer function is: 𝑀 = 𝑛𝑉s 𝑉}t = 1 I ~•€•+ 𝑗𝜔𝐿w+ ((𝑅wx + 𝑗𝜔𝐿•)||𝑗𝜔𝐿o) 𝑗𝜔𝐿o 𝑅wx + 𝑗𝜔𝐿•+ 𝑗𝜔𝐿o (2.8 ) Defining the following parameters, the updated expression of the normalized gain M is given:
Short circuit inductance: 𝐿– = 𝐿w+ 𝐿•𝐿o
𝐿•+ 𝐿o
Quality factor: 𝑄 = „— €• 𝑅wx Inductance ratios: 𝜆w = 𝐿– 𝐿o+ 𝐿w 𝜆•= 𝐿– 𝐿o+ 𝐿• Normalized frequency: 𝑓t = 𝑓 𝑓i= 𝑓 2𝜋 𝐿–𝐶i 𝑀 𝜆, 𝑄, 𝑓t = 𝑛𝑉𝑜 𝑉}t = 1 + „˜ „‰ 1 +~“”™ ’˜ I‹“”Š I‹š”Š ›‡ 1 + 𝑓tJ− 1 1 −“”Š ’‡ (2.9 )
The main advantage of this approach compared with the traditional FHA is that it identifies the correct value of the gain at the resonance frequency:
𝑀 𝑓
i = 1 +
𝐿•
𝐿o ≠ 1 (2.10 )
2.2.3 Effect of discontinuous current (DCM-FHA)
The value of Rac expressed in equation (2.1) is calculated under the hypothesis of continuous
conduction mode. However, when the switching frequency is below the resonance, or the load is particularly low, this hypothesis is not valid.
approximated with a sine pulse, which starts in J=0 and lasts for the corresponding time to the
extinction angle, a (see Figure 18):
𝑖H(𝑡) = 𝐼H,mŸ𝑠𝑖𝑛 𝜃 𝜋
𝛼 , 0 < 𝜃 < 𝛼
0 , 𝜃 ≥ 𝛼 (2.11 )
Where J=wt and w is the angular frequency.
Applying the Fourier series expansion, it is possible to calculate the amplitude of the fundamental harmonic associated to iD(t):
𝐼H I ¤¥ = 2 𝐼g𝑐𝑜𝑠 §J 1 − § q J (2.12 )
Assuming that the energy transfer is due only to the first harmonic:
I
J𝐼H I¤¥
J 𝑅
wx
𝑛J = 𝑅g𝐼gJ (2.13 )
Combining equations (2.12) and (2.13), the AC value of the resistive load referred to the primary side is:
𝑅wx = tŠ† ¨ J 1 − § q J J 𝑐𝑜𝑠J(𝛼/2) (2.14 ) In order to evaluate Rac the value of the extinction angle is needed. The resistive load current,
I0, is the average value of the rectifier input current, iD(t), therefore is possible to write that:
𝐼H¤¥ = 𝐼g𝜋J 2𝛼= 𝑉g 𝐼g 𝜋J 2𝛼 (2.15 ) Figure 19: LLC topology
Looking at Figure 19, it is clear that when the diode bridge is conducting, the voltage across L2
is constant, and as a consequence its current, iL2, is linear:
𝑖
„J(𝜗) = 𝐼„J¨+ ∆𝐼„J
𝜗
𝛼 (2.16 )
where IL20 is the initial current flowing in L2, and DIL2 is the current increment. Substituting
equation (2.15) in the current increment calculation: ∆𝐼„J =𝑛𝑉g𝛼 𝜔𝐿J = 2𝐼H¤¥ 𝑛 𝑛J𝑅 g 𝜔𝐿J 𝛼 𝜋 J (2.17 )
The voltage between the inverter bridge legs is: 𝑉w•(𝜗) = 𝜔𝐿I 𝑑 𝑖„J+}¬ t 𝑑𝜃 + 1 𝜔𝐶 𝑖„J+ 𝑖H 𝑛 𝑑𝜃 + 𝑉€g+ 𝜔𝐿J 𝑑𝑖„J 𝑑𝜃 (2.18 )
where VC0 is the initial voltage across the resonant capacitor. The voltage across L2 is
established by the rectifier:
𝜔𝐿 J 𝑑𝑖„J 𝑑𝜃 = 𝑛𝑉g (2.19 ) And therefore: 𝜔𝐿 I 𝑑𝑖„J 𝑑𝜃 = 𝑛𝑉g 𝐿I 𝐿J (2.20 )
Substituting equations (2.19) and (2.20) in (2.18): 𝑉w•(𝜗) = 𝜔𝐿I𝑑 }¬ t 𝑑𝜃 + 1 𝜔𝐶 𝑖„J+ 𝑖H 𝑛 𝑑𝜃 + 𝑉€g+ 1 + 𝐿1 𝐿2 𝑛𝑉g (2.21 )
After the derivation of equation (2.21) and the substitution of (2.11) and (2.16): 0 = 1 − 𝜔 𝜔i– 𝜋 𝛼 J 𝑠𝑖𝑛 𝜃 𝜋 𝛼 + 𝐼„J¨𝑛 𝐼HmŸ + ∆𝐼„J¨𝑛𝜋 𝜋 𝐼HmŸ 𝛼 (2.22 ) where 𝜔i– = „I
-€ .Since equation (2.22) has no analytical solutions for a, the authors of [12]
propose an approximated solution based on the assumption that:
𝐼„Jg ≪𝐼HmŸ
𝑛 (2.23 )
In this contest, the extinction angle is estimated to be the average of two solutions in particular conditions: a1 is the solution of (2.22) for the limiting case θ < 0.1a , and a2 is the solution of
(2.22) for the case θ = 0.5 a .
𝛼I 𝜋 = − 𝜋 4 𝜔𝐿J 𝑛J𝑅 g+ 𝜋 16 𝜔𝐿J 𝑛J𝑅 g J +𝜋 2 𝜔𝐿J 𝑛J𝑅 g 𝜔 𝜔i– J (2.25 ) 𝛼J 𝜋 = − 𝜋 2 𝜔𝐿J 𝑛J𝑅 g+ 𝜋 4 𝜔𝐿J 𝑛J𝑅 g J +𝜋 2 𝜔𝐿J 𝑛J𝑅 g 𝜔 𝜔i– J (2.26 )
With the estimated value of a is possible to calculate Rac using equation (2.14). With this new
value of Rac is possible to update equation (2.4) and see the effect of DCM on the transfer
function of the resonant tank.
2.2.4 FHA overview
For the preliminary design, engineers make a large use of the traditional FHA. In this section, a comparison between the results obtained with the traditional FHA and the two alternative methods is performed.
In Figure 20 is shown the comparison between the transfer function obtained with the traditional FHA and the DCM-FHA. The dashed-line curves represent the transfer function calculated with the DCM-FHA at different load conditions. From the plot is clear that, if the possibility of DCM is considered, the resonance peak is shifted to higher frequency and it has lower amplitude. The shifting is more evident in higher load condition, while the amplitude reduction is smaller in higher load condition. However, the gain at the resonance frequency is equal to 1, resulting in no difference between the traditional approach and the DCM-FHA. Introducing the DCM is possible to get information that is more precise at low and high frequency, but in the frequency interval close to the resonance the differences between traditional-FHA and DCM-FHA are not relevant.
In Figure 21 is shown the comparison between the transfer function obtained with the traditional FHA and the split-FHA. The dot-line curves represent the transfer function calculated with the split-FHA at different load conditions. When the transformer is designed and the external inductors are chosen, different choices can be made to achieve the same equivalent to primary side leakage inductance. In the plot, three different ways to achieve an equivalent leakage inductance of 75µH are shown. This value can be obtained distributing equally the leakage inductance between the primary and secondary side (graph a.), focusing the leakage on the secondary side (graph b.), and focusing the leakage on the primary side (graph c.). When the leakage inductance is correctly considered as split, the peak is shifted to higher frequency and it has higher amplitude. At the resonance frequency, the gain is higher than 1 (=1+ Lb/Lm). This
difference can be crucial in the resonant tank design. Moreover, the higher is the leakage inductance on the secondary side, the higher is the value of the gain at the resonance frequency. To conclude, when a transformer with high leakage inductance is used, for the design of the resonant tank the split-FHA should be preferred to the traditional approach.
Figure 21: Transfer functions obtained with the traditional FHA and with the split-FHA with different leakage inductances distribution: (a) balanced, (b) focused on
the secondary side, (c) focused on the primary side
a) b)
2.3 LLC resonant converter: operative modes
In [13] three possible resonant stages are described, resulting in several different operative
modes.
2.3.1 Resonant Stages
With resonant stage, the authors refer to a time interval in which a certain combination of the inverter switches state and the voltage across Lm is applied. Therefore, there are six different
resonant stages with six different evolution of currents and voltages. Since the inverter bridge is controlled with constant 50% duty ratio, it is possible to simplify the discussion considering just the three resonant stages with the positive voltage applied to the resonant tank, because the other three are symmetric.
With this assumption, the resonant stage depends only to the voltage condition across Lm:
1. When ir>im, positive voltage vm= n Vo (denoted as stage P);
2. When ir<im, negative voltage vm= - n Vo(denoted as stage N);
3. When ir=im, cut of stage vm is not fixed by the rectifier (denoted as stage O).
2.3.2 Operative Modes
The converter operative mode is a combination of the resonant stages. For this reason, the authors of [13] refer to each operative mode with a sequence of letter corresponding to the sequence of resonant stages. It is possible to classify the main operative modes due to the switching frequency of the inverter compared to the resonance frequency.
Below Resonance Frequency
PO: it starts with ir=im both equals to a negative value. Then ir>im implies a P stage where im
increases linearly and ir has a sinusoidal waveform due to the series resonance. When ir=im again,
the O stage begins. Therefore, it is a discontinuous conduction mode (DCM). In this stage vm
decreases following a sinusoidal waveform due to the parallel resonance. In this operative mode, vm does not have enough time to reach -nVo and bring the converter in N stage. ZVS is
always achieved because ir starts equal to a negative value. In fact, in this scenario before the
closing of the MOSFETs, their antiparallel diodes were conducting the current, resulting in a null voltage across them. Another positive feature is the zero-current condition when the rectifiers diodes start to conduct, resulting in the absence of reverse recovery losses.
PON: this mode has the same time evolution of the previews one until when, during the O stage,
the voltage across Lm reaches -nVo resulting in an additional N stage. There are two possible
reasons why vm can reach that voltage level. The first is a high load condition, which means
high current, resulting in a steeper decreasing waveform of vm. The second reason is low
switching frequency, resulting in a duration of the O stage long enough to reach -nVo. In this
operative mode, the rectifier diodes experience reverse recovery. In addition, ZVS condition can be lost because the ir can assume positive values at the starting point.
PN: it is a continuous conduction mode (CCM). It is possible to consider this operative mode,
as a PON were the load is high enough to reduce to zero the duration of the stage O.
Figure 23: LLC operative modes below the resonance frequency: a) PO, b) PON, c) PN [13]
Above Resonance Frequency
NP: This mode can be found under high load condition. Therefore, after the first N stage, the
current is high enough to make vm immediately equal to nVo, without any O stage. Since this
mode starts with N stage, ir<im, and im<0, ZVS is always achieved. However, due to the absence
of the O stage the rectifier diodes experience reverse recovery.
NOP: When the load is lighter compared to NP mode, at the end of N stage vm<-nVo resulting
in an additional cut-off O stage.
OPO: It exists in light load condition. At the beginning of the half cycle vm<-nVo and the diode
rectifier are consequently OFF, O stage. When vm rises enough to turn ON the rectifier the stage
P begins. The current absolute value is so small that at the end of the stage P vm it is not low
enough to enter in stage N, resulting in another O stage.
2.4 LLC resonant converter: Resonant tank design
Once the values of the nominal voltages, nominal power and resonance frequency have been chosen, it is possible to select the values of the passive resonant elements. Referring to Figure 17, four elements must be designed, Cs, Lm, La and Lb.
In order to achieve ZVS in all load conditions, the no-load current must be high enough to charge and discharge the drain-to-source capacitance of the MOSFETs, Cds, in a time interval
smaller than dead time, Tdead:
𝐼
o‰°” =
𝐶±– 𝑆 𝑉}t
𝑇±Mw± (2.27 )
where, Vin is the voltage across the resonant tank, S is the number of MOSFETs in the inverter
bridge, and Tdead is the time interval between the time between turn ON and turn OFF of the
two MOSFETs of the same leg.
In particular, during the no load condition, the only current in the bridge is the one flowing through the parallel resonant inductor, Lm. At the resonance, Cr and La result in a short circuit
therefore the voltage across Lm is equal to Vin, therefore:
𝐿
o‰‡´ =
𝑉}t
2 𝜋 𝑓i𝐼oo}t (2.28 )
Once the value of Lm is chosen, the value of La and Lb can be found analyzing the resonant tank
transfer function. A graphical analysis of the transfer function is sufficient to understand if the resonant tank can fulfill its main tasks:
1) The current must lag the voltage, in order to have ZVS. That means that the equivalent impedance must behave as an inductor, resulting in a decreasing transfer function. 2) In order to implement a voltage control based on the variation of the switching
frequency, the function that relates the switching frequency and the output voltage must be injective. To achieve this condition, the curve of the transfer function must be
monotonic in a frequency interval as large as possible.
3) The microcontroller used for the closed loop control defines the maximum slope of the V-f curves. In fact, it is not capable to increase the frequency continuously, but just with finite increments. A microcontroller with a given clock frequency (fclock) can generate a
time step equals to 1/fclock. In order to generate a triangular modulator that results in a
switching frequency equals to fsw, with a duty ratio of 50%, the microcontroller must
use the following number of steps (Nstep) :
The frequency resolution of the microcontroller, Δf, is function of its clock frequency, the switching frequency and the prescaler register.
Increasing the switching frequency, the frequency resolution decreases, see Figure 25.
𝑓 –µ = 𝑓x¶sxŸ 𝑁–¸Mm 𝑃𝑟𝑒𝑑𝑖𝑣 → 𝑁–¸Mm 𝑓–µ = 𝑓x¶sxŸ 𝑓–µ 𝑃𝑟𝑒𝑑𝑖𝑣 (2.29 ) ∆𝑓 = 𝑓–µ½½ − 𝑓–µ½ = 𝑓x¶sxŸ 2 (𝑁–¸Mm− 2)J (2.30 )
4) The minimum slope of the resonant tank droop is defined both by the voltage interval and the frequency interval in which the controller should operate. The voltage range is due to the charging profile of the battery. The frequency range is a design optimization parameter. All the passive components must be optimized in this frequency range to get the highest efficiency with the smallest possible dimensions.
Based on these assumptions good values for La and Lb can be estimated looking at the transfer
function graph. Once all the inductances are set, to calculate the resonant capacitor is sufficient to use the following expression:
Since the maximum efficiency is around the resonance frequency, the number of turns ratio (n) is an important parameter. Adjusting n, it is possible to shift the nominal output voltage corresponding to this working point:
2.4.1 Case Study
The LLC resonant converter considered as case study has the specifications listed in Table 3. Table 3 : LLC resonant converter specifications
Pnom 10 kW V1 700V-900V
fr 100 kHz V2 320-440 V
Once the values of the dead time and the MOSFETs have been chosen, the maximum value of
Lm is defined. Considering a dead time equals to 100 ns, and a common 1200 V MOSFET with
a drain-to-source capacitance equals to 1 nF :
𝐿o‰‡´ = 𝑇±Mw± 2 𝜋 𝑓i 𝐶±– 𝑆
= 100𝑒‹¾
2 𝜋 10𝑒‹¿ 1𝑒‹¾ 4 = 400 µ𝐻
As a consequence, Lm=300µH is an acceptable value, which allows to achieve ZVS even in
no-load condition.
The battery charging profile consists in a small variation of the battery voltage, e.g. between 0.8VnBatt and 1.1 VnBatt. Considering a battery with a nominal voltage of 400 V, the voltage
range is between 320V and 440V. It is important to highlight that the nominal voltage of the DC bus and the nominal voltage of the battery are not necessarily the same. In this case, the nominal voltage of the primary DC bus is 800 V, and the secondary nominal voltage is defined by the number of turns. For the sake of simplicity, the number of turns have been chosen equals to 2, resulting in a secondary DC bus nominal voltage of 400 V.
𝐶 i= 𝑉}t 2 𝜋 𝑓i J (𝐿w+„„˜„‰ ˜…„‰) (2.31 ) 𝑉s¸ = 𝑀(𝑓–µ) 𝑉}t 𝑛 (2.32 )
The frequency range can be chosen between 70 kHz and 150 kHz. These two intervals result in the minimum slope of the Vo-f characteristic.
Considering a 100 MHz microcontroller, without any predivider, the frequency resolution in a narrow interval, centered in 100 kHz, is 200Hz, see Figure 25 (right). In order to have a voltage sensitivity of 1 V, the maximum slope of the Vo-f characteristic is 1V/200 Hz.
Figure 26 shows the transfer function of a resonant tank with V2=400 V, Pout=10 kW, and Lm=300 µH varying the value of La and Lb. In this case, the best option is La =37.5 µH and Lb
=9.375 µH, because with this value the transfer function is inside the two limits and fulfill all its tasks.
To conclude, referring to equation (2.31), the resonant capacitors is equal to 35.8nF.
2.5 LLC resonant converter: PLECS
®simulation
2.5.1 PLECS
®model
The LLC converter model used for the simulations is shown in Figure 27. In order to have accurate solutions, the high frequency transformer has been modeled with a T equivalent. The primary DC bus is considered as a constant voltage source. On the secondary DC bus, a capacitor is used to stabilize the voltage, and the battery is modeled with a resistive load. Modelling the battery as a resistive load is not accurate if the analysis timeframe is the whole charging period. But, since the task is to analyze the resonant converter steady state behavior at the critical operating points, the considered timeframe is considerably smaller than the charging period. That allows to model accurately the battery with a resistive load in the steady state behavior, while the transient response of the converter results more damped with such a choice.
For the simulations, the typical charging profile of a lithium cell has been considered, see Figure 28. In literature, this charging strategy is defined IV charging, because there are two main phases: one at constant current and one at constant voltage. During the charging time, three operating points are considered critical:
1) Beginning of the constant current phase V = 0.8VBattNom, I = Imax
2) Beginning of the constant voltage phase V = 1.1 VBattNom, I = Imax
3) End of the charging phase V = 1.1 VBattNom, I à 0
Figure 28: Lithium cell charging profile Figure 27: LLC resonant converter PLECS® model
2.5.2 Case Study
The values of the passive elements are the ones selected in section 2.4.1. It is considered a battery with a nominal voltage of 400 V, nominal capacity of 25 Ah, and a charging process with the nominal current. As a consequence, the three operating points that are investigated are: P1: Vbatt = 320 V, I= 25 A, Pout= 8 kW, (Ro=12.8 Ω)
P2: Vbatt = 440 V, I= 25 A, Pout= 10 kW, (Ro=16.8 Ω)
P3: Vbatt = 440 V, I= 0.5 A, Pout= 200 W, (Ro=840 Ω)
POINT 1
Referring to section 0, the operative mode in this point is NP mode, resulting in ZVS condition, Figure 29. The switching frequency is fsw= 128 kHz, above the resonance frequency. In order
to have an estimation of the losses, important values are: - I(tOFF) = +21.7A, Irms= 16.2 A
For the selection of the resonant capacitor, the maximum voltage across it must be taken into account:
- VcMAX= 800 V
POINT 2
In this point, the operative mode is NP mode again, Figure 30. ZVS condition is achieved. The switching frequency is fsw= 108 kHz, slightly above the resonance frequency, resulting in a
current shape almost sinusoidal. The other resonant tank values are: - I(tOFF) = +13.8A ,Irms= 16.3 A, VcMAX= 950 V
POINT 3
This point is marked by low load condition. As expected the operative mode here is OPO mode, Figure 31. ZVS condition is achieved. The switching frequency is fsw= 118 kHz, above the
resonance frequency. The other resonant tank values are: - I(tOFF) = +5.8A , Irms= 3.53 A, VcMAX= 180 V
Figure 30: resonant tank waveforms for the operative point n°2
Comparing the results of the three operative points with the theoretical transfer function, see Figure 32, is possible to see that when the operative point is close to fr the error is small, while
for higher frequency the error becomes larger. This is due to the first harmonic approximation, in fact at higher frequency the higher harmonic content is more relevant affecting the accuracy of the approximation. In order to maximize the efficiency, the turn’s ratio (N1/N2) can be
increased resulting in an operating frequency closer to the resonance.
2.6 Conclusions
In this chapter, different types of resonant converter were described. The LLC topology is the most promising as a DC-DC stage for EV battery chargers, because with that is possible to achieve both ZVS in a broad range of frequency and a robust voltage control based on the regulation of the switching frequency.
Referring to the LLC topology the use of the FHA was discussed. Thanks to the comparison between the traditional FHA and both the split-FHA and DCM-FHA, it is possible to conclude that the traditional FHA is reliable when the switching frequency is close to the resonance and the series resonant inductor is focused on the primary side. On the other hand, when HF transformers with high leakage inductances are used, the split-FHA is more accurate.
After a thorough analysis of the LLC operative modes, an original design methodology for the resonant tank was proposed. As application example, a 10 kW LLC converter operating at 100 kHz rated frequency was considered as case study, assuming a secondary voltage range 320-440 Vac and a primary bus voltage of 800 Vdc. In section 2.4.1 an original design methodology
was presented, and it leaded to select Lm = 300 µH, La = 37.5 µH and Lb = 9.375 µH. This
converter was modeled with PLECS. Simulations results confirm the validity of the FHA in a frequency range near to the resonance, while the error increases at higher frequency.
transformer has been designed, external inductors can be introduced to achieve the desired values of inductances.
Based on these conclusions in the next chapters a design methodology for high frequency transformer is proposed.
Chapter 3.
High Frequency Transformer:
Preliminary Choices
As stated in the last chapter, the transformer plays a key role in the LLC resonant converter behaviour. The first step of the design is to define a set of possible components for the transformer parts. As a general indication, the class of DC-DC converter that are considered for this thesis has a nominal power of the 10 kW and a switching frequency that can vary from 70 kHz up to 150 kHz. Literature offers a huge number of combinations of different core material, core shape and windings type. The aim of this chapter is to restrict the analysis to those combinations that are more suitable to the project.
3.1 Core Material
The magnetic material selection is an important step in the design of a high frequency transformer. It has a strong effect on both efficiency and overall dimensions. In this chapter, several different soft magnetic materials are compared, taking into account the following parameters:
- Specific core losses [kW/m^3]: In order to achieve high efficiency a material which can guarantee low losses at high frequencies is needed. This information is always available in the manufacturer data sheet. To make a fair comparison one must be sure that all the components of core losses are taken into account. In fact, often manufactures perform their tests on thin toroidal cores in which eddy currents can be neglected.
- Saturation flux, Bsat [T]: A relatively small device is another goal of this design; a higher
saturation flux means a smaller core cross section with the same amount of turns, resulting in a reduction of dimensions and weight.
- Relative permeability, µr: A higher value of µr allows to achieve higher values of the
- Temperature stability: Since it is difficult to develop an accurate analytical thermal model which can evaluate the temperature inside the transformer (and for it factors like the converter cooling system, which are not defined yet, must be taken into account), it would be a positive feature if the material had the same behavior at different temperatures.
- Specific cost [€/kg]: It is hard to combine in a unique function material cost together with efficiency. It would imply an economic analysis that is beyond the scope of this thesis. Therefore, this parameter will be taken into account just to compare materials with similar values of specific core losses.
Since there is no material with excellent values of all these parameters, the selection is the result of a compromise based on the application requirements. In the next sections, the main features of the typical high-frequency magnetic materials are introduced.
3.1.1 Supermalloy
Historically one of the best materials for measurement transformers is a Nickel-Iron alloy (Ni81Fe19), also known as Permalloy. This material presents low losses in a wide range of flux
density and essentially zero magnetostriction, but in a range of frequency suitable just for distribution systems, 50-60 Hz.
In order to extend the frequency range of this material, a new alloy was developed. The composition of this alloy is 79%Ni-15%Fe-5%Mo and the commercial name is Supermalloy, distributed by Magnetics Inc [14]. Its features are listed in Table 4.
Table 4 : Supermalloy typical properties at 25 °C
Bsat [T] µr r [Wxm] Density [Kg/m^3] Curie Temp. [°C]
0.66-0.77 20k 0.57 x 10-6 8.72x103 430
From the manufacturer’s catalogue the curves of core losses vs flux density are available, and are shown Figure 33. They are measured on a laminated sheet of 0.0254 mm.
3.1.2 Amorphous metals
Many drawbacks of ferromagnetic alloys are caused by metallurgical defects due to the crystalline structure. In order to solve this problem, manufacturers developed a new metallurgic technique, called Rapid Solidification Technology (RST), which allows total absence of crystalline structure. A very thin layer (18 µm) of molten alloy is poured on a rolling structure, resulting in an ultra rapid quenching, 106 K/s. The final product of this procedure is a ribbon of amorphous metal or metallic glass, as shown in Figure 34.
Figure 34 : RST logic scheme
The main positive features of these materials are: high concentration of ferromagnetic elements, resulting in a high saturation level; low coercitivity due to the absence of crystalline defects; high electric resistivity which requires thinner insulator layer, resulting in a higher packing factor than usual crystalline alloys.
The most common amorphous metal is a Metglas patent distributed by Hitachi Metals [15]. Metglas proposes both Fe-based and Co-based alloys, their magnetic properties are listed in Table 5.
Table 5 : Fe-based and Co-based amorphous properties at 25°C
Material Bsat [T] µr r [Wxm] Density [Kg/m3] Curie Temp. [°C]
Core losses against flux density are given in Hitachi Metals data sheet, and are shown in Figure 35.
3.1.3 Nanocrystalline materials
These materials are essentially amorphous metals in which a primary crystallization is induced thanks to a special thermal treatment called annealing. A typical annealing procedure by Hitachi Metals is shown in Figure 36. The result is an amorphous matrix (20-30% of the volume) that separates the nanocrystals. The typical grain size of the nanocrystals is 10-15 nm, and they are placed at a distance of 1-2 nm.
In conventional soft magnetic material, grain size about 1µm, the reduction of the grain size implies worse performance due to, for example, the increasing of the magnetic coercitivity. In Figure 36, we can observe that below 0.1µm there is an opposite behavior, which explains the better performance of nanocrystalline materials compared to crystalline alloys.
Figure 35 : Amorphous core loss density at 25°C
Figure 36: Typical annealing technique by Hitachi Metals (a) and Magnetic coercitivity VS grain size (b)
The two most common nanocrystalline materials are Finemet (Hitachi-Metals) and Vitroperm (Vaccumshmelze), both of them with the same composition :Fe73.5%-Si13.5%-B9%-Nb3%-Cu1%. Their magnetic properties are listed in .
Table 6 , [16] [17].
Table 6: Nanocrystalline magnetic properties at 25°C
Material Bsat [T] µr r [Wxm] Density [Kg/m3] Curie Temp. [°C]
Finemet-3M 1.23 100k 1.2x10-6 7300 570
Vitroperm500F 1.2 80k 1.2x10-6 7300 600
Figure 37 shows the core loss curve of Finemet at 50kHz and 100kHz.
3.1.4 Liqualloy
One of the most innovative materials available on the market is an Alps patent, and its name comes from liquid alloy. The manufacturing process of this material starts with a Fe-based amorphous (basic composition: Fe-Cr-P-C-B-Si) which is powdered and then pressed in different possible core shapes.
Liqualloy overcomes one of the main limitations of amorphous materials, which is the lack of available cores on the market. However, it keeps the peculiar properties of amorphous materials, such as high flux density, temperature stability and good loss density related to the small coercitivity (2-5 A/m).
The core loss density at 100 kHz is shown in Figure 38.
Since liqualloy is an innovative material, not all the data are available, and at the moment Alps has not released any catalogue for the magnetic cores. Another drawback is the high specific costs. Indeed, the precursor of liqualloy is already an expensive amorphous material which then is treated again.
3.1.5 Ferrites
Ferrites belong to the family of ceramic materials; the crystalline structure is cubic and the general formula is MO-Fe2O3. Essentially their precursor is a powder, iron oxide based, with
the combination of two or more divalent metal (e.g. zinc, manganese, nickel, copper). The powder is then pressed and sintered. The various combinations of metals, the several different shapes, and their relative cost-effectiveness make these materials competitive in each kind of high frequency applications.
The two main groups of ferrites are MnZn and NiZn; the latter one has lower losses, lower saturation flux density and higher resistivity which make them suitable for ultra-high frequency application (> 1 Mhz). During the research activity, Ferroxcube (formerly Philips) appeared as the manufacturer with the largest offer of ferrites, and the one with most complete available documentation [18]. The magnetic properties of some of their ferrites are listed in Table 7.
Table 7 : Ferroxcube ferrites magnetic properties at 25°C
Material Bsat [T] µr r [Wxm] Density [Kg/m3] Curie Temp. [°C]
3C94 (MnZn) 1.23 2200 2 4800 215
3C97 (MnZn) 0.53 3000 2 4800 220
4B1 (NiZn) 0.35 250 105 4600 250
4F1 (NiZn) 0.35 80 105 4600 260
The MnZn family is more suitable for this work frequency range. They exhibit good core losses against flux density curve, as can be seen in Figure 39.
The main drawback of ferrites is their instability with temperature, which is a huge problem in power applications with the aim of small dimensions. Actually, nowadays new ferrites are available, as 3C97, and their behavior is relatively temperature invariant, see Figure 40. In particular, looking at a possible temperature range between 70°C and 110°C, can be observed that the core loss density of both 3C94 and 3C97 is flat enough to neglect the temperature dependency, at least in a first analysis.
3.1.6 Conclusions
Figure 41 shows the core loss density of all the materials analyzed above. Since the target of the project is to achieve high efficiency, the focus should be in a flux density range between 50mT and 200mT, therefore high saturation flux density is not needed. In this range, ferrites are the material with the best behavior. Another interesting material is the nanocrystalline. As a result of this consideration, in Chapter 4 this two kinds of materials will be taken into account.
Compared with the nanocrystalline materials, ferrites have a lower density resulting in a lighter device. In addition, they are more cost-effective and available in several core shapes and dimensions. On the other hand, nanocrystalline materials show a high stability with temperature, while ferrites behaviour is temperature dependent. The selection of one between 3C94 and 3C97 can overcame to this ferrites drawback, as shown in Figure 40.
3.2 Core Shape
The selection of power ferrites as core material allows to consider several different core shapes. All the different shapes can be classified as follows: E cores, pot cores and toroids, as shown in Figure 42.
Figure 41: Material core loss density comparison at 100 kHz
Figure 42 : E-core (a), pot-core (b), toroid (c)
