JOM
DOI: 10.1007/s11837-012-0350-0 2012 TMS
Soft Magnetic Materials in High-Frequency, High-Power Conversion Applications ALEX M. LEARY,1,3 PAUL R. OHODNICKI,2 and MICHAEL E. MCHENRY1 1.—Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA. 2.—Division of Chemistry and Surface Science, National Energy Technology Laboratory (NETL), 626 Cochrans Mill Road, Pittsburgh, PA 15236, USA. 3.—e-mail:
[email protected]
Advanced soft magnetic materials are needed to match high-power density and switching frequencies made possible by advances in wide band-gap semiconductors. Magnetics capable of operating at higher operating frequencies have the potential to greatly reduce the size of megawatt level power electronics. In this article, we examine the role of soft magnetic materials in high-frequency power applications and we discuss current material’s limitations and highlight emerging trends in soft magnetic material design for high-frequency and power applications using the materials paradigm of synthesis fi structure fi property fi performance relationships.
INTRODUCTION Wilson1 defines power electronics as the technology associated with the efficient conversion, control, and conditioning of electric power by static means from its available input form into the desired electrical output form. Nearly all generated electricity requires some form of conversion. Power losses during conversion dissipate as heat during transmission and distribution to the end user and developments in soft magnetic materials resulted in significant reductions in these losses over this time.2,3 Limited metering restricts precise measurement of transmission and distribution losses on a large scale.4 When generated commercial power does not exceed demand, the ratio of power sold to generated provides an estimate for these losses. Figure 1 shows the total electrical power generated for the retail market compared with the percentage that was not sold between 1949 to 2010 in the United States.5 In addition to a direct economic impact totaling $25.8 billion in lost revenue for a nominal retail price of $0.0988/kWh, the generation of this wasted power also results in additional greenhouse gas emissions that negatively impact the environment. These losses drive efficiency improvements and are a lower bound of the total transmission, distribution, and conversion losses since they do not include losses experienced by the consumer downstream of the billing meter.
The Department of Energy expects demand for electricity to rise by 30% and estimates a $1.5 trillion cost to modernize the existing United States electricity infrastructure over the next 20 years.6 These upgrades and capacity expansions provide an opportunity to build and integrate new power electronics to meet demand while reducing waste and inefficiencies. Movement toward grid-level integration of renewable energy sources and distributed storage systems requires new topologies to handle transient sources and facilitate two-way power conversion.7 Flexible alternating current (AC) Transmission Systems (FACTS) and High Voltage DC (HVDC) technologies aim to improve the efficiency of power networks and benefit from highfrequency conversion.8 Increases in DC power generation and loading also motivate research into new topologies containing high-frequency DC–DC power converters.9–13 Independent of the power generation method, the laminated electrical steels traditionally used for power cores become inefficient at high switching frequencies. Additionally, soft magnetics used in power electronics can occupy significant space, require extensive cooling, and limit designs. New large-scale systems must be cost competitive with existing systems and further cost reductions require materials advancements. These advancements will dictate the most successful topologies to take advantage of material strengths and minimize
Leary, Ohodnicki, and McHenry
12 3500 3000
10
2500 Power Losses
2000
8
Losses (%)
Electrical Power Generated (Billion kWh)
4000
1500 6
1000 500 1950
1960
1970
1980
1990
2000
2010
Fig. 1. Total retail electrical power generated (NAICS 22) in the United States and estimated transmission and distribution losses, as measured by the ratio of power sold to power generated. Data taken from Ref. 5 includes independent power producers starting in 1989.
weaknesses. This article explores the use of soft magnetic materials in power conversion applications. The first section describes the high-frequency limitations of soft magnetic materials, the ‘‘Materials Survey’’ section surveys the current state-of-theart materials, and the ‘‘Future Processing Opportunities’’ section highlights opportunities for future improvements. HIGH-FREQUENCY SWITCHING AND POWER CONVERSION Soft magnetic materials enable low loss inductive switching, which is useful in inductor, transformer and filter applications. The basic design challenge for inductive components becomes evident after considering Eq. 1, which relates Faraday’s law of induction to the voltage response of an ideal toroidal core with inductance L driven by an AC current, I = I0 sin(xt). dB dI ¼ L ¼ LI0 x cosðxtÞ dt dt lN 2 A I0 x cosðxtÞ ¼ l
V ¼ NA
(1)
For constant maximum voltage (V), permeability (l), number of turns (N), and effective length (l), the cross-sectional area (A) is inversely proportional to the frequency (x = 2pf). This relation motivates the use of high-frequency switching to reduce size and weight of passive inductive components in power converters. However, nonlinear material properties limit scaling reductions in power magnetics, especially for applications above the kilowatt power range. Several studies examine these limitations to guide transformer and inductor design.14–19 Additionally, high-frequency power converters rarely use purely sinusoidal currents to drive the magnetic
components. Instead, an active switching circuit modifies the input signal using pulse width modulation by various techniques.20 Fourier analysis describes this modulated signal as the superposition of a many frequencies, so optimally designed soft magnetic materials must have broadband capability. The semiconductors used in active switching circuits have voltage and power limitations and highvoltage converters often divide the total output into manageable quantities with a multilevel circuit.21 Multilevel circuits can have the added benefit of improving the harmonic quality of the drive current, but each additional level comes with a price as the semiconductors have associated switching and conduction losses. New SiC and GaN semiconductors have wider band gaps than currently available Si devices that result in much lower on-resistance.22 Lower losses in the active components of a power converter allow for higher power densities ðW=m3 Þ: While several high-frequency converter designs operate without magnetics, considerations such as galvanic isolation and the scaling limitations associated with air core inductors suggest the need to further develop advanced magnetics.18 Currently, no commercial magnetic materials can match the performance level of the wide band gap semiconductors.23 A successful design minimizes the combined losses of the passive magnetic material, the windings, and the switching circuit for a given power output. Typically, loss mechanisms are complex and designers rely on empirical rather than analytical models. High-frequency losses in magnetic materials are dominated by classical and anomalous eddy currents caused by the motion of domain walls.24 Eddy currents generate heat by I2R losses in the magnetic material. For continuous operation, this heat must be dissipated through the component surface to prevent excessive temperatures. Scaling limitations result when surface area decreases while the amount of generated heat remains constant. Improvements in power density for a given power rating and efficiency require increased cooling due to the reduced surface area available to smaller components. With currently available soft magnetic materials, thermal management limits converter power density below levels possible with advanced switching circuits. The steady-state temperature rise in the magnetic material for a given shape and power loss is a function of the material’s thermal conductivity and emissivity, the local heat transfer conditions surrounding the material, and the surface area of the material exposed to these conditions. Scaling models describe the effects of size reductions for given design constraints and require descriptions of heat generation and thermal responses to losses. Passive components (inductors and capacitors) operate in concert with active components in a power converter and scaling relationships must consider both. A geometric factor, such
Soft Magnetic Materials in High-Frequency, High-Power Conversion Applications
Fig. 2. Tape wound ring core geometry used for loss modeling.
as the area product25 or a component volume, combines the dimensions of passive and active components into a single variable. Here, we consider magnetic material property effects on scaling for the simple tape wound core geometry shown in Fig. 2 of outer and inner diameters (R1 and R2 ) and the core depth d. We choose the outer diameter of the ring core R1 as the geometric variable and fix the inner diameter and depth to 0.7R1 and 0.3R1. The time averaged core loss is given by the wellknown variation of the Steinmetz Eq. 2 where k, a, and b are empirical fits to loss data. PC ¼ kf a Bbm
(2)
This loss, usually determined from a sinusoidal driving frequency, incorporates the hysteresis and eddy current losses due to changes of magnetization at a frequency f. The windings produce a field H that is amplified by B = lH in the core. H¼
/IN l
(3)
where N is the number of turns over an effective length l and / is a geometric constant. We assume no DC bias and the useful portion of the induction is expressed as DB ¼ 2Bm . For a single layer of closely packed windings where l = Nw, winding losses for a given conductor resistivity (q) can be described as 1 Bm l 2 ql 2 PW ¼ Irms R ¼ (4) 2 l/N Ac The conductor cross section (Ac) decreases with increasing frequency due to the skin effect. Increasing N decreases the maximum drive current, but for high-frequency and power applications, smaller cores may limit the available winding space. Multiple winding layers lead to additional losses due to AC proximity effects. Sullivan26 accounts for these losses by defining Fr, a dimensionless factor that relates DC to AC resistance for a core wound with Litz wire.
Fig. 3. Power loss for R1 = 7 cm core for two relative permeabilities. Added power rating (orange) for a lower permeability material compared with additional winding losses (yellow) leads to higher efficiency for constant core loss (Color figure online).
PW ¼ I2 RFr
where
Fr ¼ 1 þ
p2 x2 l20 N 2 n2 d6c k (5) 768q2 b2c
The wire on the model core occupies a window with an areal dimension b2c and uses Litz wire with n = 300 strands of diameter dc = 0.2 mm wire. We first consider a case where Litz wire windings fill the center core area with N ¼ ðpR22 =w2 Þ and the wire crosssection is 50% copper ðq ¼ 2lX cmÞ. Each wire occupies a square area w2 within the winding window of size b2c = p R22. To account for additional winding layers, the length per turn increases by 8w for each additional layer. The DC winding resistance is small compared with the AC resistance. A more detailed winding loss model for tape cores is found in Ref. 27. For magnetic materials with constant permeability over the flux range DB, the power rating (PVA) can be used to estimate the inductive efficiency for a single core (gc) of volume Vc PVA ¼ Vrms Irms ¼
gc ¼
p/AlB2m f dðBHÞ Vc B2m f ¼ ¼ l dt 2l
(6)
PVA ðPC þ PW Þ PVA
(7)
Assuming Steinmetz coefficients to be constant over the frequency range of interest, core loss is linear on a log–log loss versus frequency plot. Winding losses change slope with increased frequency due to skin and proximity effects. Figure 3 shows these losses and the output of a core with R1 = 7 cm and 308
Leary, Ohodnicki, and McHenry
Fig. 4. (a) Efficiency versus frequency and (b) power density in kW=dm3 for the core geometry of Fig. 2.
turns for Bm = 0.5T with core loss values from Ref. 28. The two shaded areas show the difference between output power (VA) and total losses for two different relative permeabilities. We assume the same core loss for lower and higher permeability cores and discuss the assumption in the ‘‘Materials Survey’’ section. By lowering permeability, the material stores more inductive energy per cycle but also requires higher current (or more turns) to reach a desired induction. For this model, the additional stored inductive energy is greater than the added winding losses. If core loss is greater than winding loss, then materials with low permeability give efficiency benefits at high frequencies, as shown in Fig. 4a. For volume and weight limited applications, low permeability also gives high power density. Figure 4b shows the theoretical power density for this core geometry over a range of inductions and relative permeabilities. The 60 kW DC–DC converter in Ref. 29 has a 40 kW=dm3 power density. Kolar et al.23 show a 10-fold increase in converter power density every 20 years. Published power density values vary depending on the inclusion of a cooling system. Magnetic components occupy a significant portion of the volume. In the following, we extend this core model to estimate desirable magnetic material properties for high-frequency, high-power conversion. Reasonable designs must consider thermal limitations. In Refs. 14, 18, and 30, the relation between temperature rise and power loss relies on extrapolations from experimental data. We can also estimate the temperature rise DT for a material based on the thermal conductivity k as in Ref. 31. kDT ¼
PT h A
(8)
The cooling system determines the heat transfer conditions at the surface, but the heat generated by the power loss PT = Pc + Pw must first conduct
through the thermal path h within the material. We assume a cooling system to be able to remove PT from the surface at T1 and use the thermal parameter ðkDTÞ to describe the maximum possible efficiency of the inductive components in a 1 MVA power converter. Ring core geometries with many windings present a challenge because the windings limit heat transfer from the core. For this reason, we consider ring cores with three winding layers and define the thermal path length as h = R1 R2. Each core and winding form a subcomponent within the converter and losses for the model subcomponents were calculated using the Monte Carlo method by randomly assigning model parameters over the following design space: (I) f ¼ 1 kHz ! 1 MHz; (II) Bm ¼ 0:5 ! 1:3T; (III) lr ¼ 200 ! 5000; and (IV) R1 ¼ 7 ! 20 cm. Core losses were calculated in mW=cm3 units from Eq. 2 using Finemet loss values from Ref. 28 with k = 3.935, a = 1.585, and b = 1.88 where the frequency is in kHz and the induction in Tesla. The measured core losses were accurate within 1% to 500 kHz. For converters that require multiple subcomponents to achieve a desired power rating, the connection arrangement effects the overall efficiency (gt). Figure 5a shows the efficiencies for individual subcomponents compared with the thermal parameter from Eq. 8. These efficiency values correspond to the gt for subcomponents connected in parallel and successful designs have high efficiencies and require low thermal parameters. The power ratings (PVA) form a banded pattern, and the 20 kVA and 80 kVA lines indicate the respective boundaries. For gc > 0.95, higher frequencies (Fig. 5b) and lower permeabilities (Fig. 5c) produced higher power ratings but require higher thermal parameters. The allowable temperature rise and thermal conductivity varies for different soft magnetic materials. Ferrites with k 4W=mK have operating limits below 200C
Soft Magnetic Materials in High-Frequency, High-Power Conversion Applications
Fig. 5. Performance measures for randomly designed sub-components with (a) efficiency versus thermal parameter and power rating (PVA) versus thermal parameter. Higher frequencies (b) and lower permeabilities (c) yield higher PVA ratings.
1.00
MATERIALS SURVEY
Efficiency
0.99
0.98
0.97
0.96 f > 40 kHz 20 kHz < f ≤ 40 kHz f ≤ 20 kHz
10
2
3
10
10
4
10
5
1 MVA Mass (kg) Fig. 6. 1 MVA efficiency versus total mass of soft magnetic material required. With the modeled material, higher frequencies reduce the amount of material required but result in lower efficiencies.
and nanocomposites maintain low losses above 200C with k 9W=mK.32 The improved thermal properties of nanocomposite materials greatly expand the envelope of acceptable designs. The total converter power level and the individual core power rating determine the number of subcomponents required for a converter design. Figure 6 shows the converter efficiency compared with the mass of soft magnetic material (density = 7.9 g/cm3) required to obtain 1 MVA. For the modeled material, higher frequencies reduce the required mass but sacrifice efficiency. This illustrates the need for improved high-frequency magnetics to maintain high efficiency. A cost analysis is needed to determine the best overall design and is the subject of future work. The shape ratios used to define R2 and d may not be optimal and were chosen based on assumed manufacturing limitations, such as ribbon width and structural integrity.
Magnetic materials store inductive energy ð12 LI 2 Þ and filter unwanted signals in power converters. The majority of heat generated in a circuit arises from this storage function and a good inductive material stores the most energy with the lowest loss. As shown in Eq. 1, L is largely a function of the permeability (l). Figure 7 shows the energy stored for different permeabilities. The area enclosed in the BH hysteresis curve for a material equals the core loss per cycle. The high induction levels approaching 2T commonly used at 50/60 Hz in Si steels are not achievable at higher frequency with currently available materials due to high coercivities (Hc). High-permeability materials (lr > 10,000) store very little energy prior to saturation. Materials with lower permeabilities store more energy per cycle at lower inductions but require higher driving fields and increased winding losses. Designers can achieve low-permeability cores by introducing an air gap or cutting a core made of highpermeability material. Cut cores introduce additional losses through flux fringing around the gaps that can also induce eddy currents in nearby conductive material.28 Poor manufacturing techniques greatly influence cut core properties and can lead to much higher losses than expected.33 Materials with low permeability with respect to the driving field direction are preferred in order to avoid complications due to cut cores. Cores with induced anisotropies transverse to the drive field restrict domain wall motion and show low losses at high frequency.34 Alves et al.35 demonstrated improved performance in a low power flyback converter design with a low permeability stress annealed Finemet core compared to a gapped ferrite core. The nanocomposite core was half the size of the ferrite core and produced 333% more power. For highpower, low-loss applications, low permeability is best achieved by inducing a controlled anisotropy perpendicular to the drive field in a material that exhibits a high permeability and low coercivity as measured along the easy axis. Therefore, figures of merit for lowfrequency applications including high saturation
Leary, Ohodnicki, and McHenry
Fig. 7. Inductive energy storage for low-coercivity materials with different permeabilities. Low permeability materials store more energy per cycle but must maintain low coercivity to prevent losses.
magnetization and high permeability may not directly apply to power magnetic materials for relatively high frequency applications (10 kHz–1 MHz), though high permeability prior to inducing anisotropy is a good predictor of low losses. Therefore, materials with tunable permeabilities through carefully designed thermomagnetic or thermomechanical processing allow designers to optimize the magnetic material to the active components. Several factors determine the performance of a magnetic material as a high-frequency inductor. The quality factor (Q) in Eq. 9 where l0 and l00 are the real and imaginary parts of complex permeability is a performance measure for an inductor. Q¼
xL l0 ¼ 00 R l
(9)
High permeability materials saturate under low fields. For high power applications, the amount of energy stored must be considered as well as the losses, but the quality factor does not account for magnetic saturation. A figure of merit in Eq. 10 compares the inductive energy stored per unit volume during a half cycle to the measured losses for a sinusoidal driving field during that period. Power Ratio ¼
1 Stored Power 2 Bm H2f a ¼ Power Loss 1;000k f Bb 1;000
¼
B2b m
f 1;000
kl0 lr
m
1a ð10Þ
This quantity is valid for materials with constant permeability over the frequency range of interest.
The empirical constants are defined as in Ref. 28 to describe core loss in mW=cm3 . Materials with a high power ratio must store large amounts of power efficiently. Although the actual amount of power stored in the material will differ due to the pulse width modulation and the duty cycle used, sinusoidal excitations are assumed here as most loss data is published using this waveform. Losses in soft magnetic materials consist of both static and dynamic hysteresis losses. To limit static hysteretic losses in bulk metal alloys such as silicon steels, metallurgists have sought to obtain large grain sizes in order to minimize domain wall pinning, lower coercivity, and hence reduce low-frequency losses. Hasegawa36 showed the advantages of magnetic materials with small crystalline grains within amorphous alloys. The random anisotropy model developed by Alben et al.37 for amorphous ferromagnets was applied by Herzer38 to nanocrystalline ferromagnets and showed that a reduction in grain size well below the ferromagnetic exchange length can lead to a rapid decrease in coercivity. The review of amorphous and nanocomposite soft magnets in Ref. 39 describes the properties of these alloys in more detail. Dynamic losses consist of classical eddy current and anomalous or excess losses. Bertotti40 describes the classical eddy current power loss in Eq. 11, where t is the material thickness and q is the resistivity, as Pcl ¼
p2 t2 B2m f 2 6q
(11)
This expression is valid when the material thickness is much less than the skin depth. Nanocomposite materials with q 130 lX cm and lr = 1,000 have a skin depth of 61 lm at 100 kHz and ribbons produced by rapid solidification are usually
