Sizing the propulsion motor

An electric machine is at the core of hybrid propulsion regardless of whether or not the vehicle is gasoline–electric, diesel–electric or fuel cell electric. Propulsion is via an ac drive system consisting of an energy storage unit, a power processor, the M/G and vehicle driveline and wheels. Figure 4.8 is a schematic of the hybrid propulsion system in a multi-converter architecture. The system in Figure 4.8 can be upgraded by the addition of an interface converter (e.g. booster) to the ultra-capacitor bank for maximum performance when non-alkaline electrolyte storage batteries are used. For example, a lead–acid battery system benefits the most from a converter interface to an ultra-capacitor bank. In that case the total energy storage system weight and cost are minimised. With alkaline electrolyte advanced batteries the benefits of adding an ultra-capacitor begin to diminish and with lithium ion the benefits are minimal [4].

The motor-generator, M/G, is sized as follows: maximum input speed at trans-mission is restricted to <12 000 rpm from the engine side by the rev-limiter function in the electronic engine controller and on the transmission side by the proper gear selection. It is possible to over-speed the M/G and engine by improper downshifting of the transmission while at highway speeds.

Most electric machines rated for vehicle traction applications are limited to 12 000 rpm for several inherent reasons: rotor burst limits, rotor position sensing encoders and their attendant digital interface, bearing system, and critical speeds of the M/G geometry. M/G torque and power is dictated by the electric fraction, EF, defined as the ratio of M/G peak power to total peak power. For virtually all hybrid propulsion

M/G ICE

Trans. FD

Wheels

Batt.

Ultra-cap.

Figure 4.8 Hybrid vehicle drivetrain

systems this fraction ranges from 0.1 < EF < 0.4. At EF > 0.4 the vehicle electrical storage capacity must be increased to accommodate the electric-only range, otherwise, the vehicle will not perform well on grades or into strong headwinds without electric torque to augment the ICE.

4.2.1 Torque and power

Motor-generator capability curves for torque and power define the peak operating capability of the hybrid electric system. It is necessary to be clear in understanding that the capability curve defines the operating bounds of the hybrid ac drive system.

Figure 4.9 shows the defining characteristics of the torque-speed envelope regardless of M/G technology. Intermittent, or peak, output is generally 4/3 to 5/3 of continuous, or rated, output as shown.

It is instructive to walk through the operational regions of Figure 4.9 so that no misunderstanding exists regarding what the M/G is capable of. The horizontal line labeled peak torque is 250% of continuous operating torque and represents a sizing specification carried over from industrial induction motors. Industrial motors have continuous ratings that reflect their thermal limitations of typically 40^◦C to 60^◦C temperature rise over ambient necessary to protect their insulation systems from cumulative degradation and eventual failure. In the past this meant that the industrial induction motor was capable of momentary (10s to 30s) overdrive conditions without incurring thermal excursions beyond 180^◦C at stator hot spots.

In automotive applications, particularly hybrid propulsion, the M/G rating retains this industrial rating nomenclature for continuous and peak intermittent operation. But there are mitigating factors. Whereas the industrial motor generally did not have an electronic interface, it could be overloaded to its breakdown torque, typically 250%

Peak torque (38Nm)

Intermittent output

Continuous output

Torque, Nm

400 350 300 250 200 150 100 50 0

0 500 1000 1500 2000 2500

Speed, rpm

3000 3500 4000 4500 80

85 90

90 ₆₅ 65

Figure 4.9 M/G torque-speed capability envelope (unique-mobility hightor motor)

of the thermal limited torque in class-B designs, for short durations. The region bounded by the speed axis, the torque axis, the flat line representing constant torque, and a vertical to trapezoidal boundary back to the speed axis represents the constant torque operating region. In the constant torque operating region the power electronics inverter has sufficient voltage from the dc bus (battery or ultra-capacitor or generator or some combination) to synthesise currents for injection into the electric machine.

When the machine speed increases to the corner point speed defining the break point between constant torque and constant power the inverter has essentially run out of voltage, the modulator that regulates current synthesis begins pulse dropping, and the process ends with the inverter entering six step mode (also called block mode).

Constant power is the region of field weakening bounded by the already mentioned constant torque region plus the hyperbola that defines the continuous or intermittent power envelope, and the speed axis. Useful operation ceases when the machine enters second breakdown. This last bit of terminology may not be as widespread as first breakdown (i.e. corner point or base speed) is for the region where constant torque transitions into constant power.

In the second breakdown region different processes begin to dominate the electric machine’s ability to produce torque, and these processes are technology dependent.

We saw that first breakdown is dependent on ac drive system power supply and machine design in that its corner point is defined as that speed at which the machine’s internal voltage approximates the input dc supply voltage. During field weakening this internal voltage effect is mitigated so that current can continue to be injected into the machine at rated value – hence constant power. Now, when the electric machine reaches the final limits of holding constant power the power begins to break down.

In an asynchronous machine second breakdown is reached when the slip parame-ter increases from rated slip to breakdown slip. Torque is at its breakdown limit (∼Vs²/ωL_leakage, where the parameters are supply voltage and leakage inductance) and the machine slip is held constant at its breakdown value (again, typically 250%

of rated). Beyond this second breakdown speed the current drops reciprocally with speed so power also drops with the reciprocal of speed and torque is dropping as 1/speed².

In a permanent magnet synchronous machine of any variety the second break-down speed occurs when the injected current can no longer be held constant while field weakening is in progress. This occurs in a surface magnet machine or to some extent in an inset magnet machine when the angle control of the injected currents exceeds about 30^◦. For an interior magnet machine the second breakdown point is much further out in field weakening and occurs when the d-axis, or magnet axis current, is no longer able to hold the machine internal voltage constant because it has reached the rated value of input current, i.e. there is no longer any component of input current left to develop torque. When this condition occurs the machine is completely out of torque. In a variable reluctance, or switched reluctance, machine the conditions of second breakdown are somewhat similar to the permanent mag-net machine. During constant torque operation of the variable reluctance machine the current dwell angle is controlled while operating at fixed advance angle. Dur-ing constant power operation the dwell is fixed as the advance angle of current is

progressively shifted ahead in time. When the advance angle is no longer capable of being advanced the machine enters second breakdown and power drops reciprocally with speed.

We can say that operating at peak torque on the capability curve is not the case in hybrid propulsion M/G design practice. True, the electric machine retains some overdrive capacity, but in general the electric machine is designed for operation at near its maximum capability during intermittent use (10s to 30s). It is the limitation of the power electronics that determines the envelope of the M/G capability. The semiconductor power driver stage has no provision for overdrive conditions. The semiconductor devices have thermal time constants of milliseconds so that a 10s overdrive condition in reality is steady state for power electronics. Therefore, the intermittent operation envelope shown in Figure 4.9 represents the limit of the power electronics more so than for the machine. The following definitions are made to emphasize the limitations of such capability curves:

• Continuous rating: The ac drive can be operated within its continuous rated region indefinitely provided: (1) the motor thermal management system is operated at or below its cooling medium maximum inlet temperature conditions for the coolant used (air or liquid); (2) the power inverter thermal management system is within its maximum inlet temperature of coolant (air or liquid); and (3) the power electronics electrical parameters are within nominal stress levels of 50% . For example, the operating voltage of power switching devices should be at 50% of the device rated breakdown voltage.

• Intermittent overload operation is permitted for short durations (<30s) to contain low energy transients such as responding to fast gear changes or clutch actuation intervals when the M/G may be called upon to furnish additional torque and power.

• Peak overload operation is within the capability of the electric machine but outside the capability of the power electronics. There have been attempts to redefine this peak condition to contain fast transients having low energy but very high power – for example, an ISA mild hybrid in which engine cranking is desired under cold conditions. Some specifications may call for peak overdrive torque for <50 ms in order to overcome engine crankshaft striction. The application of a very high torque impulse is necessary to breakaway the engine and permit sustained cranking at the ac drive system intermittent rating. At issue here is the need for the power electronics to sustain overcurrents at the peak overdrive condition. Such requirements generally do not pan out because the electronics must still be sized for the peak operating envelope.

• Thermal management systems for passenger car hybrids consist of auxiliary coolant reservoirs, pumps and fans, along with a small radiator. The M/G will have a separate coolant supply from either the vehicle’s engine coolant (<115^◦C) or transmission oil cooler (<120^◦C). The power electronics coolant is restricted to glycol–water mixtures having a maximum inlet temperature of 65^◦C. With this thermal boundary condition on the power electronics internal cold plate the temperature fluctuations at the semiconductor junctions can be held to <40^◦C temperature rise and thereby achieve high durability (>6000 h life).

In Figure 4.9 the continuous operating boundary contains efficiency contours.

Hybrid propulsion simulations are best performed with the M/G torque-speed capabil-ity inserted into the driveline definition. Driveline loss mapping utilises the efficiency contours (map) to extrapolate loss components at each operating point. The M/G for a hybrid propulsion system is designed differently from either a M/G for a battery-electric vehicle or an industrial application. For a battery-battery-electric vehicle the M/G is designed to have the peak efficiency island trend toward zero and be as broad as possible through the constant torque region and out into constant power. An industrial electric machine may have its peak efficiency plateau situated near the capability curve corner point so that operation at rated conditions is most efficient.

A hybrid, on the other hand, has no rated point, rather a drive cycle dependent scatter of operating points so its peak efficiency should extend from constant torque into constant power regions.

4.2.2 Constant power speed ratio (CPSR)

In Section 4.2.1 the discussion covered operation in constant power mode. Figure 4.10 is given here to emphasize the point that ac drives employed as hybrid propulsion components operate in both motoring (1st and 3rd quadrants) and generating (2nd and 4th quadrants). In mild hybrid, ISA applications the M/G operates in the 1st and 4th quadrants only because the engine is not to be back driven. However, in power split and other hybrid propulsion architectures the M/G can and does operate over all four quadrants as shown.

T (Nm) 300

86 90 93 92

88 84

90 86 92 93

88

Speed (krpm) 84 Speed (krpm)

Quadrant II CCW-Generate

Quadrant I CW-Motor

Quadrant III CCW-Motor

Quadrant IV CW-Generate

6 5 4 3 2 1 0 1 2 3 4 5 6

Figure 4.10 M/G operating envelope for hybrid propulsion

Motoring operation of the M/G occurs for positive torque and positive (CCW) speed or for negative torque and negative (CW) speed. When the sign of either torque or speed are reversed the M/G is in generating mode. With modern power electronic controllers the machine is capable of operating anywhere within the confines of its torque–speed envelope shown in Figure 4.10. For example, a transition from motoring at 2.5 krpm and 100 Nm of torque to generating at 2.5 krpm and−100 Nm of torque is simply a sign change in the power electronics controller. The speed and hence machine voltages remain constant, or perhaps the voltage gets boosted somewhat by charging demands, but the machine currents slew at their electrical time constant to resume operation as a generator with phase currents in phase opposition to phase voltages (generally sinusoidal variables). Since the machine transient electrical time constants are easily 10s if not 100s of times faster than the mechanical system, the torque change is viewed as occurring nearly instantaneously.

Now, if the machine were operating in motoring mode at 2.5 krpm and+100 Nm of torque, which is basically in boosting mode for, say, passing, and the driver aborts the manoeuvre and slows to re-enter traffic, the M/G may be commanded to switch to generating at−100 Nm of torque, for example, but at a lower speed, say 1.5 krpm.

Since the M/G was operating well into field weakening (according to the chart in Figure 4.10) initially and the new operating point is basically on the constant torque boundary (full field), the controller must boost the field to maintain the commanded generating level. This process is slower than simply changing the torque at constant speed. The flux in the machine must be readjusted to its new and higher level, and this occurs at the electrical time constant of field control in the machine (depends on machine size/rating and ranges from 30 ms to >100 ms for hybrid traction motors).

Whereas torque control was responding in sub-millisecond times, field control takes much longer. However, this is still about 10 times faster than the mechanical sys-tem. The same process occurs going from CCW motoring to CW generating except that the speed is now determined by the mechanical system at its much slower time constant. The M/G power controller easily tracks the speed changes of normal oper-ation. We will see later that some manoeuvres can be more demanding on the M/G response.

The four major classes of electric machines suitable for hybrid propulsion appli-cations are highlighted in the taxonomy of electric machines in Figure 4.11. There are only two major classes of electric machines, those that are synchronous with applied excitation and those that are asynchronous to it. When excitation of the elec-tric machine rotor is direct current, dc, via field windings or permanent magnets, the machine is a synchronous type. When excitation of the electric machine rotor is ac, then operation is asynchronous. The definition gets vague when inside out motors are used, such as brushed dc motors with stationary permanent magnets. However, the distinction persists in how the machine excitation is applied, be it dc or ac.

The acronyms defined in Figure 4.11 will be used throughout this book. These are IM for induction machine of cage rotor (cast aluminium) or wound rotor (i.e.

slip rings), IPM for interior magnet designs, SPM for surface permanent magnet and VRM for variable reluctance, doubly salient designs. There are many variants of these electric machines such as drum versus axial, normal versus inside out, rotary

Electric machines for hybrid vehicle ac drives

Asynchronous Synchronous

Figure 4.11 Taxonomy of electric machines

versus linear, and various excitation dependent nuances such as trapezoidal versus sinusoidal waveshape and many other distinctions. The intent of Figure 4.11 is to capture the high level differences in machine types and to showcase the origins of the four most popular types.

It is also important to re-emphasize the fact that the constant power speed range of these four electric machine types ranges from 1.6 : 1 for the SPM without use of a novel cascade inverter (the dual mode inverter concept, DMIC discussed later) to 3 : 1 for IM and VRM, to 5 : 1 for IPM. Wide CPSR in these machines comes at a price: generally IPMs with 5 : 1 CPSR are physically larger and heavier than their counterparts having the same power rating. One difference is the DMIC power electronics driver for an SPM in which 6 : 1 CPSR has been demonstrated provided the rotor structure can withstand the stress.

4.2.3 Machine sizing

We now turn our attention to M/G sizing for a hybrid propulsion system. As is well known, the electric machine is physically sized by its torque specification. Since electric machine torque is determined by the amount of flux the iron can carry and the amount of current the conductors can carry plus the physical geometry of the machine, the following can summarise the sizing process. Torque is proportional to scaling constants times the product of electric and magnetic loading times the stator bore volume. Electric loading is defined as the total amp-conductors per circumferential length (A, in units of A/m) – in effect, it is the description of a current sheet. The electric loading is limited by thermal dissipation of the conductor bundles. Magnetic loading is set by the material properties of the lamination sheets (B, in units of Wb/m²) and of the physical dimensions of the airgap. The product of electric and magnetic loading is a volumetric shear force, AB (Nm/m³). The stator bore volume,

D²L, defines the airgap surface area (π DL) times the torque lever arm (D) of the rotor on which the volumetric shear force acts. The scaling constants and coefficients are absorbed into the proportionality constant for M/G torque in terms of its design loading and geometry. For electric machines of interest to hybrid propulsion the volumetric shear force ranges from 25 000 to 80 000 Nm/m³. The relationship for machine torque is

T = kABD²L (4.3)

where k is a constant that includes geometry variables, and excitation waveshape variables for voltage and currents. The bore diameter D, or more accurately the rotor OD, is the main sizing variable in electric machine design. Sizing is constrained by four fundamental limits. Two of the fundamental sizing constraints have been discussed thus far: electric and magnetic loading. To further explain these sizing constraints it is important to understand the limitations on current carrying capacity of copper (aluminium for induction machines). Current carrying capacity of copper wire is limited by its thermal dissipation, which in turn sets bounds on current density, J_cu. In electric machine design practice these bounds are

Jcu=

Equation (4.4) has contained in it the thermal constraints of the machine sizing design. Higher current densities, up to 2× 10⁸A/m² for copper, define its fusing current limit.

Conductors are placed in slots in the stator iron. The tooth surface to tooth-slot pitch must maintain sufficient surface area in order to support the magnetic loading for the materials used and the particular choice of machine technology. Table 4.4 summarises magnetic loading for the four major classes of electric machines.

The electric loading, A, for the various machine technologies listed in Table 4.4, is determined by using the current density limitations (4.4), from which the bounds

Table 4.4 Electric machine sizing: magnetic loading

Type Symbol Airgap mm BWb/m²

Surface permanent magnet machine SPM <1.5 ∼0.82

Interior/inset permanent magnet machine IPM ∼1.0 0.7 Asynchronous, induction machine (also sync. rel.) IM ∼0.6 0.7 Variable/switched reluctance machine VRM <0.5 0.8*

*Highly localized in gap between surfaces of opposing double saliencies.

on electric loading can be found as:

on electric loading can be found as: