**2.2 Additional losses in the solid copper bars**

In order to be able to effectively implement the technique of winding with single bar per slot, it is mandatory to fully control the additional copper losses associated with the operation at high electrical frequency.

The different phenomena related to alternating flux density inside the copper yielding to excessive loss are well describes in the literature [6, 7], however we recall here the two main ones.

In order to quantify the loss increase, the kAC coefficient is introduced, which is the ratio of the total AC copper loss, PAC, to the DC copper loss, PDC, in the winding, at given current:

$$\mathbf{k}\_{\rm AC} = \mathbf{P}\_{\rm AC} / \mathbf{P}\_{\rm DC} \tag{2}$$

The best known phenomenon causing these additional losses is called "skin effect", it appears in any electrical conductor carrying an alternating current. The skin effect tends to push the current back to the periphery of the conductor, as shown in the following **Figure 6**.

The current density, J, in a round conductor, as a function of the distance from the periphery, r, in sinusoidal regime, is expressed by the following relationship:

$$J(r) = J\_0 e^{-\frac{r}{\delta}} \cos \left(at - \frac{r}{\delta}\right) \tag{3}$$

where δ represents the skin depth at a conductivity σ of the conductor:

$$\delta = \frac{1}{\sqrt{\sigma \mu\_r \mu\_0 \pi \xi}}\tag{4}$$

The current density at the skin depth is roughly equal to 37% of its value at the surface, while it is only equal to 5% at three times δ.

In the case of a rectangular conductor the relationships of the skin effect are more complex. The following equation [1, 6] is valid for both cases round conductor and rectangular conductor, and allows to precisely quantify the increase in copper loss due to the skin effect:

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

#### **Figure 6.**

*Current density distribution in two conductors having the same cross-section with round and rectangular shape at different frequencies [1].*

S and p respectively represent the cross section area and the perimeter of the conductor.

**Table 1** gives the values of KAC for different bar shapes (used in the prototypes presented later) and different frequencies. The dimensions of the bar are defined in **Figure 7**.

According to the **Table 1**, in the worst case scenario, the increase in copper loss due to the skin effect is less than 1%, so this phenomenon is not significant at the considered frequencies.

The second observed phenomenon causing excess copper loss is known as field effect or inductance effect. Unlike the skin effect, it only takes place in the copper volume surrounded by a magnetic circuit (stator). This phenomenon is depicted in **Figure 8**. In this case, the additional loss is due to the transverse flux (slot leakage flux) produced by the armature current, which closes in the slot width (tenc), creating induced currents in the solid bar which will lead to an uneven current density distribution, being much higher in the lower part (near the slot opening) than in the upper part of the solid bar.

The field effect phenomenon is the main cause of increased losses, where the KAC coefficient can be greater than 4 if it is not well controlled, which would cancel out most of the benefits introduced by the use of the solid bar winding.

The coefficient KAC related the field can be precisely calculated using the following analytical relationship [1, 7]:

$$\mathbf{k}\_{\rm AC} = \frac{h\_{bar}}{\delta} \sqrt{\frac{t\_{bar}}{t\_{\rm env}}} \tag{6}$$


**Table 1.**

*Skin effect for different copper bar dimensions.*

**Figure 7.** *Main dimensions of the slot and the copper conductor.*


#### **Table 2.**

*Field effect for different copper bar dimensions.*

This relationship is only valid when KAC > 1. **Table 2** summarises the value of KAC for exactly the same configurations considered in **Table 1**.

According to the results presented in **Table 2**, it can been clearly seen that, as expected, the increase in copper loss due to the use of solid bars is significant, however, the solid bar still beneficial even at high frequencies when considering the overall performance of the machine. Indeed, in order to illustrate this point, we can consider the configuration # 2 operating at a nominal frequency of 1666 Hz. The use of a solid bar would increase the current in the slot, at constant DC losses, by about 50% (cf. relation (1)), while the increase in losses in AC mode would require it to be reduced by 20% ( ffiffiffiffiffiffiffiffiffiffi 1, 44 <sup>p</sup> ), hence, the overall increase in torque and current is equal to 25%.

The remaining examples of **Table 2** will be analysed when their corresponding products are presented later in this chapter.

#### **3. Low voltage power electronics converter**

#### **3.1 Power converter for electric vehicle**

In electric vehicles, the electric motors can be fed by one or more power converters depending on one or multiple energy sources. Whether it is an airplane, an

#### *High Power Very Low Voltage Electric Motor for Electric Vehicle DOI: http://dx.doi.org/10.5772/intechopen.99134*

electric vehicle or a boat, several energy sources are available with different characteristics, operating modes and architectures. The most characteristic quantities are the voltage and the current levels requiring the use of specific power and passive components. The architecture design of these converters, whether forward, isolated or segmented, is a first issue that must be specific to the application. Another problem is the integration of static converters in order to increase their compactness (power-to-weight and power-to-volume ratios) because the high power and the low voltage imply very high currents which are not very favourable to a high efficiency and to a volume reduction. Of course, cost constraints are very important in the automotive field and must be integrated from the start of the design process.

The complex power conversion and management functions implemented in the vehicle concern the electric motor, its control electronics, the transmission and management of energy by the charger and the converters used to power the navigation and entertainment systems. All these elements are supplied with very low voltages ranging from 12 V to 48 V, sometimes 60 V, which leads to favouring the use of 100 V components. At the drive train level, it is recommended to stay at low voltage, in order to simplify the control and most important to optimise the efficiency and therefore enhance the autonomy by avoid putting converters in series to adapt the voltage levels (for example, low-voltage battery and high-voltage motor). In other words, it is better to avoid a DC/DC stage between the battery and the inverter and therefore to only have the inverter between the battery and the motor. Furthermore, in order to recover the energy during braking phases, the DC/DC converter has to be reversible which would make its design more complex. A classical architecture is given in **Figure 9**.

The electrical connection must also be appropriately designed because for a small vehicle, whether it is full electric or micro/mild hybrid type, with for example a power of around 30 kW at 48 V the currents are very high (650A for 48 V). The wiring with a large cross section must therefore be as short as possible and the inverter placed as close as possible to the motor and the battery, ideally in the same compartment and taking advantage of the car structure to dissipate the heat rejection.

Increasing the power of the electric motor quickly becomes a problem if the supply voltage does not increase proportionally because high DC bus and phase currents lead to an unreasonable increase in the number of semiconductor and passive components required. To reach the required switching capability, the surface area of the PCB, the volume of the cooling system and the size of the connectors should be increased accordingly, thus resulting in a weight increase of the

**Figure 9.** *Example of a drive train with a single power inverter.*

electronic system and also a high cost incompatible with the requirements of the automotive field.

Alternatively, when the power becomes too high (at VLV) and therefore the currents are very high (>500A), the solution would be to segment the machine winding into many stars and supply them with several synchronised inverters as shown in **Figure 10**.

In **Figure 10**, the power is shared between two inverters, which mean that there are not too many components in parallel in each inverter arm, and that the inverters are less complex, less cumbersome and easier to build, and, also, that the connections are less bulky with less losses.

#### **3.2 Power components for low-voltage converters**

The static converters contains power modules which allow the classical energy conversion functions (AC/DC or DC/AC) and which are generally designed based on two main categories of components, namely the MOSFETs (Metal Oxide Semiconductor Field Effect Transistor) for low voltage inverters or IGBTs (Insulated Gate Bipolar Transistor) for high voltage ones. The field of application and the necessary integration of this static converter make it possible to determine the most suitable components according to several parameters such as power and voltage as well as the switching frequency. **Figure 11** gives a detailed breakdown of the use of these components.

For electric vehicles, the silicon MOSFETs and IGBTs are mainly used. In this field, the battery DC voltage is switched at frequencies ranging from 5 to 20kHz. This switching level is usually achieved by the use of well-adapted control laws. The components required for the DC/AC conversion function are usually packaged in modules. The electric motor of a power train system is three-phase, this implies that the inverter structure must be composed of at least six switches that are bidirectional in current formed by the association of an IGBT with a freewheeling diode or MOSFET in parallel that are naturally bidirectional in current due to their intrinsic integrated diode.

**Figure 10.** *Distributed system for segmented winding.*

*High Power Very Low Voltage Electric Motor for Electric Vehicle DOI: http://dx.doi.org/10.5772/intechopen.99134*

**Figure 11.** *Use of the different types of switchers depending on the application [8].*

#### **Figure 12.** *Distribution of failure sources in a power converter [9, 10].*

It is also useful to keep in mind that failures can be experienced in a power converter, it is essential that the reliability of this power converter is as high as possible in the case of an electric vehicle for the obvious safety reasons. Several studies show that the power modules can be the most weak part of a converter [9, 10]. The causes of failure are mainly due to temperature (frequent thermal cycling of components and high steady state current), but also to moisture, vibrations and contaminations during the manufacturing process. The **Figure 12** shows the results of two studies carried out on the failure modes of power converters.

The choice of a very low voltage supply, in this case 60 V, allows the use of commercial converters. However, as soon as the required power imposes a current higher than 500 A, it is necessary to design a bespoke power converter or, alternatively, to associate several of them in parallel. The technological constraints and standardisation lead to given silicon chip sizes which are then the building blocks of larger components. The increase in current capacity is thus achieved by combining elementary units in parallel.

**Figure 13** shows some examples of power modules used in some conventional electrified vehicles.

We can note here that the semiconductors are associated in parallel in order to be able to switch important currents which depends on the power and the supply voltage of the machine and thus on the range of the EV (low range, high range, commercial vehicle...).

For example, the Tesla Model S has 10 IGBT chips per phase (i.e. 30 per module) to provide the 800 kW needed to power this vehicle whereas a Renault Zoé only needs 12 IGBT chips per module to ensure its nominal operation at 400 V/300 A.

**Figure 13.** *Examples of inverters in the realm of electric vehicles [11, 12].*

The inverter should be compactly designed and should preferably be mounted as close as possible to the motor. The elements that contribute to the performance of the power module and therefore of the inverter are:


In addition to conduction losses, switching losses must also be minimised to ensure optimum efficiency and minimal impact on the vehicle autonomy.

The design of the converter must also take into account the control boards, the drivers and the cooling system. **Figure 14** shows the controller and driver circuitry for the Lexus hybrid vehicle.

Nowadays, new materials are emerging to replace silicon such as: silicon carbide (SiC) and Galium nitride (GaN). These materials allow higher switching

**Figure 14.** *Examples of controllers and driver circuitry [13].*

frequencies, greatly reduced losses and higher operating temperatures resulting in more compact cooling systems, however, they also require a better control of the EMC and the PCB routing.
