**2. Problem description**

At the same time, distances between these magnetic field generators and the passengers are relatively short in most vehicles; for instance, it is usual to place the battery pack as far as possible from the bodywork to minimize the risk of battery damage and its consequences in case of crash; this implies positioning them just under or behind the passenger seats [1]. Consequently, there could be hundreds of amperes circulating some centimeters away from

The combination of high currents and short distances involves some risks due to the presence of strong magnetic fields. These fields can potentially have undesired effects on electric and electronics devices, but also on living beings inside the vehicle, or close to it. The first effects are known as electromagnetic interference (EMI) and are analyzed within the discipline of electromagnetic compatibility (EMC), whose main goal is to ensure proper operation of operational equipment in a common electromagnetic environment. This is usually done by limiting or conditioning the electromagnetic fields (EMFs) emitted by each device, but mostly by immunizing them so that they are not affected by EMI coming from the rest of the devices. The second effects are named electromagnetic radiation (EMR) and belong to the field known as bioelectromagnetism or bioelectromagnetics, which studies all kinds of interactions between EMFs and biological systems. EMR is usually classified into ionizing and nonionizing radia‐ tion, depending on its capability to ionize atoms and therefore to break chemical bonds. This is only possible if the radiation carries a high amount of energy, and hence ionizing capability is directly associated with wavelength and thus with frequency. The boundary between nonionizing and ionizing EMR is located in the ultraviolet range of the electromagnetic

spectrum. In this sense, all the radiation emitted by an electric vehicle is nonionizing.

scientific community.

The relationship between nonionizing EMR and human health has been studied for decades. In 1996, the World Health Organization (WHO) established the *International EMF Project* to assess the scientific evidence of possible health effects of low‐frequency EMR (from 0 to 300 GHz), encouraging focused research to fill important gaps in knowledge and the development of internationally acceptable standards limiting EMF exposure [2]. At present, some possible consequences of low‐frequency EMF exposure are still Unclear. Namely health effects caused by long‐term exposure (such as cancer or neurodegenerative disorders) are mentioned in the literature, although conclusive results have not been obtained. Many long‐term studies have been described as questionable and of low repeatability. Moreover, it could be argued that long‐term effects are impossible to determine with certainty, since they take years or even decades to appear. Hence, long‐term consequences are a source of discussion within the

On the other hand, short‐term nonionizing effects are well established, and their mechanisms are well known. These biological effects occur as soon as the exposure begins, and they disappear when it ceases, or shortly after. They are caused by extremely strong low‐frequency (up to a few hundred kHz) and strong medium‐frequency EMFs (radio waves and microwaves up to 300 GHz), and thus they are also known as acute effects. They may be classified into two main groups: electrostimulant effects and thermal effects. The former are a consequence of the coupling between low‐frequency fields and living matter, an example of this would be induced currents in some organic tissues generated by an external magnetic field. The latter are due to

the passengers during strong accelerations or deep regenerative braking.

48 Modeling and Simulation for Electric Vehicle Applications

Electric vehicles are one of the most relevant applications in which power devices and general public share a common space. Other well‐known precedents are power lines close to houses or buildings, electric trains and trams, and household appliances, to cite a few examples. However, the specific characteristics of EVs could make this issue particularly worrying from the point of view of magnetic field exposure. The combination of high current levels, short average distances between equipment and passengers, and long exposure duration is espe‐ cially detrimental in this application.

As mentioned in the "Introduction" section, power levels in electric vehicles are of the order of tens of kW, while voltage levels rarely exceed 600 V, as shown in **Table 1**. This implies that current levels usually reach hundreds of amperes. There are not many applications in which people are close to wires or devices carrying such high currents. Besides, the present trend in EVs nowadays consists in reducing voltage levels as much as possible, which implies even higher currents. Paradoxically, lower voltages imply improved safety in case of short circuit or electrocution, but also reduced safety from the point of view of magnetic field exposure.

Second, distances between the traction drive and the passengers are usually short. For a typical electric car, values range from 0.2 to 3.0 m depending on the location of all the power devices and power cables. In this sense, the topology and the configuration of the vehicle (i.e., how the power devices are located within the available space) are particularly relevant:


Third, regarding the duration of the exposure, it is important to note that general public is subject to electromagnetic fields generated by EVs for a considerable amount of time, signifi‐ cantly longer than other daily exposures such as household appliances. From the results presented in [5, 6], it can be concluded that European citizens spend an average of 1 h and 25 min per working day driving their cars. Even if an appreciable part of that time is spent with the vehicle stopped (e.g., traffic lights or traffic jams), situation in which magnetic fields should be minimum, the duration of the exposure is still rather long. In the United States of America, these average times are probably even longer, up to 2 hours in average. It is impor‐ tant to note here that, in the case of low‐frequency magnetic fields and health effects, it is not

necessary to take exposure duration into account at the moment, since there is no scientific proof of any health consequences due to this type of exposure.


BEV = battery electric vehicle; HV = hybrid vehicle; PHV = plug‐in hybrid vehicle.

**•** For instance, there are some differences between those vehicles that add a DC‐DC converter connecting the batteries and the inverter as those who do not (see **Figure 1**). Without such DC‐DC, the battery must have enough voltage for the inverter to drive the electrical machine in every required operating point (torque‐speed). This is usually done reaching a compro‐ mise between battery voltage, which should not be too high (using too many cells in series increase balancing and safety requirements) and machine voltage, which should not be too low (lower voltages imply higher currents and lower number of turns in the windings). In general, adding a DC‐DC allows for higher voltages in the drive, which improves magnetic field exposure but could worsen electric field exposure. However, in most cases the DC‐DC aims to reduce battery voltage, and thus battery current increases. Hence, if the batteries are

placed close to the passengers, they could suffer from higher magnetic fields.

exposure levels than hybrid vehicles.

50 Modeling and Simulation for Electric Vehicle Applications

passengers.

**•** There are also some differences between pure electric vehicles and hybrid electric vehicles. The former have simpler traction systems, with fewer devices and mechanisms, which can be easily accommodated within the available space. On the other hand, the power train of the latter comprises more equipment, and thus they are more prone to suffer from room issues. Having more flexibility to distribute the power devices within the vehicle is always a good thing, and magnetic field exposure is another aspect that benefits from it, since certain parts can be moved away from the passengers. Nevertheless, pure electric vehicles use more electric power than their counterparts. Considering that voltage levels are similar (see **Table 1**), this means that pure EVs use higher currents and thus they generate stronger magnetic fields. In general, it could be expected that the second factor (stronger fields) weighs more than the first one (longer distances), so that pure EVs should imply higher

**•** Finally, the type of drive also has some influence over passenger field exposure, namely those vehicles with rear‐wheel drives usually place most of the traction equipment (i.e., the electrical machine and the inverter) in the rear part of the vehicle, while front‐wheel vehicles place it in the front part. As cars are given aerodynamic shapes to minimize aerodynamic drag, the front part is usually longer than the rear part, and distances between the front wheels and the front seats are usually longer than those between the rear wheels and the rear seats, as shown by the two examples in **Figure 2**. This means that vehicles with front‐ wheel drives will usually have longer distances between these power devices and the closest

Third, regarding the duration of the exposure, it is important to note that general public is subject to electromagnetic fields generated by EVs for a considerable amount of time, signifi‐ cantly longer than other daily exposures such as household appliances. From the results presented in [5, 6], it can be concluded that European citizens spend an average of 1 h and 25 min per working day driving their cars. Even if an appreciable part of that time is spent with the vehicle stopped (e.g., traffic lights or traffic jams), situation in which magnetic fields should be minimum, the duration of the exposure is still rather long. In the United States of America, these average times are probably even longer, up to 2 hours in average. It is impor‐ tant to note here that, in the case of low‐frequency magnetic fields and health effects, it is not **Table 1.** Power and voltage levels of some commercial models of hybrid and electric vehicles.

**Figure 1.** (a) Most common topology in electric cars nowadays. (b) Alternative topology, in which a DC‐DC converter is added between the batteries and the inverter.

**Figure 2.** Schematics of two well‐known pure EVs, showing the position of the main power devices: batteries, inverter, and electrical machine. (a) Rear‐wheel drive and (b) front‐wheel drive. Original images extracted from [3, 4] and modi‐ fied by the authors.

In summary, magnetic fields in EVs could become an issue from the point of view of human health due to a combination of three factors: average and peak current levels, short distances between field generators and the passengers, and lengthy exposures.

#### **2.1. Characteristics of the magnetic field generated by an EV**

Under static electromagnetic conditions, electric fields basically depend on the voltage levels and on the distances between the passenger and the corresponding power equipment (Cou‐ lomb's law). Similarly, magnetic fields depend on the current levels and on that same distances (Biot‐Savart law). In other words, when these physical magnitudes do not change over time, both fields are not coupled and they can be studied separately.

However, most electrical systems, EVs included, are characterized by time‐varying electric magnitudes. In the most general case, and according to Maxwell's equations, both fields are coupled and their dependence with respect to variables such as voltages and currents is much more complex than those given by Coulomb and Biot‐Savart laws. Fortunately, it is not necessary to work with Maxwell's equations in many cases, in which quasistatic approxima‐ tions are applicable. Specifically, when the frequencies of the electromagnetic phenomena are low—so that propagation speed can be considered infinite [7]—a quasistatic model can be used, which provides an intermediate solution between the most general dynamic case (Maxwell's equations) and the purely static case (Coulomb and Biot‐Savart laws). In this sense, a quasistatic system evolves from one state to another as if it was a static system [8].

Depending on the particular quasistatic model employed (each variant represents a different approximation of Maxwell's equations), the simplifications adopted will vary. In this particular case, Darwin's model is used, which considers both capacitive and inductive effects and which incorporates magnetic field contribution to total electric field (Faraday's law) [8]. In Darwin's model, Biot‐Savart law is directly applicable, the only difference being that currents and magnetic fields are time‐varying variables. However, Coulomb's law must be extended to account for magnetic induction. In other words, magnetic fields still depend on currents and distances, but also on time, while electric fields depend on voltages, distances, time, and on magnetic fields.

Electric vehicles constitute an application in which quasistatic models are appropriate, since frequencies are generally low. There are basically two types of frequencies in an electrical drive, such as those propelling EVs:

**1.** Fundamental frequencies: These are the lowest frequencies in the system, and they are related to the operating point of the drive. For example, in a steady‐state situation, fundamental frequency would be roughly 0 Hz (DC) for the battery current and 100 Hz for a 2000‐rpm 50 Hz synchronous machine working at 4000 rpm in the flux‐weakening region. During transients, some of these fundamental frequencies will show harmonic content. One example of this is power peaks in the batteries, which involve low‐frequency harmonics in battery current. In general, fundamental frequencies will be very low, of the order of hundreds of Hertz at most. However, the absence of steady state in some situations, such as urban driving, implies a wide‐frequency spectrum.

**2.** Switching frequencies: These frequency values and their corresponding harmonic components are given by the operation of power semiconductors such as insulated‐gate bipolar transistors (IGBTs) and diodes. They are defined by many factors, starting with the modulation technique (hysteresis band, pulse width modulation (PWM), space vector modulation (SVM), direct torque control (DTC), etc.), and also on the inductance value of the corresponding filters. For those which use variable‐switching frequency, its values will depend on the operating point as well.

More importantly, switching frequencies change significantly with power electronics technology. For instance, there is a huge difference between conventional IGBTs, fast IGBTs, and silicon carbide (SiC) metal‐oxide‐semiconductor field‐effect transistors (MOSFETs). The former usually work at frequencies ranging from 2 to 20 kHz. Fast IGBTs can reach up to 50 kHz in many applications, while SiC MOSFETs are already exceeding frequencies over 150 kHz. Given the voltage levels usually employed in commercial EVs, there is no way to exclude any of the above three major technologies, so all of them are eligible for this application.

In summary, magnetic field frequencies can change considerably from one vehicle to another. According to current EV designs, and considering the technologies implemented in them (conventional IGBTs, and synchronous or asynchronous machines), it seems reasonable to expect fundamental and switching frequencies up to 10 kHz, with relevant harmonic compo‐ nents up to 300 kHz. These values are classified as "low and extremely low frequencies" from the point of view of electromagnetic exposure. Be that as it may, electromagnetic fields generated by EVs present a relatively wide‐frequency spectrum, from 0 Hz to hundreds of kHz.

### **2.2. Other considerations**

In summary, magnetic fields in EVs could become an issue from the point of view of human health due to a combination of three factors: average and peak current levels, short distances

Under static electromagnetic conditions, electric fields basically depend on the voltage levels and on the distances between the passenger and the corresponding power equipment (Cou‐ lomb's law). Similarly, magnetic fields depend on the current levels and on that same distances (Biot‐Savart law). In other words, when these physical magnitudes do not change over time,

However, most electrical systems, EVs included, are characterized by time‐varying electric magnitudes. In the most general case, and according to Maxwell's equations, both fields are coupled and their dependence with respect to variables such as voltages and currents is much more complex than those given by Coulomb and Biot‐Savart laws. Fortunately, it is not necessary to work with Maxwell's equations in many cases, in which quasistatic approxima‐ tions are applicable. Specifically, when the frequencies of the electromagnetic phenomena are low—so that propagation speed can be considered infinite [7]—a quasistatic model can be used, which provides an intermediate solution between the most general dynamic case (Maxwell's equations) and the purely static case (Coulomb and Biot‐Savart laws). In this sense,

a quasistatic system evolves from one state to another as if it was a static system [8].

Depending on the particular quasistatic model employed (each variant represents a different approximation of Maxwell's equations), the simplifications adopted will vary. In this particular case, Darwin's model is used, which considers both capacitive and inductive effects and which incorporates magnetic field contribution to total electric field (Faraday's law) [8]. In Darwin's model, Biot‐Savart law is directly applicable, the only difference being that currents and magnetic fields are time‐varying variables. However, Coulomb's law must be extended to account for magnetic induction. In other words, magnetic fields still depend on currents and distances, but also on time, while electric fields depend on voltages, distances, time, and on

Electric vehicles constitute an application in which quasistatic models are appropriate, since frequencies are generally low. There are basically two types of frequencies in an electrical drive,

**1.** Fundamental frequencies: These are the lowest frequencies in the system, and they are related to the operating point of the drive. For example, in a steady‐state situation, fundamental frequency would be roughly 0 Hz (DC) for the battery current and 100 Hz for a 2000‐rpm 50 Hz synchronous machine working at 4000 rpm in the flux‐weakening region. During transients, some of these fundamental frequencies will show harmonic content. One example of this is power peaks in the batteries, which involve low‐frequency harmonics in battery current. In general, fundamental frequencies will be very low, of the order of hundreds of Hertz at most. However, the absence of steady state in some

situations, such as urban driving, implies a wide‐frequency spectrum.

between field generators and the passengers, and lengthy exposures.

**2.1. Characteristics of the magnetic field generated by an EV**

52 Modeling and Simulation for Electric Vehicle Applications

both fields are not coupled and they can be studied separately.

magnetic fields.

such as those propelling EVs:

There are many magnetic field generators in a vehicle, besides the traction drive itself. Examples present not only in EVs but also in conventional ICE‐based vehicles are other power equipment such as the air‐conditioning system, but also magnetized steel‐belted tires, which are one of the main sources of extremely low‐frequency magnetic fields in conventional vehicles. This unintentional magnetization is a consequence of the manufacturing process, and the result is a magnetic field whose frequency depends on the vehicle speed, ranging from 0 to 20 Hz [9, 10]. This field is of considerable strength but attenuates very quickly as distance increases. Hence, maximum exposure values usually take place in the area of the feet [11, 12]. According to some authors, this source of magnetic field is negligible when considering magnetic field exposure inside hybrid and electric cars [13], but this point is not completely clear.

Nonetheless, all magnetic field generators contribute to overall magnetic field exposure, and therefore should be included in EMR studies. It is important to state here that magnetic field exposure must be assessed globally (total magnetic field), and not individually (magnetic field generated by each device or piece of equipment). See Section 3.1 for further information and corresponding references about exposure assessment.

There are other factors that may influence magnetic field exposure in a positive way. For instance, the results presented in Ref. [14] suggest that the car body shell could behave as a minor magnetic shield for some frequencies. Therefore, constructive aspects such as the shape, material, and thickness of the body shell could affect magnetic exposure.

It is also convenient to consider which operating points are potentially more hazardous for human health. Under normal operation of the vehicle, power/current peaks will be higher during strong accelerations than during deep regenerative braking. This is due to two main reasons: the passive nature of some of the movement resistances (rolling resistance and aerodynamic drag), which implies that both of them will always oppose movement, and the global energy efficiency of the traction drive. Notice that driving style will heavily impact total magnetic exposure in EVs: the more aggressive the driving style the higher the magnetic fields within the vehicle.

Nevertheless, there is another situation which could involve potentially hazardous exposure for passengers, or even for pedestrians that are close to the vehicle: fast charging. As battery technology improves, higher recharge rates are achieved, which obviously imply higher currents, and hence stronger magnetic fields. Nowadays, charge rates of 2–4 C are already usual, with even higher values reachable in the near future [15, 16]. Therefore, magnetic field generation must be studied not only during normal operation of the vehicle but also during fast charging. As a general rule, it is highly advisable to remain outside of the vehicle, and at some distance from it, while fast charge is in process.

Finally, it is important to consider the wide variety of electric vehicles that exit nowadays, and how their different configurations, topologies, and power levels affect magnetic field exposure. Some considerations have already been mentioned in this chapter about vehicle configuration (front‐wheel vs. rear‐wheel traction, for instance; another example would be battery place‐ ment), and also about the power topology (significant differences arise when adding a DC‐DC converter, or when using hybrid energy storage systems that combine batteries and superca‐ pacitors for increased performance [17]). The largest differences, however, appear when considering electric vehicles of different types, such as motorbikes, buses, racing cars, or even electric planes [18, 19]. Magnetic exposure in these other vehicles could be very different when compared to electric cars, depending on the power levels involved and on the distances between the power equipment and the closest passengers.
