**4. Simulation model**

410 Induction Motors – Modelling and Control

+field weakening (CF+FW), and the LMA approach.

Figure 4 represents the optimal Id generation for conventional approach, i.e. constant flux

Inspecting these results one can find that the LMA influence on Id\* is mostly visible for low torques (T<20 N.m). It is interesting to note that in the high speed zone (>2000 rpm), LMA and conventional flux regulation tend to present closer Id\* values, as the speed increases. Also, for high torque values (above 30 N.m) both approaches have similar performances.

From the above analysis, it is expectable that the differences in the generation of Id\* lead to different efficiencies curves of the induction motor, which is, indeed, observed in the maps

A complementary perspective is presented in figure 6. It can be seen that the main LMA influence region is below 15 N.m (about 30% of motor nominal torque), with a slight behavior difference, according to n<2000 rpm or n>2000rpm: in the former case (coincident with the

speed [rpm]

<sup>1000</sup> <sup>2000</sup> <sup>3000</sup> <sup>4000</sup> <sup>5000</sup> <sup>0</sup>

0.94

0.94

0.94

0.92

0.92

0.92

0.9

0.85 0.75 0.7

0.9

0.85 0.82 0.75 0.7

0.95

0.95

0.95

T [N.m]

0.94 0.92

(a) (b)

(a) (b)

0.94

0.95

**Figure 5.** Induction motor efficiency maps: a) CF+FW; b) LMA

0. 0.92

9 85

speed [rpm]

<sup>0</sup> <sup>1000</sup> <sup>2000</sup> <sup>3000</sup> <sup>4000</sup> <sup>5000</sup> <sup>0</sup>

0.9

4

0.

0

0.9

0.94

0.94

0.92

0.9

0.92

0.92

0.9

0.9

0.85 0.82 0.75 0.7

0.75

0.82

0.85

0.85 0.82 0.75 0.7 0.65

0.85

0.75 0.65

.92

**Figure 4.** Ids\* generations: a) CF+FW; b) LMA

illustrated in Figure 5.

T [N.m]

To evaluate the LMA´s contributions to the EV energy consumption reduction, and comparing it to the conventional flux regulation, a simulation study was performed with four diferent driving cycles: ECE-R15, Europe: City, 11-Mode (Japan) and FTP-75. Simulation with other drive-cycles was also implemented, but results achieved with these four give a wide overview of LMA´s features. For that purpose, a Matlab/Simulink model was built, which is represented in figure 7.

Basically, Id\* is generated through (CF+FW) method or by the LMA – blocks (3a) and (3b), respectively. The induction motor is controlled by conventional rotor FOC (block 4); the motor model in block 5 is presented in section 4.4. The motor load and speed references are generated based on a particular drive cycle features (block 1), which includes the vehicle dynamic and mechanical transmission models. Finally, block 2 implements the speed controller (based on a proportional+integral(PI) control law) which generates the motor torque reference. In the following sections, the main model blocks are discribed.

Evaluation of an Energy Loss-Minimization Algorithm for EVs Based on Induction Motor 413

Where:

Mt - vehicle mass + equivalent mass of rotating parts; v(t) – vehicle instantaneous longitudinal speed;

Cr, Cw – rolling friction coefficient, aerodynamic drag coefficient;

order to increase simulation accuracy, its value was fixed in 0,01 s. Vehicle and transmission parameters are shown in Tables 3 and 4:

Besides the inertia force, associated to vehicle displacement, the inertia of rotating parts (i.e., kinetic energy stored on it caused by rotational movement) should also be considered, since it is the motor(s) who supply it. This is considered in the "equivalent mass of rotating parts" Mt term (see Table 3). It should be noted that driving cycle block output speed (v) and acceleration (dv) are discrete values. The time step size default value is 1 s; however, in

> Total vehicle's mass (kg) 350 Rotating mass (%) 5 Vehicle´s cross section (m2) 1,5 Wheel diameter (m) 0,3 Aerodynamic drag coefficient 0,3 Rolling friction coefficient 0,008

Gear ratio 5 Efficiency (%) 98 Idling losses by friction (W) 10

Figure 9 presents the developed LMA block set. Rd and Rq are inputs for the block regions "we<wn" and "we>wn". Basically, these two elements generate Ids\*, according to 3.1.3. As it was described, for zones in the (ids; iqs) plane limited by restrictions (10), (11) and idsIdn, equation (27) is applied. For the border lines, the three defined regions must be considered: in region 1, Ids\* is restricted to its maximum allowable value (Idn); for regions 2 and 3, only voltage limit is considered in Ids\* generation restriction. Since Tp2= Tp3, the same block can be

Since the flux level should not decrease below a minimum value (Id\_min), in order to guarantee

that Id\_min≤Ids≤ Idn, two saturation blocks are placed at "we<wn" and "we>wn" outputs.

1

Minimum wheel speed beyond which losses are generated (rad/s)

Fd(t) – instantaneous driving force;

, A – air density; vehicle´s cross section.

g – gravity acceleration;

**Table 3.** Vehicle Parameters

a. LMA

**Table 4.** Mechanical Transmission Parameters

**4.2. Rotor flux setpoint generation** 

used for generating Ids\* in these two regions.

**Figure 7.** Global simulation model
