**4.1. Drive cycle+vehicle model**

The drive cycles plus the vehicle and mechanical transmission models were implemented with the QuasiStatic Simulation Toolbox (QSS TB), based on Matlab/Simulink, developed by (Guzzella, Amstutz, 2005). The QSS TB library integrates a set of several elements, such as driving cycles, vehicle dynamics, internal combustion engine, electrical motor and mechanical transmisson. Batteries, supercapacitor and fuel cell are also included.

Essentially, it considers a backward (wheel-to-engine) quasi-satic causal model which, based on driving cycle speeds (at discrete times), calculates accelerations and determines the necessary forces, based on the vehicle features and an eventual mechanical transmission. The implemented model includes the QSS TB elements depicted in figure 8.

**Figure 8.** Drive cycle and vehicle/transmission models

The load power demanded to the induction motor (Tload\*r) considers the drive cycle, vehicle dynamics (rolling and aerodynamic resistance, only in the plane) and also a mechanical transmission with a fixed gear ratio. The vehicle dynamics is modelled by the following equation:

$$\mathbf{M\_t \frac{d\mathbf{v(t)}}{dt}} = \mathbf{F\_d(t)} - \mathbf{M\_t}\mathbf{gC\_t} - \frac{1}{2}\rho\mathbf{C\_w}\mathbf{Av(t)}^2\tag{33}$$

Where:

412 Induction Motors – Modelling and Control

**Figure 7.** Global simulation model

**4.1. Drive cycle+vehicle model** 

**Figure 8.** Drive cycle and vehicle/transmission models

<sup>2</sup>

following equation:

The drive cycles plus the vehicle and mechanical transmission models were implemented with the QuasiStatic Simulation Toolbox (QSS TB), based on Matlab/Simulink, developed by (Guzzella, Amstutz, 2005). The QSS TB library integrates a set of several elements, such as driving cycles, vehicle dynamics, internal combustion engine, electrical motor and

Essentially, it considers a backward (wheel-to-engine) quasi-satic causal model which, based on driving cycle speeds (at discrete times), calculates accelerations and determines the necessary forces, based on the vehicle features and an eventual mechanical transmission.

The load power demanded to the induction motor (Tload\*r) considers the drive cycle, vehicle dynamics (rolling and aerodynamic resistance, only in the plane) and also a mechanical transmission with a fixed gear ratio. The vehicle dynamics is modelled by the

t d tr w

dv(t) <sup>1</sup> M F (t) M gC <sup>ρ</sup>C Av(t) dt <sup>2</sup> (33)

mechanical transmisson. Batteries, supercapacitor and fuel cell are also included.

The implemented model includes the QSS TB elements depicted in figure 8.

Mt - vehicle mass + equivalent mass of rotating parts;

v(t) – vehicle instantaneous longitudinal speed;

Fd(t) – instantaneous driving force;

g – gravity acceleration;

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

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

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 order to increase simulation accuracy, its value was fixed in 0,01 s.

Vehicle and transmission parameters are shown in Tables 3 and 4:


**Table 3.** Vehicle Parameters


**Table 4.** Mechanical Transmission Parameters

### **4.2. Rotor flux setpoint generation**

### a. LMA

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 used for generating Ids\* in these two regions.

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.

Evaluation of an Energy Loss-Minimization Algorithm for EVs Based on Induction Motor 415

**Figure 11.** Ids\* generation for regions 2 and 3 (green and gray paths in figure 3)

Equations (1) and (2) are the basis of "Iq reference" block. Equations (3)-(6) are implemented in "e calculation" block (notice that e=slip + r). The bottom block considers the coordinates change of instantaneous stator currents, from phase domain to d-q synchronous frame. To do so, the following well known coordinate transformation matrix is applied:

Figure 12 shows the block structure for indirect FOC.

**Figure 12.** Rotor indirect FOC implementation

**4.3. Rotor indirect FOC** 

**Figure 9.** LMA block contents

Figure 10 shows the interior of "we<wn" block.

As it can be seen, Ids\* is generated by (27), while Ids<Idn; after that Ids\*=Idn. It should be noted that the absolute value of Iqs must be used, in order to consider both motor and braking modes.

**Figure 10.** Ids\* generation in region 1 (blue path in figure 3)

The block "we>wn" is represented in figure 11. Equation (27) regulates Ids\* generation until (31) is no longer true (notice that the absolute value of iqs is compared to the product of "Vmax restriction" by (Rd/Rq)1/2). After that, Ids\* is given by zone 3 solution in table 1 (s3)– "Id\* for Vmax restriction border" block. It also should be pointed that when a load point overcomes the voltage limit, the result given by (s3) is a complex value. In order to deal with this issue, for these situations Ids is taken from the conventional flux regulator.

In contrast with the LMA, the conventional flux regulation (depicted as block (3b) in Figure 7) generates a Ids setpoint according to the following strategy:

$$\begin{cases} I\_{ds} = I\_{dn} & n \le n\_n \\ I\_{ds} = n\_n / n \cdot I\_{dn} & n > n\_n \end{cases} \tag{34}$$

**Figure 11.** Ids\* generation for regions 2 and 3 (green and gray paths in figure 3)

### **4.3. Rotor indirect FOC**

414 Induction Motors – Modelling and Control

**Figure 9.** LMA block contents

Figure 10 shows the interior of "we<wn" block.

**Figure 10.** Ids\* generation in region 1 (blue path in figure 3)

for these situations Ids is taken from the conventional flux regulator.

൜

7) generates a Ids setpoint according to the following strategy:

As it can be seen, Ids\* is generated by (27), while Ids<Idn; after that Ids\*=Idn. It should be noted that the absolute value of Iqs must be used, in order to consider both motor and braking modes.

The block "we>wn" is represented in figure 11. Equation (27) regulates Ids\* generation until (31) is no longer true (notice that the absolute value of iqs is compared to the product of "Vmax restriction" by (Rd/Rq)1/2). After that, Ids\* is given by zone 3 solution in table 1 (s3)– "Id\* for Vmax restriction border" block. It also should be pointed that when a load point overcomes the voltage limit, the result given by (s3) is a complex value. In order to deal with this issue,

In contrast with the LMA, the conventional flux regulation (depicted as block (3b) in Figure

ܫௗ௦ ൌ ܫௗ݊ ݊ ܫௗ௦ ൌ ݊Ȁ݊ ή ܫௗ݊ ݊

(34)

Figure 12 shows the block structure for indirect FOC.

**Figure 12.** Rotor indirect FOC implementation

Equations (1) and (2) are the basis of "Iq reference" block. Equations (3)-(6) are implemented in "e calculation" block (notice that e=slip + r). The bottom block considers the coordinates change of instantaneous stator currents, from phase domain to d-q synchronous frame. To do so, the following well known coordinate transformation matrix is applied:

$$
\begin{bmatrix}
\mathbf{i\_{qs}} \\
\mathbf{i\_{ds}}
\end{bmatrix} = \frac{2}{3} \begin{bmatrix}
\sin \theta\_{\mathbf{e}} & \sin(\theta\_{\mathbf{e}} - \frac{2}{3}\pi) & \sin(\theta\_{\mathbf{e}} + \frac{2}{3}\pi) \\
\cos \theta\_{\mathbf{e}} & \cos(\theta\_{\mathbf{e}} - \frac{2}{3}\pi) & \cos(\theta\_{\mathbf{e}} + \frac{2}{3}\pi) \\
\end{bmatrix} \begin{bmatrix}
\mathbf{i\_{sa}} \\
\mathbf{i\_{sb}} \\
\mathbf{i\_{sc}}
\end{bmatrix} \tag{35}
$$

Evaluation of an Energy Loss-Minimization Algorithm for EVs Based on Induction Motor 417

**Figure 14.** Induction motor model of figure 15 (stator d-q reference frame)

regulation energy performances is also presented.

**5.1. ECE-R15** 

2500 5000 n [rpm]

> 10 20 Id [A]

0 20 Iq [A]

250 500 Motor losses [W]

> 0 5000

Pu [W]

represents the load torque demanded by the drive cycle, while in the third one the motor limits and working points imposed by the drive cycle are illustrated, together with the most significant LMA´s efficiency gain zones. Finally, a table with LMA and conventional flux

From a general perspective, these results confirm the main LMA features, described in section 3.2 visible differences from conventional flux regulation occur for low load torque, particularly for relative low speeds. This agrees to the fact that in regions where Ids has a large regulation

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>0</sup>

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>0</sup>

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> -20

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>0</sup>

**Figure 15.** Drive-cycle; (Id; Iq; Motor losses) – [blue:LMA; red dashed line: conventional regulation]; Pu

time [s]

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> -5000

flexibility, LMA and conventional flux regulation have clearly different performances.

The "Current Control" block generates stator reference voltage (Vsdq\*) in synchronous frame (through PI´s current ids and iqs controllers), which is applied to the motor model, in phase coordinates, in order to make the real instantaneous stator currents to achieve the reference values.

## **4.4. Induction motor model**

Figure 13 presents the induction motor model considered in simulations, which also includes motor iron losses.

**Figure 13.** Induction motor model simulated (space vectors in stator reference frame)

When comparing this model to the one considered in LMA (figure 2), the major differences are in parallel (magnetizing) branch. Since core losses currents are not considered in the major circuit, it is expectable that the voltages (Vedm and Veqm) on the independent sources are larger compared to the parallel branch voltages in the equivalent model of figure 13. Since core losses are given by ((Vedm)2+(Veqm)2)/Rm, it seems plausible to admit that the core losses in LMA model are higher than the ones in figure 13 model.

Figure 14 shows the simulink implementation of the considered induction motor model (block 5 in figure 7).
