## Multilevel Modeling for Rapid Prototyping

### Introduction

Model-based design can considerably reduce the cost associated with system development. The development of models for complex systems such as electric vehicles includes the following phases:

Definition of functional specifications

System design

Tests and validation

Implementation

This case study focuses on the first two phases and shows how the simulation could help the system designer in decision making. The simulation is a very complex art. It can represent simple model with precision which can be arguable whereas complex models can be represented with accurate precision, very close to reality. The developer of models must always make a compromise between the complexity of the models and the required precision. Of course, it is always preferable to have an ultra-accurate model, but the parameters required by these models are usually difficult to determine, especially during the first phases of system development. Moreover, the simulation of these accurate models is very slow.

It is therefore necessary to use different detail level of simulation models. At first, the system designer will need a first level model in order to have an overview of all the power flow in the system. This will help in the design of different elements in the system to meet the power flow requirement. Then, a more accurate model is required in order to adjust different systems, to fine tune the parameters of the energy management system and to design power electronics converters. Finally, a detailed model will allow the validation of the system behavior with a high degree of accuracy and to perform other adjustments if required.

### The System Architecture

The system architecture under study is based on the Toyota Prius THSII:

More precisely, the study focuses on the different detailed levels of the electrical system model.

A NiMH battery of 201 V, 6.5 Ah (just as the one used in the Toyota Prius) is considered. For this model, it is not necessary to use different detailed level as it is very easy to use and offers a good precision.

### The Simplified Model

The simplified electrical model is based on the power balance principle on different elements. Note that these simplified models have energy efficiency of 100%.

#### The DC/DC Converter

For the DC/DC converter, it is assumed that the DC bus voltage, which supplies the motor and the generator, is maintained constant by a regulator. For this model, a DC bus of 500 V is required. The voltage at the DC bus side is maintained constant using a fixed voltage source. From the power balance principle, the corresponding current is requested from the battery. A filter is necessary to break the algebraic loop. Below is the simplified DC/DC converter model:

#### The Motor Drive

The electrical motor applies a mechanical torque on the system. The required torque is determined by the energy management system. It is assumed that the torque regulator is well designed so that the reference torque is directly applied on the motor shaft. By measuring the shaft speed and the DC bus voltage, it is possible using the power balance principle to determine the corresponding DC bus current. Below is the simplified model of the electrical motor:

#### The Generator Drive

The generator is represented exactly as the electrical motor. A negative torque is requested by the energy management system in order to generate electrical power. As it is assumed that the generator control system is ideal, the reference torque is directly applied to the mechanical system. The corresponding current is deduced using the power balance principle.

#### Simulation Results

The simulation of the simplified electrical system is useful as it shows the performance of the energy management system, the mechanical system and different electrical components. In fact, the short simulation time (around 0.7 times the real time in normal mode) allows fast adjustments of the energy management system for better performances. For this phase of simulation, the accelerator position is set to 100% and the following results are obtained:

It should be noted that in this phase of modeling, it is not possible to determine the stator current for the motor and generator; that explains why these currents are nulls. The simplified model can now help in the dimensioning of each component of the electrical system. The next section focuses on the architecture of each component, including the electrical machines and different regulators.

### The Average-Value Model

In this phase of simulation, the level of precision is improved. The different electrical machines and regulators architectures are chosen.

#### The DC/DC Converter

The average value DC/DC converter uses a voltage regulator based on a Proportional-Integrator (PI) controller to maintain the DC bus voltage equal to the voltage reference (of 500 V). The simulation allows the selection of the inductor and capacitors and the adjustment of the PI controller parameters in order to obtain the results similar to the simplified model. Below is the DC/DC converter model:

As an average value converter is used, only the duty cycle is required by the boost converter. The battery voltage is set by the boost converter based on the duty cycle and the DC bus voltage. On the high voltage side, the DC bus current is set based on the duty cycle and the battery current. For more information regarding this system, see Two-Quadrant Chopper DC Drive.

#### The Motor Drive

The motor is a permanent magnet synchronous machine (PMSM). From the simplified model results, the motor requirement is determined. It should be able to produce a maximum torque of 400 Nm and a maximum power of 50 kW up to 6000 rpm (this speed is obtained by simulating the simplified model for 60 seconds, in order for the vehicle to reach 160 Km/h).

The motor control is done using vector control. As the machine
uses an interior permanent magnet rotor, it is possible to use the
reluctance torque to increase the total output torque and operate
at very high speed. For more information on this configuration, see
the` ac6_IPMSM`

example. The electric drive consists
of the motor, the inverter and the vector controller.

Similar to the DC/DC converter model, the inverter is represented by an average value model and the effect of power semiconductors switching is not taken into consideration. The reference currents (from the vector controller) are directly applied on the motor via controlled current sources. Moreover, this inverter allows the modeling of the saturation current when the DC bus voltage is not high enough to power the motor (at a given speed and torque). Below is the average value model:

In normal operation, the current sources are used to supply the machine. In the saturation, mode, voltage sources are used instead. For more details on this system, see the PM Synchronous Motor Drive.

#### The Generator Drive

The generator is also a permanent magnet synchronous machine. From the simplified model results, it should be able to provide a maximum power of 30 kW and a maximum speed of 15 000 rpm. A vector controller is used to assure a proper operation of the generator. As a non-salient pole machine is used, the classical control method (id = 0) is used throughout the operating region. Below is the model of the complete system:

The average value model is identical for both the motor and generator.

#### Simulation Results

The simulation of the average value model allowed the dimensioning of electrical components (inductor, capacitor, motor and generator) and the adjustment of different controllers systems. At this stage, it is now possible to clearly visualize the electrical signals. This helps in fine tuning the regulators and the energy management system. The longer simulation time (16 times the real time in normal mode and 3.5 times the real time in accelerator mode) allows to represent more precisely the behavior of the electrical system. Below are the results from different systems:

### The Detailed Model

In this phase of modeling, the average value models of converters are replaced by power semiconductors switches. A method to generate the pulse width modulated (PWM) signals is also determined.

#### The DC/DC Converter

For the detailed model of the DC/DC converter, the output of the PI controller is sent to the pulse width modulator, which selects the pulse sequence required to maintain the DC bus voltage close to the reference value. The PWM signals are then sent directly to the single leg power semiconductor switch.

#### The Motor and the Generator Drives

For the detailed model of these elements, the average value inverter is replaced by a 3 legs power semiconductors switches consisting of 6 pairs of IGBT/diode. The output signal of the vector controller is sent to the hysteresis controller, which generates the required PWM signals. For more information about these systems see the PM Synchronous Motor Drive.

#### Simulation Results

The simulation of the detailed model gives a lot of information regarding the power converters. In fact, it allows the selection of the PWM generation method, the adjustment of the switching frequency (for the DC/DC converter) and the tuning of the hysteresis band of the current regulator necessary for vector control (motor and generator). Moreover, it allows the dimensioning of the converters as the instantaneous values of currents are accurately known. The selection of power semiconductors switches and the dimensioning of heat sinks can be made afterwards.

In a broader view, this simulation helps to validate with a high precision the operation of the electrical circuit and allows the detection of any problems caused by instability, over voltage or over current. This high degree of precision is obtained of course, at the price of a longer calculation time. In fact, the simulation time is around 90 times the real time in accelerator mode. Below are the results from different systems:

### Comparison of the Multilevel Modeling Precision

Regarding the precision, the mechanical signals (the vehicle speed and torque) and the electrical signals (the average power from different elements) are very close for all the three models. In fact, the error on the vehicle speed is less than 2 Km/h and 1.5 Km/h for the simplified and the average value models respectively. Regarding the motor power, the dynamics of the simplified and average value models are also close to the detailed model. The main difference resides on the high frequency component present on the detailed model signals due to the switching frequency of the inverter. The maximum error from the two models is less than 5000 W (below 10%) and the average error is below 5%.

Regarding the vehicle torque, the three models are very close with a maximum error of 5%. By closely looking at the differences (right figure), it is noted that the simplified model reacts instantaneously to the reference torque required by the energy management system. For the average value model, the torque increases progressively to the desired torque with a greater accuracy compared to the detailed model. Again, the detailed model is characterized by the high frequency signal generated by the switching frequency of the electrical system.

As for the battery signals, the simplified and the average value models follow exactly the dynamics of the detailed model with no high frequency component.

One of the main differences between the simplified and the average value models resides on the electrical signals from the motor and the generator. In fact, the simplified model cannot represent the motor or the generator current. The difference between the average value and the detailed models is the presence of the high frequency component on the detailed model. The amplitude of currents is exactly the same for the two models whereas the phase could be different due to variations on the mechanical speed.

Here is a table which summarizes the differences between the different detailed levels:

### Conclusion

To conclude, the level of precision chosen depends on the stage of development the engineer is working on. For example, at the beginning of the process, the system engineer wants to simulate its system to have an idea on how it operates, with the objective to effectively adjust the energy management system. The simulation of the simplified model helps to determine the speeds, torques and electrical powers present in the system. As this model requires less calculation time (less than 1 times the real time), it is possible to study several configurations and obtain results close to reality in a very short time.

Subsequently, the average value model allows the electrical engineer to design different control systems and to select the motor and the generator based on the results from the simplified model. The simulation time (less than 4 times the real time in accelerator mode) is acceptable. It allows the validation of the system behavior and the adjustment of both the control system and the energy management system.

Finally, the specialist in power electronics can use the detailed model to select the power semiconductors components based on the instantaneous and average values of currents and voltages. The losses can be evaluated (for heat sink design), the switching frequency can be adjusted in order to assure the electromagnetic interference (EMI) will not affect other systems. Moreover, the complete simulation of the detailed model allows to validate the behavior of different elements in the system and to fine tune the energy management system if necessary. Of course, this high level of accuracy comes with a larger calculation time, around 90 times the real time. But this large time is still acceptable if compared with the time required in an experimental setup.

Obviously, in the development of the detailed or the average value model, it is possible to isolate some blocks, such as the DC/DC converter or the motor and generator drives in order to preliminary adjust each system. The block can be added to the complete model when it operates properly.

Finally, when the simulation model is completed, it represents the reality with a high degree of accuracy. The next phase, which consists of the realization of the system experimentally, can be made with less time and at lower cost.