Question

Design DC to AC Inverter for electric vehicles using (MATLAB/SIMULINK)

Answer 1

Model Development Process:
The model development process consists of

1) determining how the model will be used,

2) identifying the key equations, parameters, and assumptions,
3) building and refining the model,
and then
4) the actual model application and evaluation. The model can be used to evaluate the energy flow of a DC motor drive train, and to determine the ability of the system to meet specific drive cycle speed and torque requirements. The major components of the model are input road torque, input road speed, motor model, motor controller model, battery model, and PI controller.
A block diagram of the model is presented below in Figure 2: DC Drive Simulation Model. In the model the required Road Speed and Road Torque are inputs, and the major model blocks are
the Motor Model, Controller Model, Battery Model, PI Controller Model, and feedback from the PI Controller to the main power controller. The feedback includes a one-sample delay with an
initial condition to prevent an algebraic loop in the Simulink model.

Key Equations
Determining the key equations and their corresponding variables and parameters is a necessary first step in model development. Each block in this simplified model represents one or more major equations as listed below.
DC Motor:
As noted earlier, Battery Electric Vehicles (BEV) and Hybrid Electric Vehicles (HEV) frequently use special, high efficiency Permanent Magnet Synchronous Motors (PMSM). This type of motor may be referred to as a brushless DC motor because it runs from DC voltage but does not have brushes. PMSM motors actually use AC voltage that is supplied by the Motor Controller. The motor controller inverts the DC voltage to produce an AC voltage at the proper voltage and frequency. The motor voltage is frequently a 10-20 KHz Pulse Width Modulated AC voltage where the voltage and frequency are adjusted to provide the proper motor speed and magnetic field values.
A DC permanent magnet motor was used in the simulation model presented below. This type of motor is not appropriate for BEV or HEV applications due to weight and efficiency considerations. This motor was used in the simulation because it frequently covered undergraduate engineering education.
The motor model includes some terms and parameters for power loss and time lag while other terms were omitted from the model. The model accounts for power loss in the winding
resistance and time lag due to the energy storage in the magnetic field of the winding inductance.
There is no field power loss because it is a permanent magnet field.

The model does not include power loss due to friction and other rotational losses of hysteresis, eddy current, and windage. The model also does not include the time lag due to energy storage
in the rotor inertia. The motor model is based on the following equations.
Developed Torque is proportional to armature current:
Equation 1: Td(Nm) = Km*IA(Amp) Developed motor torque
Developed Voltage is proportional to armature speed:
Equation 2: VD(Volt) = WD (rad/sec)/Km Developed motor voltage Motor armature input or terminal voltage is equal to the sum of developed voltage plus resistance and inductance voltage drops. In addition, the motor High Side voltage and current are directly connected to, and therefore identical to, the motor controller High Side voltage and current.
Equation 3: VH(Volt) = IH(Amp)*RA(Ohm) + LH(Henry)*di(t)/dt(A/s) + VD(V) Motor Voltage
Shaft output torque is equal to developed torque minus friction loss (Bw) and inertial loss (J*dw(t)/dt). Friction and inertial were not specified in the model and are assumed equal to zero.
Therefore developed torque and output torque are equal in this model. However, the model could be easily modified to include these parameters in the future.
The motor physical constant, Km , is a physical parameter that depends upon the construction of the motor. In the SI system Km has units of (Amp/Nm) or (Volt/(rad/sec)). At the electrical –
mechanical interface inside the motor the developed electrical power (P = IA* VD* Km ) is equal to the developed mechanical power (P = Km* Td* WD).
As noted earlier, in the motor model the mechanical friction and inertia as well as the magnetic power losses have been set to zero. Therefore, the power loss will only occur in the armature
resistance, and the time lag will only occur in the armature inductance.
Motor Controller:
The motor controller is assumed to be an ideal controller with no power loss and no time lag.
The controller simply raises the battery voltage to meet the higher voltage needs of the motor.
The dimensionless constant gain or K ratio of the input and output voltages is determined in order to meet the motor’s needs. The same K ratio is used to adjust the current so that input and output power values are equal.
High side voltage is equal to K times the low side voltage:
Equation 4: VH = K*VL Controller High Side Current
High side current is equal to 1/K times the low side voltage:
Equation 5: IH = (1/K)*VL Controller High Side Voltage
Battery:
The battery is modeled as a voltage source with an internal resistance. The model accounts for internal power loss in the resistance of the battery. There is no time lag component in the model.
The battery is assumed to have a constant internal voltage, EB . The battery terminal voltage,VB , is equal to the sum of the internal voltage and resistance voltage drop. The battery voltage and battery current are equal to the controller low side voltage and current.
Equation 6: VB (Volt) = IA(Amp) *RA(Ohm) + EB(Volt). Battery model calculation
VL (Volt) = IL(Amp) *RA(Ohm) + EB(Volt). Assuming: VB = VL and IA = IL
The battery model uses the current and voltage information from the Motor Controller to calculate the required battery’s internal voltage. This voltage is compared with the actual EB
value to create a battery voltage error, BEER, and that error is used by the PI controller model to adjust the loop gain.
Equation 7: BERR = EB (actual) - EB (calculated) Error Voltage Calculation
Proportional Integral (PI) Controller:
The PI controller accepts the BERR signal from the Battery Model and uses proportional (Kp) and integral (Ki) to calculate the gain K value that is used by the Motor Controller.
Equation 8: K = ( Kp + s*KI)*BERR PI Calculation
The simulation includes eight equations and eight variables.

Simulation Model Blocks
Motor Model
The simulation block for the motor includes Equations 1 – 3 for the motor. The block is shownbelow in Figure 3: Motor Model Block

Motor Controller Model
The simulation block for the Motor Controller includes Equations 4 and 5 for the motor controller. The block is shown below in Figure 4: Motor Controller Model Block

Battery Model
The simulation block for the battery model includes Equations 6 & 7 for the battery. The block is shown below in Figure 5: Battery Model Block

PI Controller Model: The block model includes Equation 8 for the controller.
The Gain (K) of the Motor Controller is determined by the output of the PI Controller model.
The gain has an initial starting value of 0.1. This value was preset within the controller’s integration block to minimize the possibility of a Simulink simulation error due to an algebraic
loop. An algebraic loop is basically a divide by zero operation when the simulation is trying to solve the set of linear equations.
The PI Controller checks to see that the output is not zero. If the output is zero then the controller outputs a small value ( 0.001). This is done to prevent model analysis failure due to dividing by zero when solving the linear equations. The controller also includes a gain limiting block to prevent excess feedback signals.
The block is shown below in Figure 6: PI Controller Model Block

Drive System Model
The Speed and Torque values were written to the MATLAB Workspace, and the values were then read into the model speed and torque look-up tables. The Clock input to the look-up tables
used the following time base values that were setup in the model parameters table: Tmin = 0, Tstep = 0.01, Tstop = 100 seconds.
The displayed Scope values were also written to the MATLAB Workspace as Structures with Time. A MATLAB script was used to pre-load the speed and torque data in the Workspace, Run
the Simulation, obtain the key data from the Scope Structures, and plot the data. The complete Motor Drive Model is shown below in Figure 7: Motor Drive Model.

Simulation results are as follow