Creating a Simulink Model to Generate Duty Cycle

1) Efficient operation of Power electronics

Power electronics is the application of Solid-state electrnics to the control and conversion of electric power.

In contrast to electronic systems concerned with transmission and processing of signals and data, in power electronics substantial amounts of electrical energy are processed.

Power electronic devices may be used as switches, or as amplifiers.

The first high power electronic devices were mercury-arc valves. In modern systems, the conversion is performed with semiconductor switching devices such as diodes, thyristors, and power transistors such as the power MOSFET and IGBT.

Now a days IGBT is most commonly used as switiching device for controlling purposes.

Power electronic devices may be used as switches, or as amplifiers.

An ideal switch is either open or closed and so dissipates no power; it withstands an applied voltage and passes no current, or passes any amount of current with no voltage drop. Semiconductor devices used as switches can approximate this ideal property and so most power electronic applications rely on switching devices on and off, which makes systems very efficient as very little power is wasted in the switch. By contrast, in the case of the amplifier, the current through the device varies continuously according to a controlled input. The voltage and current at the device terminals follow a load line, and the power dissipation inside the device is large compared with the power delivered to the load.

Losses in Power electronic devices

Generally speaking, there are three main contributors to losses in a power semiconductor

• conduction
• switching
• blocking (or reverse leakage)

Conduction Losses:

Conduction losses occur when the device is in full conduction. The current in the device is whatever is required by the circuit and the voltage at its terminals is the voltage drop due to the device itself. These losses are in direct relationship with the duty cycle.

Conduction losses are the product of the current flowing through a switch or diode when it is forward biased (i.e. – turned on) and the voltage drop across it.

Switching Losses:

Switching losses occur when the device is transitioning from the blocking state to the conducting state and vice-versa. This interval is characterized by a significant voltage across its terminals and a significant current through it. The energy dissipated in each transition needs to be multiplied by the frequency to obtain the switching losses.

Power is proportional to the energy stored multiplied by the frequency. Efficiency of a converter decreases with the increase of the switching frequency. But, there exist a certain critical value of a frequency which the efficiency decreases drastically.

Overall losses can be pictured as below given figure.

a) Voltage across the device

b) Current flowing through the device

c) power losses in the device

2) Generation of duty cycle control signal for a simple power converter ciruit using a MATLAB model

A simple DC-DC power convertor is modelled in matlab. Mainly DC-DC convertors are classified as followed.

Buck convertor

• A buck converter (step-down converter) is a DC-to-DC power converter which steps down voltage (while stepping up current) from its input (supply) to its output (load).

Boost convertor

• A boost converter (step-up converter) is a DC-to-DC power converter that steps up voltage (while stepping down current) from its input (supply) to its output (load).

To take advantage of both these convertors a combined model Buck-boost convertor is used widely

Buck-Boost convertor

• The buck–boost converter is a type of DC-to-DC power converter that has an output voltage magnitude that is either greater than or less than the input voltage magnitude. It is equivalent to a flyback converter using a single inductor instead of a transformer.

Operation of a Buck-Boost convertor

• while in the On-state, the input voltage source is directly connected to the inductor (L). This results in accumulating energy in L. In this stage, the capacitor supplies energy to the output load.
• while in the Off-state, the inductor is connected to the output load and capacitor, so energy is transferred from L to C and R.
• If duty cycle is less than 50 percentage then it acts as Buck converter and if duty cycle is more than 50 percentage it acts as boost converter.
• Due to the inverting nature of the converter the output voltage is of negative value.

Formula for output voltage where V_i is input voltage, V_o is output voltage, D is duty cycle

Compared to the buck and boost converters, the characteristics of the inverting buck–boost converter are mainly:

• polarity of the output voltage is opposite to that of the input;
• the output voltage can vary continuously from 0 to (for an ideal converter).

In MATLAB SIMULINK an Buck-Boost converter is modelled in two ways.

• Open loop Buck-Boost converter
• Closed loop Buck-Boost converter

Open Loop Buck-Boost converter

In open loop system there is no feedback control given to control the output voltage of the converter.

The duty cycle can be changed and its effect on the output voltage can be observed

Components used in open loop converter

• DC voltage Source
• Voltage Measurement block
• Series RLC circuit
• Power Diode
• Mosfet (acting as switch)
• Pulse Generator ( for generating duty cycle signals)
• Scope (to view output voltage)

Matlab model of open loop Buck boost converter

Input voltage - 100 V

Duty cycle - 0.6

frequecny - 1000 Hz

Output voltgae is - 100*(0.6/(1-0.4)) = 150 V

The output voltage is viewed using scope block

Closed Loop Buck-Boost converter

In closed loop Buck-boost converter a feedback mechanism is constructed using a PID controller.

Components used in closed loop system

• DC voltage Source
• Voltage Measurement block
• Series RLC circuit
• Power Diode
• Mosfet (acting as switch)
• Pulse Generator ( for generating duty cycle signals)
• Relay
• PID controller
• Gain
• Scope (to view output voltage)

Here, a reference voltage value is given as input and the PID controller will change the duty cycle values such that the output voltage reaches the refernce voltage value.

Input voltage - 48V

Reference voltage - 65V

Output voltgae - -64.82 V

Closed loop system offers much robust ouput control than open loop system.

The controller block subsystem gets the output voltage and reference voltage as input and generates appropriate duty cycle signal to get desired output.

The output voltage variation is seen using scope block

3) Comparison of square wave inverter output voltage with sine modulated one.

Inverters are devices which convert input DC voltage into Output AC voltage

The output nature of sin and square wave inverters are shown as below

Sin wave inverter output Square wave inverter output

Sine wave inverter output is very close to the AC current. It is very pure form compared to Square wave output.

Square wave inverter is has abrubt changes in voltage signals which damages devices.

Many devices gets heated up if you use on Square wave inverter and make humming noise too. Because of this reason square wave inverters in few European countries is banned.

Features	Square Wave Inverter	Sine Wave Inverter
Supported Appliances	Square wave inverters are usually used to support motors alone.	Sine wave inverters are used to support household appliances such as refrigerators ovens, computers, laptops, etc.
Overall Safety Level	Square wave inverters are less reliable and also unsafe to use for appliances.	Sine inverters are highly safe to use.
Noise Interference	Square wave inverters produce a very loud noise when used.	Sine wave inverters produce normal sound only.
Cost	Square wave inverters are less expensive than Sine wave inverters.	Sine wave inverters are more expensive than Square wave inverters.

4) Difference between VFD and Vector control drive.

VFD control

Scalar methods for VFD control work by optimizing the motor flux and keeping the strength of the magnetic field constant, which ensures constant torque production.

Often referred to as V/Hz or V/f control, scalar methods vary both the voltage (V) and frequency (f) of power to the motor in order to maintain a fixed, constant ratio between the two, so the strength of the magnetic field is constant, regardless of motor speed.

Advantages

Easy and simple control method

Constant Torque can be maintained

Disadvantages

Range of control is less than Field oriented control.

Efficiency is reduced due to stator drop compensation.

Vector Control drive (or) Field Orieneted Control

Vector control, also called field-oriented control (FOC), is a variable-frequency drive (VFD) control method in which the stator currents of a three-phase AC electric motor are identified as two orthogonal components that can be visualized with a vector. One component defines the magnetic flux of the motor, the other the torque. The control system of the drive calculates the corresponding current component references from the flux and torque references given by the drive's speed control.

Esentially in FOC the induction motor is controlled similar to a seperatley excited DC motor. Thus gives the ability to control field current and torque current component seperately.

If a,b,c are three pahse currents then following transformations are done.

(a, b, c) → (α, β) (the Clarke transformation), which gives outputs of two coordinate time variant system.

(a, β) → (d, q) (the Park transformation), which gives outputs of two coordinate time invariant system.

The i_sd and i_sq components are contrasted to the references

i_sdref (the flux reference)

i_sqref (the torque reference)

These values are similar to DC current and thus they can be easily controlled by a PID controller. Then park clarke and inverse clarke transformation are done to get the input values for the inverter.

Advantages:

• Improved torque response.
• Torque control at low frequencies and low speed.
• Dynamic speed accuracy.
• Reduction in size of motor, cost and power consumption.
• Four quadrant operation.
• Short-term overload capability.

Disadvantages:

Complex method of control

In Electric Vehicles efficiency is the most important factor. VFD is simple but has higher amount losses in form of staor drop compensation and thus it is not so widely used in the EV industry.

On the other hand Vector control method offers much better control at higher efficiency, hence it is preferred in Electric Vehicles