Vector Control of Im

SÖ 080121

Electrical Machines and Drives (EJ2200)

Project Work

Vector Control of Induction Motor

Objectives:

The objective of this project is to become familiar with most aspects of a vector controlled induction motor in a simulation environment. After completing the project, you should be able to:

Identify the equivalent parameters of an induction machine. Adapt the machine model to different reference systems (Transformation between

two and three phase systems; transformation between stator reference frame and synchronous reference frame).

Implement current and speed regulation loops and calculate PI-controllers. Implement position estimation (sensorless control) and analyze its limitations. Implement a PWM inverter.

Requirements:

To pass the project, you need to: Register as a group of max. two persons before February 21, 2009 (see task 3.1). Develop simulation models for the different tasks and analyze the results. Write a technical report presenting the outcomes of your project. Submit the report before March 20, 2009 and implement possible corrections

asked by the project assistant by April 17, 2009.

Reference:

Electrical Machines and Drives Compendium, Division of Electrical Machines and Power Electronics, KTH, Sweden.

The relevant chapters are chapter 4 and 5.

EJ2200: Project Work: Vector Control of the Induction Motor

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1. Project assistance Project e-mail:

All correspondence should be sent to [email protected].

Project assistants Rathna Chitroju, Teknikringen 33, room 3324

Role of the project assistant:

Do not hesitate to contact the project assistants if you have problems with the simulation models or the project tasks. The project assistants can be reached in their rooms during normal working hours or by sending an e-mail to the above address. 2. Rules for this project work:

Plagiarism:

It is not allowed to complete the project using the parameter values given by another group.

It is not allowed to copy simulation models (even parts) developed by another group.

It is not allowed to copy any part of the report submitted by another group. Reports will be checked for plagiarism.

However, it is encouraged to discuss different possibilities to solve the tasks with other students.

Report:

The results are to be presented in a written report of approximately 12-15 pages. It can be written in either English or Swedish. The content of the report should follow the normal format for a technical paper including:

Abstract (Summary) (maximum 150 words)

Explanation of the methods you applied.

Presentation of the results, including useful and commented simulation curves.

Discussion and analysis of the results.

Appendix with all your simulation models.

Think about the balance between the amount of text and pictures and the quality of the appearance. If you do not have your own report template, the course compendium can be taken as an example.

Late submissions: Delayed submissions (i.e. after deadline) will be corrected after the re-sit examination in May 2008.


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3. Tasks This project is done in Simulink®, which allows the simulation of differential equations described by blocks available in a large library. Simulink® is embedded in Matlab®. All the simulations are based on an induction motor (IM) model, that is implemented in the Simulink® model "imsim.mdl" (see Figure 1). The file can be downloaded from the course web-page http://www.eme.ee.kth.se/undergraduate.php?course=EJ2200

Figure 1: Main Simulink® model "imsim.mdl".

The IM model has the following connections and parameters:

Inputs: stator voltage vector components in stator coordinates (u_alpha, u_beta).

Outputs: stator current (i_alpha, i_beta) and rotor flux (psi_alpha, psi_beta) vector components in stator coordinates, rotor speed ωr.

Electrical parameters: rotor resistance rR′ , stator resistance Rs, leakage inductance Ll and magnetising inductance Lm.

Mechanical parameter: viscous damping constant b.

The rotor speed is governed by the following differential equation:

re L e r

dJ b

dtω

τ τ τ ω= − = −

where J is the moment of inertia. It was identified as 50 p.u. in the used induction motor and is already set inside the IM model. As seen from the equation the load torque is assumed to increase linearly with the rotor speed rω . The load torque can be adjusted through the constant b.

All quantities in the simulation are given in normalised or per unit (p.u.) values, which is common practice in electrical engineering. p.u. notation makes design and control algorithms applicable for similar systems of different size. Normalised values also simplify the programming by defining the same range and scale for all quantities, which is an advantage especially in fixed point digital signal processors (DSP. Fixed point DSP's are today fast and cheap and widely used in industrial applications.


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The base values of the induction motor used in the first laboratory work are given below. From these fundamental base values, all other machine parameters can be normalised.

The base voltage Ubase is the nominal line-to-neutral stator voltage (230 V / 3 ).

The base current Ibase is the nominal stator current (7.8 A). The base angular frequency ωbase can be considered to be 2π · 50 rad/s. The angular

frequency defines the normalised time (tn = ωbase · t).

Task 3.1:

The measured machine parameters are obtained during the first laboratory work called "Induction Machines". Normalise the electrical machine parameters Rs, rR′ , Lm and Ll . Check that the normalised machine parameters are within a reasonable range. Enter the values in the IM model. From now on, the electrical machine parameters should not be changed anymore.

Send an email to [email protected] containing the following information: Measured machine parameters. Normalised machine parameters. Name, personal number and email-address of both team members.

Task 3.2:

Identify the induction machine parameters Rs, rR′ , Lm, Lsl and Lrl by simulating the no-load and short-circuit tests you conducted during the laboratory work. (It can be assumed that Lsl = Lrl = Ll/2).

Task 3.3:

The nominal load of the motor is simulated by putting the viscous damping constant b equal to 0.5. Implement a current control loop in the synchronous reference frame using a constant stator frequency. The goal is to control the currents so that a rise time of 1 ms is obtained.

Task 3.4:

Analyze the influence of the cross-coupling. Implement a cross-coupling cancellation.

Task 3.5:

Modify the coordinate transformation so that the synchronous reference frame is field oriented. The choice of flux estimation strategy is yours but the flux components of the IM model should not be used. Check that your motor has the right level of magnetization ( sdψ should be equal to 1 p.u. at steady-state).


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Task 3.6:

Implement a closed-loop speed control according to Figure 2. Tune the PI-controller so that the peak q-axis current is equal to 1 p.u for a speed step from 0.5 to 0.6 p.u. The speed response should not have any overshoot and the d-axis component of the flux should reach its steady-state value before the speed step is applied.

refrω

(flux reference) refsdi

(torque reference) refsqi rω

Figure 2: Vector control system augmented with a speed control loop.

Task 3.7:

Evaluate the parameter sensitivity of the field orientation model you implemented by changing the rotor time constant. What happens to the speed and the flux levels?

Task 3.8:

Finally, replace the direct supply of stator voltage components with a three-phase PWM inverter. How does it affect the currents, the flux orientation and the speed control?

The PWM inverter can be modelled in different ways. Observe that the PWM should create a three-phase voltage whereas the induction machine model is in αβ -coordinates.

4. Simulink® and Matlab®

4.1 Getting started

All simulations are performed in Simulink® (dynamic system simulation in Matlab®). In order to get started, it is important to create a good working environment:

Download the IM model "imsim.mdl" and save it in the directory where you want to work. You find the file on http://eme.ekc.kth.se/undergraduate.php?course=EJ2200.

Open the file imsim.mdl by double-clicking on the icon. This automatically opens Matlab® and Simulink®. Then save it first under a new name, e.g. "task1.mdl", before you start building new models. Save the final model from every task - you will need it for documentation and possible corrections.


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You can also save your simulation results by adding a 'To workspace' block in your model for each signal you want to save. After running the simulation, you can use the 'save' command in the Matlab® window, e.g. 'save xyz.mat t wr' to save t and wr in the file "xyz.mat"). In the future, you can load this file in the workspace with 'load xyz.mat'.

To simulate, select in the model window 'Simulation Start'. Check before that the simulation parameters are OK by selecting 'Simulation Parameters'. You can choose the numerical method to solve the differential equations, the start and stop time and the min and max steps as well as the tolerance (1e-3). Usually, the Runge-Kutta method with order 4 or 5 and same value for min and max time step works well. Adapt the stop and step time so that the signals look good and the number of samples is not too high.

4.2 Working in Simulink® To add a block in a model, select it from the library and move it to the model with

the left mouse button pressed. You can duplicate any block already in the model by clicking with the right mouse button on it and move it with the mouse button pressed.

To draw a line between two blocks, click on the output of the first block with the left mouse button and move to the input of the other block while keeping the mouse button pressed. Alternatively you can first choose the first block (by left clicking on it) and then left click on the second block while holding the 'Crtl' button.

If you double clicking on a block, a small window with the parameters of the block and the help button appears. You can then change the parameters of the block.

In Matlab® you have access to the help files by typing 'help name_function'. To know more about a block, read its help file. Alternatively, create a new model with the block, an auto-scale graph and a generator input and run a simulation.

5. Report guidelines Report guidelines can be downloaded from the course web page.

Documents

Vector Control of Im