TIDUF56 January   2024

 

  1.   1
  2.   Description
  3.   Resources
  4.   Features
  5.   Applications
  6.   6
  7. 1System Description
    1. 1.1 Terminology
    2. 1.2 Key System Specifications
  8. 2System Overview
    1. 2.1 Block Diagram
    2. 2.2 Design Considerations
    3. 2.3 Highlighted Products
      1. 2.3.1 TMS320F28P65x-Q1
      2. 2.3.2 DRV3255-Q1
      3. 2.3.3 LM25184-Q1
      4. 2.3.4 TCAN1044A-Q1
  9. 3System Design Theory
    1. 3.1 Three-Phase PMSM Drive
      1. 3.1.1 Field-Oriented Control of PM Synchronous Motor
        1. 3.1.1.1 Space Vector Definition and Projection
          1. 3.1.1.1.1 ( a ,   b ) ⇒ ( α , β ) Clarke Transformation
          2. 3.1.1.1.2 α , β ⇒ ( d ,   q ) Park Transformation
        2. 3.1.1.2 Basic Scheme of FOC for AC Motor
        3. 3.1.1.3 Rotor Flux Position
    2. 3.2 Field Weakening (FW) Control
  10. 4Hardware, Software, Testing Requirements, and Test Results
    1. 4.1 Hardware Requirements
      1. 4.1.1 Hardware Board Overview
      2. 4.1.2 Test Conditions
      3. 4.1.3 Test Equipment Required for Board Validation
    2. 4.2 Test Setup
      1. 4.2.1 Hardware Setup
      2. 4.2.2 Software Setup
        1. 4.2.2.1 Code Composer Studio™ Project
        2. 4.2.2.2 Software Structure
    3. 4.3 Test Procedure
      1. 4.3.1 Project Setup
      2. 4.3.2 Running the Application
    4. 4.4 Test Results
  11. 5Design and Documentation Support
    1. 5.1 Design Files
      1. 5.1.1 Schematics
      2. 5.1.2 BOM
      3. 5.1.3 PCB Layout Recommendations
        1. 5.1.3.1 Layout Prints
    2. 5.2 Tools and Software
    3. 5.3 Documentation Support
    4. 5.4 Support Resources
    5. 5.5 Trademarks

Space Vector Definition and Projection

The 3-phase voltages, currents, and fluxes of AC motors can be analyzed in terms of complex space vectors. With regard to the currents, the space vector can be defined as follows. Assuming that ia, ib, ic are the instantaneous currents in the stator phases, then the complex stator current vector is defined in Equation 3.

Equation 3. i ¯ s = i a + α i b + α 2 i c

where

  • α = e j 2 3 π and α 2 = e j 4 3 π represent the spatial operators

Figure 3-3 shows the stator current complex space vector.

GUID-20210322-CA0I-RGRT-RLDX-DWJZZPRJBHXJ-low.svg Figure 3-3 Stator Current Space Vector and Component in (a, b, c) Frame

where

  • a, b, and c are the three-phase system axes

This current space vector depicts the three-phase sinusoidal system which still needs to be transformed into a two time invariant co-ordinate system. This transformation can be split into two steps:

  • ( a ,   b ) ( α , β ) (Clarke transformation) which outputs a 2-coordinate time-variant system
  • α , β ( d ,   q ) (Park transformation) which outputs a 2-coordinate time-invariant system