AN204389 FM0+Family 3-Phase ACIM Scalar Control Associated Part Family: FM0+Family This document describes the scalar control of a 3-phase squirrel cage induction motor. Contents 1 Introduction ............................................................... 1 1.1Purpose ................................................................. 1 1.2Definitions, Acronyms and Abbreviations ................ 1 2 Induction Motor Theory............................................. 2 2.1Motor Category ...................................................... 2 2.2Phasor Model of an Induction Motor ........................ 2 3 Scalar Control of Induction Motor ............................. 5 3.1Scalar Control of Induction Motor ............................ 5 3.2Speed Open Loop V/f Control ................................. 5 1 Introduction 1.1 Purpose 3.3Speed Close Loop Constant Slip Control ................ 7 3.4Field Weakening Control ...................................... 9 3.5Braking Control .................................................... 10 4 Construct a Scalar Control System ........................ 11 5 Summary ................................................................ 11 6 Additional Information ............................................. 12 7 Reference Documents ............................................ 12 Document History............................................................ 13 This document describes the scalar control of a 3-phase squirrel cage induction motor. Firstly, the phasor model of an induction motor is introduced. Based on the scalar model of motor, different prototypes of scalar control schemes are followed. 1.2 Definitions, Acronyms and Abbreviations ACIM AC Induction Motor SVPWM Space Vector Pulse Width Modulation V/f Voltage per Hertz FOC Field Oriented Control DTC Direct Torque Control MTPA Maximum Torque per Ampere www.cypress.com Document No. 002-04389 Rev. *A 1 FM0+Family 3-Phase ACIM Scalar Control 2 Induction Motor Theory 2.1 Motor Category Induction motor, also known as asynchronous motor, is further divided by different stator or rotor types. According to the stator structure, there are single phase, two-phase (symmetrical or asymmetrical), and three-phase induction motors. In another hand, the rotor of an induction motor could be equipped with wounded windings or squirrel cage windings, named squirrel cage induction motor and wound rotor induction motor, respectively. In this document, a three-phase squirrel cage induction motor is described. Figure 1. Motor Category Electric Motors DC Motors AC Motors Synchronous Motors Asynchronous Motors BLDC Squirrel Cage PMSM Wound Rotor Reluctance Motor Step Motor 2.2 Phasor Model of an Induction Motor The phasor model of an induction motor considering the steady state of motor variables is widely cited in scalar control method. Before deriving motor model, a few assumptions are made that: (a) stator windings are identical and sinusoidal distributed, (b) linear magnetic system. The voltage equations with respect to machine variables may be expressed as = + (2-1) 0 = + (2-2) Where is stator voltage phasor, is stator current phasor, is stator flux linkage phasor, is rotor current phasor, and is rotor flux linkage phasor. And is synchronous speed, is rotor electrical speed, and = − is slip speed. For a magnetic linear system, flux linkage phasor is = + (2-3) = + (2-4) In above equations, is stator resistance, is rotor resistance, is mutual inductance, is stator selfinductance, and is rotor self-inductance. www.cypress.com Document No. 002-04389 Rev.*A 2 FM0+Family 3-Phase ACIM Scalar Control Figure 2 shows the phase equivalent circuit of an induction motor. The notation = − is stator leakage inductance, = − is rotor leakage inductance, and = / is slip rate. Figure 2. Phase Equivalent Circuit of Induction Motor / According to equation (2-1) ~ (2-4), stator voltage and current are related as 2 � 2 ) = � + 2+( And stator flux linkage is written as = + 2 +2 ( 2 − 2 ) 2 +( )2 (2-5) +2 � 2 − 2 �− 2 2 +( )2 (2-6) Figure 3 depicts the phasor map of motor variables when an induction motor operates in motor modes. Figure 3. Phasor Map of Motor Variables Image Real To describe a pole-pair induction motor, the generated toque may be expressed with respect to current and voltage as equation (2-7) and (2-8) show. = www.cypress.com 3 2 2 ∙ 2+2 2 | |2 (2-7) Document No. 002-04389 Rev.*A 3 FM0+Family 3-Phase ACIM Scalar Control = 3 = 3 2 2 ∙ � + �2 − �� +[ + ]2 ∙ 2 2 �2 − � +2 2 2 | |2 (2-8) Where |∙| indicates the magnitude of a phasor. Further ignoring the stator resistance, equation (2-8) is simplified as 2 2 2 � � (2-9) Figure 4 shows the torque-speed curve of a typical induction motor where a certain stator voltage is synchronous speed. It can be seen that the electrical torque is a function of the slip speed, and normally motor operates in the green shadowed region with small slip. Figure 4. Torque-Speed Curve of a Typical Induction Motor Startup torque Breaking-down torque Ordinary operation range www.cypress.com Document No. 002-04389 Rev.*A 4 FM0+Family 3-Phase ACIM Scalar Control 3 Scalar Control of Induction Motor 3.1 Scalar Control of Induction Motor The controlling of an induction motor mainly consists two categories: 1. Scalar control Scalar control is a sort of steady state control method, which ignores electric-magnetic dynamics and assumes stationary current and voltage. The most widely implemented scalar control schemes are V/f control and slip control. 2. Vector control Different from scalar control, vector control also controls motor dynamics. Based on the state space motor model, field oriented control (FOC) and direct torque control (DTC) are widely applied. In this section, the scalar control of induction motor is introduced, and both speed open loop and close loop control are conveyed. 3.2 Speed Open Loop V/f Control 3.2.1 Constant V/f Control Theory Constant V/f control is the simplest and least expensive scheme of driving an induction motor, and it is designed based on two observations: 1. The torque-speed characteristic is steep in normal operation region, and the rotor speed is near to the synchronous speed. Therefore, the rotor speed is approximately controlled by controlling the synchronous speed. 2. According to voltage equation (2-1), and ignoring voltage drop on stator resistance, flux linkage is proportional to V/f ratio. To avoid magnetic saturation and optimally utilize stator and rotor core, a constant flux level should be maintained. This suggests a constant V/f ratio should be imposed. Figure 5. Stator Voltage versus Synchronous Speed with Constant V/f Control Constant torque Constant power Voltage limitation Figure 5 shows the stator voltage as function of synchronous speed in constant V/f control scheme. A boost voltage is added in low speed region when take reckon of voltage drop on resistance term. Depending on the specific system, the boost voltage could be designed differently to meet system requirement. www.cypress.com Document No. 002-04389 Rev.*A 5 FM0+Family 3-Phase ACIM Scalar Control 3.2.2 Constant V/f Control Structure Figure 6 shows the block diagram of constant V/f control implemented in speed open loop control. The black solid lines indicates the simplest way to control an induction motor, and the auxiliary red dashed lines are optional compensation schemes for better performance. Each block functions as below: 1. Speed limitation Speed limitation module limits the range of synchronous speed, as well as acceleration/deceleration rate to ensure a proper torque-speed operation point. 2. V/f curve Figure 6. Block Diagram of Speed Open Loop Constant V/f Control 1 ∗ + + Speed limitation ∗ = 0 0 + V/f Curve + SVPWM Voltage boost Slip compensation ACIM Figure 7. Speed Dependent Five-segment V/f Curve Zero/low V/f 1 speed V/f 2 V/f 3 V/f 4 Other than single constant V/f curve, a varying V/f curve is preferred considering toque-speed characteristic. Figure 7 shows an example of a five-segment V/f curve. The flux level varies with function of synchronous speed to meet application requirement. www.cypress.com Document No. 002-04389 Rev.*A 6 FM0+Family 3-Phase ACIM Scalar Control 3. Slip compensation As target speed is approximately controlled by synchronous speed, slip speed always exists, which results in speed error. To perform a higher accuracy speed control, a slip speed compensation scheme is implemented to estimate actual slip speed and super imposed on reference speed. 4. Voltage boost The voltage boost is performed to overcome voltage loss due to stator resistance and dead time effects at low speed region. In case stator current is available, a current based compensation could be adopted. Otherwise an offline boost curve (linear or nonlinear) can also start the motor quickly. 3.3 Speed Close Loop Constant Slip Control When a speed sensor is equipped in a scalar control system for higher speed control accuracy, a constant slip control scheme is a good choice with consideration of control system response and power consumption. From torque equations (2-7), (2-8), and (2-9), an electrical torque is a function of slip speed and current (or voltage). Therefore, if keeping a constant slip level, a torque control is realized by voltage or current control. Figure 8 shows the constant slip control scheme with current sampling. In this scheme, both speed and current loop are implemented to ensure speed response. Due to current feedback, the current amplitude control is introduced. From (2-7), since the slip speed is set as a constant, the electrical torque is uniquely decided by current amplitude. This indicates an independent torque control is realized by current control. Figure 8. Constant Slip Control with Current Feedback + + ∗ ∗ + www.cypress.com Speed limitation 1 PID ∗ = 0 PID Calculation Document No. 002-04389 Rev.*A SVPWM ( ) ACIM 7 FM0+Family 3-Phase ACIM Scalar Control Figure 9. Constant Slip Control without Current Feedback ∗ ∗ + + + + + ∗ 1 Voltage limitation = 0 PID Speed limitation SVPWM ( ) ACIM Figure 9 shows an alternative constant slip control scheme. Because current sampling is removed, a less expensive control is realized. Torque equation (2-9) suggests that when the slip speed is constant, the electrical torque is uniquely decided by V/f ratio. Thus the regulation target of a speed regulator could be V/f ratio or voltage, depending on the case of individual application. 3.3.1 M a x i m u m T o r q u e p e r Am p e r e ( M T P A) C o n t r o l The MTPA control maximizes the torque to current ratio to minimize stator core loss, and its mathematical solution is derived from the following equation: | |2 =0 (3-1) This resultant expression of slip speed is = (3-2) Equation (3-2) indicates that the MTPA control is realized by setting slip speed to equal to the reciprocal of rotor electrical time constant. 3.3.2 Maximum Efficiency Control The maximum efficiency control minimizes the power loss on stator and rotor core. When a motor runs in balanced load condition, which means = , the power loss is calculated as = − = 3( ) − = 2 2 + ( )2 � 2 + � (3-3) And the mathematical solution of maximum efficiency control is derived from the following equation: =0 (3-4) Thus slip speed is determined as below equation. 2 = �2 +2 ≈ www.cypress.com 1 √2 Document No. 002-04389 Rev.*A (3-5) 8 FM0+Family 3-Phase ACIM Scalar Control 3.4 Comparing to MTPA control, the slip speed of maximum efficiency control is approximately 1/√2 of MTPA value. Field Weakening Control Considering stator voltage equation (2-1), and ignoring the voltage drop on stator resistance, the voltage equation is simplified as = (3-6) The field weakening control decreases the stator flux level to increase the rotor speed with maximum available voltage. Investigating flux equation and torque equation, and assuming a constant load torque requirement, stator flux linkage may be written as the function of load torque and slip speed, as equation (3-7) shows: | | = � 2 3 ∙ 2 � 2 +2 � 2 − 2 �� +� 2 � 2 [2 +( )2 ] 2 (3-7) Figure 10 shows the constant torque curve of the induction motor. With a constant load torque, the stator flux is a monotonous function of slip speed, and field weakening control is thus realized by slip speed control. When introducing field weakening control in speed open loop V/f control system, the magnetizing flux level is determined by V/f ratio, and this V/f ratio could be designed by pre-commissioning process. For a speed close-loop control system, since rotor speed is available, slip speed control is a more efficiency way for field weakening control, as Figure 11 shows. Figure 10. Constant Torque Curve of Induction Motor www.cypress.com Document No. 002-04389 Rev.*A 9 FM0+Family 3-Phase ACIM Scalar Control Figure 11. Block Diagram of Field Weakening Control with Speed Feedback ∗ + PID Speed limitation Slip limitation ∗ + 1 = 0 SVPWM = ACIM 3.5 Braking Control The braking control of an ACIM is realized by generating a negative torque. One method is to give a constant negative slip speed, which generates a constant braking torque. However, a considerable voltage boost on DC bus may damage hardware. An alternative method of braking is possible by injecting a DC voltage into a stator. In this case, the braking torque is = − 3 2 2 ∙ 2 2 +( ) 2 | |2 (3-8) And the current amplitude is determined by the DC voltage and stator resistance only, as equation (3-9) shows | | = | | (3-9) Figure 12 shows the braking torque of the DC voltage injection, which depicts the braking torque under different DC voltage level. Particularly, as rotor speed decreases, braking torque increases. Figure 12. Braking Torque of DC Voltage Injection www.cypress.com Document No. 002-04389 Rev.*A 10 FM0+Family 3-Phase ACIM Scalar Control 4 Construct a Scalar Control System Figure 13 shows the selection of control schemes for different application requirements. The easiest way to construct an induction motor driving system is forming a completely open loop control with a proper designed V/f curve and SVPWM, as block 1 shows. In some cases, phase current or DC bus current sampling is implemented for protection or other requirements. If the phase current is available, the slip compensation is thus able to realize a more accurate speed control, as block 2 shows. Once the rotor speed is known, the constant slip control is possible to apply. And this scheme provides a faster response, as well as power consumption saving. Furthermore, block 4 with a phase current sampling offers the best performance since the current is also controlled and torque response is further enhanced. Figure 13. Scalar Control Schemes for Different Applications Speed accuracy (HIGH) Current sensor YES 2 1. Speed open loop V/f control 2. Slip compensation 1 4 1. Constant slip control 2. Speed control 3. Current control Performance And Cost (HIGH) 3 NO Speed sensor 5 1. Speed open loop V/f control 2. NO feedback NO 1. Constant slip control 2. Speed control Load condition (Complicate) YES Summary In this document, the scalar control of induction motor is introduced. Comparing to vector control schemes, the scalar control is less complicated and easy to construct. Depending on application occasions, both speed open loop and close loop schemes are available to meet customer requirements. Additionally, if current sampling is available, current close loop control can be implemented for better performance. www.cypress.com Document No. 002-04389 Rev.*A 11 FM0+Family 3-Phase ACIM Scalar Control 6 Additional Information For more Information on Cypress semiconductor products, visit the following websites: English version address: http://www.cypress.com/cypress-microcontrollers Chinese version address: http://www.cypress.com/cypress-microcontrollers-cn Please contact your local support team for any technical question http://www.cypress.com/cypress-solutionsnetwork 7 Reference Documents [1]. P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Electric Machinery and Drive Systems. IEEE Press, 2002. www.cypress.com Document No. 002-04389 Rev.*A 12 FM0+Family 3-Phase ACIM Scalar Control Document History Document Title: AN204389 – FM0+Family 3-Phase ACIM Scalar Control Document Number: 002-04389 Revision ECN Orig. of Change Submission Date Description of Change ** - CBZH 02/15/2015 Original version *A 5233034 CBZH 04/26/2016 Migrated Spansion Application Note AN710-00001-1v0-E to Cypress format. www.cypress.com Document No. 002-04389 Rev.*A 13 FM0+Family 3-Phase ACIM Scalar Control Worldwide Sales and Design Support Cypress maintains a worldwide network of offices, solution centers, manufacturer’s representatives, and distributors. To find the office closest to you, visit us at Cypress Locations. PSoC® Solutions Products ARM® Cortex® Microcontrollers cypress.com/arm PSoC 1 | PSoC 3 | PSoC 4 | PSoC 5LP Automotive cypress.com/automotive Cypress Developer Community Clocks & Buffers cypress.com/clocks Interface cypress.com/interface Lighting & Power Control cypress.com/powerpsoc Memory cypress.com/memory PSoC cypress.com/psoc Touch Sensing cypress.com/touch USB Controllers cypress.com/usb Wireless/RF cypress.com/wireless Forums | Projects | Videos | Blogs | Training | Components Technical Support cypress.com/support PSoC is a registered trademark and PSoC Creator is a trademark of Cypress Semiconductor Corporation. All other trademarks or registered trademarks referenced herein are the property of their respective owners. Cypress Semiconductor 198 Champion Court San Jose, CA 95134-1709 Phone Fax Website : 408-943-2600 : 408-943-4730 : www.cypress.com © Cypress Semiconductor Corporation, 2015-2016. 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You shall indemnify and hold Cypress harmless from and against all claims, costs, damages, and other liabilities, including claims for personal injury or death, arising from or related to any Unintended Uses of Cypress products. Cypress, the Cypress logo, Spansion, the Spansion logo, and combinations thereof, PSoC, CapSense, EZ-USB, F-RAM, and Traveo are trademarks or registered trademarks of Cypress in the United States and other countries. For a more complete list of Cypress trademarks, visit cypress.com. Other names and brands may be claimed as property of their respective owners. www.cypress.com Document No. 002-04389 Rev.*A 14

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