AN204389 FM0+ Family 3-Phase ACIM Scalar Control.pdf

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
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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
𝑽𝒔 = 𝑅𝑠 𝑰𝒔 + 𝑗𝜔𝑒 𝝀𝒔
(2-1)
0 = 𝑅𝑟 𝑰𝒓 + 𝑗𝜔𝑠 𝝀𝒓
(2-2)
Where 𝑽𝒔 is stator voltage phasor, 𝑰𝒔 is stator current phasor, 𝝀𝒔 is stator flux linkage phasor, 𝑰𝒓 is rotor current
phasor, and 𝝀𝒓 is rotor flux linkage phasor. And 𝜔𝑒 is synchronous speed, 𝜔𝑟 is rotor electrical speed, and
𝜔𝑠 = 𝜔𝑒 − 𝜔𝑟 is slip speed.
For a magnetic linear system, flux linkage phasor is
𝝀𝒔 = 𝐿𝑠 𝑰𝒔 + 𝐿𝑀 𝑰𝒓
(2-3)
𝝀𝒓 = 𝐿𝑀 𝑰𝒔 + 𝐿𝑟 𝑰𝒓
(2-4)
In above equations, 𝑅𝑠 is stator resistance, 𝑅𝑟 is rotor resistance, 𝐿𝑀 is mutual inductance, 𝐿𝑠 is stator selfinductance, and 𝐿𝑟 is rotor self-inductance.
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Figure 2 shows the phase equivalent circuit of an induction motor. The notation 𝐿𝑙𝑠 = 𝐿𝑠 − 𝐿𝑀 is stator leakage
inductance, 𝐿𝑙𝑟 = 𝐿𝑟 − 𝐿𝑀 is rotor leakage inductance, and 𝑠 = 𝜔𝑠 /𝜔𝑒 is slip rate.
Figure 2. Phase Equivalent Circuit of Induction Motor
𝑰𝑠
𝑽𝑠
𝑅𝑠
𝐿𝑙𝑠
𝐿𝑀
𝑅𝑟 /𝑠
𝐿𝑙𝑟
𝑰𝑟
𝐼𝑚
According to equation (2-1) ~ (2-4), stator voltage and current are related as
𝜔 𝜔 𝐿2 𝑅𝑟
� 𝑰𝒔
2
𝑠 𝑟)
𝑟
𝑒 𝑀
𝑽𝒔 = �𝑅𝑠 + 𝑅2𝑠+(𝜔
𝐿
And stator flux linkage is written as
𝝀𝒔 =
+𝑗
𝐿𝑠 𝑅𝑟2 +𝜔𝑠2 (𝐿𝑠 𝐿2𝑟 −𝐿𝑟 𝐿2𝑀 )
𝜔𝑒 𝑰𝒔
𝑅𝑟2 +(𝜔𝑠 𝐿𝑟 )2
(2-5)
𝐿𝑠 𝑅𝑟 +𝜔𝑠2 �𝐿𝑠 𝐿2𝑟 −𝐿𝑟 𝐿2𝑀 �−𝑗𝜔𝑠 𝑅𝑟 𝐿2𝑀
𝑰𝒔
𝑅𝑟2 +(𝐿𝑟 𝜔𝑠 )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
𝑽𝑠
𝝀𝑠
𝑰𝑠
Real
To describe a 𝑃 pole-pair induction motor, the generated toque may be expressed with respect to current and voltage
as equation (2-7) and (2-8) show.
𝑇𝑒 =
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3𝑃
2
𝐿2 𝑅 𝜔
∙ 𝑅2𝑀+𝐿𝑟2 𝜔𝑠2 |𝑰𝒔 |2
𝑟
𝑟
(2-7)
𝑠
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𝑇𝑒 =
3𝑃
𝑇𝑒 =
3𝑃
2
𝐿2𝑀 𝑅𝑟 𝜔𝑠
∙
�𝑅𝑠 𝑅𝑟 +𝜔𝑠 𝜔𝑒 �𝐿2𝑀 −𝐿𝑠 𝐿𝑟 �� +[𝑅𝑟 𝜔𝑒 𝐿𝑠 +𝑅𝑠 𝜔𝑠 𝐿𝑟 ]2
∙
2
𝜔𝑠2 �𝐿2𝑀 −𝐿𝑠 𝐿𝑟 � +𝑅𝑟2 𝐿2𝑠 𝜔𝑒
2
|𝑽𝒔 |2
(2-8)
Where |∙| indicates the magnitude of a phasor. Further ignoring the stator resistance, equation (2-8) is simplified as
2
𝐿2𝑀 𝑅𝑟 𝜔𝑠
𝑽 2
� 𝒔�
(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
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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
𝑉𝑠
Constant torque
𝑉𝑏𝑜𝑜𝑠𝑡
Constant
power
Voltage
limitation
𝜔𝑒
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.
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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
𝜃𝑒
1
𝑠
𝜔𝑟∗ +
+
Speed
limitation
𝜔𝑒∗
𝑉𝑑 = 0
𝑉𝑠0 +
V/f
Curve
+
𝑉𝑏𝑜𝑜𝑠𝑡
SVPWM
𝑉𝑞
Voltage
boost
Slip
compensation
ACIM
𝑖𝑎𝑏𝑐𝑠
Figure 7. Speed Dependent Five-segment V/f Curve
𝑉𝑠
Zero/low V/f 1
speed
V/f 2
V/f 3
V/f 4
𝜔𝑒
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.
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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
𝜔𝑟
+
+
𝜔𝑠∗
𝜔𝑟∗ +
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Speed
limitation
𝜔𝑟
𝜔𝑒
1
𝑠
PID
𝐼𝑠∗
𝐼𝑠
𝜃𝑒
𝑉𝑑 = 0
PID
𝐼𝑠
Calculation
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SVPWM
𝑉𝑠 (𝑉𝑞 )
𝑖𝑎𝑏𝑐𝑠
ACIM
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FM0+Family 3-Phase ACIM Scalar Control
Figure 9. Constant Slip Control without Current Feedback
𝜔𝑠∗
𝜔𝑟∗ +
+
𝜔𝑟
+
+
+
𝜔𝑒∗
𝜔𝑒
1
𝑠
Voltage
limitation
𝑉𝑑 = 0
PID
𝜔𝑟
Speed
limitation
𝜃𝑒
SVPWM
𝑉𝑠 (𝑉𝑞 )
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:
𝜕
𝑇𝑒
𝜕𝜔𝑠 |𝑰𝒔 |2
=0
(3-1)
This resultant expression of slip speed is
𝜔𝑠 =
𝑅𝑟
(3-2)
𝐿𝑟
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 𝑇𝑙𝑜𝑎𝑑 = 𝑇𝑒 , the power loss is calculated as
𝑃𝑙𝑜𝑠𝑠 = 𝑃𝑖𝑛𝑝𝑢𝑡 − 𝑃𝑜𝑢𝑡𝑝𝑢𝑡 = 3𝑟𝑒𝑎𝑙(𝑽𝒔 𝑰𝒔 ) − 𝑇𝑙𝑜𝑎𝑑 𝜔𝑟 =
2𝑇𝑙𝑜𝑎𝑑 𝑅𝑠 𝑅𝑟2 +𝑅𝑠 (𝜔𝑠 𝐿𝑟 )2
𝑃
�
𝜔𝑠 𝐿2𝑀 𝑅𝑟
+ 𝜔𝑠 �
(3-3)
And the mathematical solution of maximum efficiency control is derived from the following equation:
𝜕
𝑃
𝜕𝜔𝑠 𝑙𝑜𝑠𝑠
=0
(3-4)
Thus slip speed is determined as below equation.
𝑅 𝑅2
𝜔𝑠 = �𝐿2 𝑅 𝑠+𝐿𝑟2 𝑅 ≈
𝑀 𝑟
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𝑟 𝑠
1 𝑅𝑟
√2 𝐿𝑟
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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
𝑽𝒔 = 𝑗𝜔𝑒 𝝀𝒔
(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:
|𝝀𝒔 | = �
2𝑇𝑙𝑜𝑎𝑑
3𝑃
∙
2
�𝐿𝑠 𝑅𝑟2 +𝜔𝑠2 �𝐿𝑠 𝐿2𝑟 −𝐿𝑟 𝐿2𝑀 �� +�𝜔𝑠 𝑅𝑟 𝐿2𝑀 �
𝐿2𝑀 𝑅𝑟 𝜔𝑠 [𝑅𝑟2 +(𝐿𝑟 𝜔𝑠 )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
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Figure 11. Block Diagram of Field Weakening Control with Speed Feedback
𝜔𝑟∗ +
PID
𝜔𝑟
Speed
limitation
Slip
limitation
𝜔𝑠∗
+
1
𝑠
𝑉𝑑 = 0
𝜃𝑒
SVPWM
𝑉𝑞 = 𝑉𝑚𝑎𝑥
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
𝑇𝑒 = −
3𝑃
2
𝐿2 𝑅 𝜔
𝑀 𝑟 𝑟
∙ 𝑅2 𝑅2 +(𝑅
𝜔 𝐿
𝑠
𝑟
𝑠
𝑟 𝑟)
2
|𝑉𝐷𝐶 |2
(3-8)
And the current amplitude is determined by the DC voltage and stator resistance only, as equation (3-9) shows
|𝑰𝒔 | =
|𝑽𝒔 |
(3-9)
𝑅𝑠
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
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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.
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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.
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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.
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circuit described in this document. Any information provided in this document, including any sample design information or programming code, is
provided only for reference purposes. It is the responsibility of the user of this document to properly design, program, and test the functionality and
safety of any application made of this information and any resulting product. Cypress products are not designed, intended, or authorized for use as
critical components in systems designed or intended for the operation of weapons, weapons systems, nuclear installations, life-support devices or
systems, other medical devices or systems (including resuscitation equipment and surgical implants), pollution control or hazardous substances
management, or other uses where the failure of the device or system could cause personal injury, death, or property damage (“Unintended Uses”). A
critical component is any component of a device or system whose failure to perform can be reasonably expected to cause the failure of the device or
system, or to affect its safety or effectiveness. Cypress is not liable, in whole or in part, and you shall and hereby do release Cypress from any claim,
damage, or other liability arising from or related to all Unintended Uses of Cypress products. 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
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