1. Electromechanical Motor Control
석사 1기 김대정
Systems & control Lab.

2. 목차 Modulation for Power Electronic Converters
2. Current control of Generalized Load 2.1 Current Control of Single-Phase Load
2.2 Current Control of a Three-Phase Load
Drive Principles
Concepts and control of DC machine
Synchronous Machine Modeling Concepts
Control of Synchronous Machine Drives
Switched Reluctance Drive Systems

3. Hysteresis Current Control
2. INTRODUCTION
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Current Control Targets
Current Control Techniques
A Single-Phase Load
Hysteresis Current Control
Model Based Current Control & Augmented Model Based Current Control
A Three-Phase Load

4. 2.1 Current Control of Single-Phase Load
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▣ Hysteresis Current Control
the output state y = −1, then the output will change to y = 1 when the condition x ≥ ε/2 occurs. Vice-versa, when the output is y = 1, a change to y = −1 will take place as soon as the condition x ≤ −ε/2 occurs.

5. 2.1 Current Control of Single-Phase Load
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▣ Hysteresis Current Control
: user defined reference current
: load current
u : load voltage
Z : load impedance
Sw : switch
This topology is readily adapted to hysteresis type current control by adding a current controller module and a current sensor.
The current controller module must provide the switching signals for the converter on the basis of the instantaneous measured load current and user defined reference current.

6. 2.1 Current Control of Single-Phase Load
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▣ Hysteresis Current Control
Comparator A : A normal hysteresis type comparator with a bipolar output ±1
Comparator B : To generate a logic signal Sw used by the two switches

7. 2.1 Current Control of Single-Phase Load
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▣ Hysteresis Current Control – Tutorial 1
▣ Pros and Cons of Hysteresis Current Control
The structure is simple.
The transient response nature is excellent.
Pros
The acoustic noise signature that may appear with this type of control strategy.
Cons

8. 2.1 Current Control of Single-Phase Load
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▣ Model Based Current Control
: required voltage needed to drive said error to zero
: load voltage
: reference current
: load current
: load impedance
: non-sampled reference current
: typical (for PWM based control) converter current

9. 2.1 Current Control of Single-Phase Load
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▣ Model Based Current Control
The converter generates (during a given sampling interval Ts) an average voltage quantity U(tk) which corresponds to the reference average voltage value U∗(tk) that is provided by the controller module.
The control objective aimed at driving the current error to zero during each sample interval may be written as
(Shown figure. 3.6)
(3.1)
(needed to drive said error to zero)
(3.2)
The load is formed by a series network which consists of a resistance R, inductance L and voltage source ue.
(3.3)
Use of (3.3) with (3.2) allows the latter to be written as
(3.4)
A first order approximation technique may be used, provided the sampling time is sufficiently small, which leads to
(3.5)

10. 2.1 Current Control of Single-Phase Load
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▣ Model Based Current Control
(Shown figure. 3.6)
(3.6)
Use of (3.6) with (3.5) leads to
(3.7)
(3.8a)
(3.8b)
the condition L/Ts > R/2 should be satisfied

11. 2.1 Current Control of Single-Phase Load
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▣ Model Based Current Control – Tutorial 2
▣ Pros and Cons of Model Based Current Control
It is not outweigh the acoustical noise signature that comes with the use of a variable switching frequency hysteresis current controller.
Pros
In practical implementations, the PI controller is prone to windup.
A priori knowledge of the load is required.
Cons

12. 2.1 Current Control of Single-Phase Load
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▣ Augmented Model Based Current Control =
(Shown figure. 3.6)
(3.9)
▣ Pros and Cons of Augmented Model Based Current Control
This type of controller does not require access to the measured current. (Open loop control mode)
Pros
In reality such errors exist in which case a PI controller with reduced gain.
It must be considered with caution as the model may contain differential terms, which can be prone to noise.
Cons

13. 2.2 Current Control of a Three-Phase Load
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▣ Introduction
: the load voltage vector
: a flux vector
: current reference vector
: angle with respect to the stationary reference frame
: the rotational speed of the vector
(3.10)
the term Ri is small in comparison to the term L di/dt and is neglected in this analysis.
(3.11)
For changing the instantaneous current vector from i→ i + Δi over a time interval ΔT in terms of the direction and amplitude.
The variable ΔT determines the actual magnitude of current change in a particular direction as may be observed.

14. 2.2 Current Control of a Three-Phase Load
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▣ Three-Phase Hysteresis Current Control
: reference current vector
: measured current vector
: load voltage vector
The load module consists of three star connected load phases.
The controller outputs are the three converter switch signals Swa, Swb, Swc, which in effect identify the voltage vector u{Swa,Swb,Swc} and its required duration ΔT to minimize the error between measured and reference current vectors.

15. 2.2 Current Control of a Three-Phase Load
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▣ Three-Phase Hysteresis Current Control
: measured current vector
: direct-axis current vector reference
: quadrature-axis current vector reference
: size of the box
: the load voltage vector
: angle with respect to the stationary reference frame
The orientation of this reference frame is realized with the aid of the voltage vector ue and a Cartesian to polar conversion module which identifies the instantaneous angle of vector ue with respect to a stationary reference frame.
A phase angle shift of −π/2 rad is to arrive at the required reference angle ρe for the direct-axis of the synchronous reference frame.
A box rules module which generates the required converter vector u{Swa,Swb,Swc}

16. 2.2 Current Control of a Three-Phase Load
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▣ Three-Phase Hysteresis Current Control
: the eight converter voltage vectors
: voltage vector
: flux vector = -
Tied to the current reference vector is a box shaped contour with sides numbered 1 to 4.
Boundary 1: Check if the active vector u{Swa,Swb,Swc} currently in use lags the vector ue. If this is the case, select the next counter clockwise active vector. If for example vector u{010} is the active vector in use, the controller would switch to vector u{011} when boundary 1 was encountered by the error vector endpoint.
Boundary 2: Check which active vector u{Swa,Swb,Swc} is in use and switch to the nearest (with the minimum number of switching actions) zero vector. If for example vector u{010} is the active vector, then the controller would switch to zero vector u{000}, when boundary 2 was encountered by the error vector endpoint.

17. 2.2 Current Control of a Three-Phase Load
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▣ Three-Phase Hysteresis Current Control
Boundary 3: Check if the active vector u{Swa,Swb,Swc} currently in use leads the vector ue. If this is the case, select the next clockwise active vector. If for example vector u{011} is the active vector in use, the controller would switch to vector u{010}, when boundary 3 was encountered by the error vector endpoint.
B oundary 4: Check which active vector u{Swa,Swb,Swc} was used last and reactivate this vector. For example, if vector u{010} was active prior to encountering the zero vector u{000}, then the controller would switch to vector u{010}, when boundary 4 was encountered by the error vector end-point.

18. 2.2 Current Control of a Three-Phase Load
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▣ Three-Phase Hysteresis Current Control – Tutorial 3

19. 2.2 Current Control of a Three-Phase Load
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▣ Three-Phase Hysteresis Current Control – Tutorial 3

20. 2.2 Current Control of a Three-Phase Load
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▣ Three-Phase Hysteresis Current Control – Tutorial 3

21. 2.2 Current Control of a Three-Phase Load
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▣ Model Based Three-Phase Current Control
: reference current vector
: measured current vector
: load voltage vector
: required voltage needed to drive said error to zero
may be rewritten in space vector form as
(3.15)
The task of the controller module is to determine the average voltage reference space vector U ∗(tk) that is needed to satisfy condition 3.15.
(3.16)

22. 2.2 Current Control of a Three-Phase Load
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▣ Model Based Three-Phase Current Control
(3.17)
Transformation of the vectors u,i, ue to this complex plane requires use of the general vector transformation
(3.18)
The sampling frequency 1/Ts is normally much higher than the vector rotation speed ωe in which case the term can be taken at unity value.
(3.19)
Substituting (3.19) into (3.18) and combining the real and imaginary terms of the latter yields
(3.21a)
(3.21b)

23. 2.2 Current Control of a Three-Phase Load
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▣ Model Based Three-Phase Current Control
Clearly identifiable are the terms with gain L which serve to decouple the direct axis (active) and quadrature-axis (reactive) current components.
present is the back-EMF voltage term ue which appears in the quadrature-axis. Furthermore, a differentiator module is used to determine the frequency ωe of the load vector ue or flux vector ψe.

24. 2.2 Current Control of a Three-Phase Load
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▣ Augmented Three-Phase Model Based Current Control
(3.22a)
(3.22b)

25. 2.2 Current Control of a Three-Phase Load
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▣ Frequency Spectrum of Hysteresis and Model Based Current Controllers
Figure 3.23 shows the spectrum for both control techniques of the phase voltage with respect to the amplitude of the fundamental component over a frequency range 0 → 10 kHz.

26. 감사합니다