Electromechanical Motor Control 석사 1기 김대정 2015. 10. 6 Systems & control Lab.

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

Hysteresis Current Control 2. INTRODUCTION 3 / 26 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

2.1 Current Control of Single-Phase Load 4 / 26 ▣ 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.

2.1 Current Control of Single-Phase Load 5 / 26 ▣ 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.

2.1 Current Control of Single-Phase Load 6 / 26 ▣ 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

2.1 Current Control of Single-Phase Load 7 / 26 ▣ Hysteresis Current Control – 3.3.1 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

2.1 Current Control of Single-Phase Load 8 / 26 ▣ 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

2.1 Current Control of Single-Phase Load 9 / 26 ▣ 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)

2.1 Current Control of Single-Phase Load 10 / 26 ▣ 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

2.1 Current Control of Single-Phase Load 11 / 26 ▣ Model Based Current Control – 3.3.2 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

2.1 Current Control of Single-Phase Load 12 / 26 ▣ 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

2.2 Current Control of a Three-Phase Load 13 / 26 ▣ 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.

2.2 Current Control of a Three-Phase Load 14 / 26 ▣ 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.

2.2 Current Control of a Three-Phase Load 15 / 26 ▣ 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}

2.2 Current Control of a Three-Phase Load 16 / 26 ▣ 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.

2.2 Current Control of a Three-Phase Load 17 / 26 ▣ 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.

2.2 Current Control of a Three-Phase Load 18 / 26 ▣ Three-Phase Hysteresis Current Control – 3.3.3 Tutorial 3

2.2 Current Control of a Three-Phase Load 19 / 26 ▣ Three-Phase Hysteresis Current Control – 3.3.3 Tutorial 3

2.2 Current Control of a Three-Phase Load 20 / 26 ▣ Three-Phase Hysteresis Current Control – 3.3.3 Tutorial 3

2.2 Current Control of a Three-Phase Load 21 / 26 ▣ 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)

2.2 Current Control of a Three-Phase Load 22 / 26 ▣ 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)

2.2 Current Control of a Three-Phase Load 23 / 26 ▣ 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.

2.2 Current Control of a Three-Phase Load 24 / 26 ▣ Augmented Three-Phase Model Based Current Control (3.22a) (3.22b)

2.2 Current Control of a Three-Phase Load 25 / 26 ▣ 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.

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