design and analysis of discrete current regulators for vsis · q,ref (t) = 0v, v d,ref (t) = 50v, e...
TRANSCRIPT
Institute of Electrical Power Engineering | Power Electronics and Electrical Drives
University of Rostock, Albert-Einstein-Str. 2, 18059 Rostock, Germany
Michael Schütt, Hans-Günter Eckel
Design and Analysis of Discrete
Current Regulators for VSIs
Introduction
Compared dq-Decoupling Techniques
A1z−1
1 ─ A3z−1
j A4
A1
+-
j A2
A1
A1^
A2^
A1^ 2
+ A2^ 2
j
++A1
^
A2^
++
j A4^
A1^
KITs
1 ─ z−1
Kp ++
+-
* -
≈1
MICC -
Manipulated Input
Cross-CouplingMID - Manipulated Input Decoupling
DCCSFb - Decoupling Cross-Coupling State Feedback
DID – Disturbance Input Decoupling
Control Structure
-+
Idq (z) Idq (z)
Edq (z)
Vdq (z)
K
*
++- e−Ts/
e−j∙e[k − 1]∙Ts
+- +1
1 – z−1
Idq (z)
Idq (z)
Vdq (z)
1 ─ e−Ts/
R
R e
−je[k ─ 1]Ts e−Ts/
1 ─ e−Ts/
+e−je[k ─ 1]Ts eje[k ─ 1]Ts
R e−Ts/s
1 ─ e−Ts/
≈1
MICCMID
DCCSFb
Idq (z) Vdq (z)
z−1 +V‘dq (z)
+-
• This paper compares the quasi-continuous dq-decoupling techniques to various discrete modeling
approaches for Voltage Oriented Control (VOC)
• To analyze the different techniques, this paper provides both Frequency Response Functions (FRFs)
for Command Tracking (CT) and Dynamic Stiffnes (DS), and time domain tests
• Two Voltage Source Inverter (VSI) topologies have been used:
1. Small-Scale Laboratory HVDC-MMC 2. Industrial Converter of a 3 MW Wind Turbine Generator
This paper was made within the framework of the research project Netz-Stabil
and financed by the European Social Fund (ESF/14-BM-A55-0015/16). This
paper is part of the qualification program Promotion of Young Scientists in
Excellent Research Associations - Excellence Research Programme of the
State of Mecklenburg-Western Pomerania.
Proposed discrete-time complex vector synchronous frame PI current regulator
with discrete DCCSFb and DID (red), MICC (blue), and MID (yellow).
Discrete State Block Diagram of the RL-plant of a VSI with
MICC (blue) and MID (yellow) and full DSFb (red).
Discrete complex vector synchronous frame PI current
regulator obtained via direct modeling (Briz, et.al, 2000).
Discrete-Time PI controller with DID and continuous DCCSFb
approach in blue.
• Four different dq-decoupling techniques are presented and compared during dynamic events:
1. Discrete CCVC 2. Quasi-Continuous DCCSFb 3. Discrete DCCSFb w/ MID 4. Full DSFb
1 3
2 4
Idq (z) z−1
(1 ─ e− (R/L)Ts)
1 ─ e− (R/L)Tsz
−1
jeL
Ts
1
R
Ts
1 ─ z−1 KI
Kp
*
jeL^
+ --
Edq (z)
Vdq (z) +
++
Idq (z) +- +
+
Ts
sampling
Institute of Electrical Power Engineering | Power Electronics and Electrical Drives
University of Rostock, Albert-Einstein-Str. 2, 18059 Rostock, Germany
Delay Compensation and Analysis of Different Decoupling Techniques (State-Feedback-based)
Conclusion
Determination of Required InductanceDetermination of Required InductanceDetermination of Required InductanceDynamic Analysis of the Control Techniques
|I
d(z
)/I d
(z)
*|
in A
/A
Frequency in Hz Frequency in Hz Frequency in Hz
(a) (b) (c)
---: est = 3Lest = 1.5L, Rest = 0.5R), e = 2500 rad/s ─: est = ; e = 2500 rad/s
---: est = 3Lest = 1.5L, Rest = 0.5R), e = 250 rad/s ─: est = ; e = 2 rad/s
|E
d(z
)/I d
(z)|
in V
/A
Frequency in Hz Frequency in Hz Frequency in Hz
(a) (b) (c)
---: est = 3Lest = 1.5L, Rest = 0.5R), e = 2500 rad/s ─: est = ; e = 2500 rad/s
---: est = 3Lest = 1.5L, Rest = 0.5R), e = 250 rad/s ─: est = ; e = 2 rad/s
K
*
++-1
1 – z−1 Idq (z)
Idq (z)
Vdq (z)
R̂ e−Ts/ ^
1 ─ e−Ts/ ^
─
Full DSFb
ej∙e[k ─ 1]∙Ts
MID
+
Edq (z)
DID
|Id
(z)/
I d(z
)*
| in
A/A
|E
d(z
)/I d
(z)|
in
V/A
Frequency in Hz Frequency in Hz
(a) (b) (c)
---: est = 3Lest = 1.5L, Rest = 0.5R), e = 2500 rad/s ─: est = ; e = 2500 rad/s
---: est = 3Lest = 1.5L, Rest = 0.5R), e = 250 rad/s ─: est = ; e = 2 rad/s
MID MICC D1z−1
1 ─ D3z−1
j D4
D1
+-+
Idq (z) Vdq (z) V‘dq (z)
z−1
V‘‘dq (z)
D1^
1 ─ D3^
z−1
j D4^
D1^
+-I^
dq (z) z−1
I^
dq (z) k+1
I^
dq (z) k+1
z−1
+Controller
+-
Discrete Luenberger Style Observer
Feed-Forward
MID Manipulated Input
Decoupling
MICC Manipulated Input
Cross-Coupling
DCCSFb Decoupling Cross-
Coupling State Feedback
DLSO Discrete Luenberger Style
Observer – for delay
compensation
X estimated parameter /
estimated states
+
^
DCCSFb
or DSFb
Delay
i
q(t
), i
d(t
) i
n k
A
Time in s Time in s
---: w/o MID & DCCSFb ---: w/ discrete MID & full DSFb (exp.) w/o delay comp.
---: continuous DCCSFb (L) ---: w/ discrete MID & DCCSFb (trig.) w/o delay comp. ---: w/ discrete MID & full DSFb (exp.) & delay comp. (DLSO – see Fig.14) ---: w/ discrete MID & DCCSFb (trig.) & delay comp. (DLSO – see Fig.14) △ : iq(t); : id(t); Left: fsw = 3 kHz, Ts/= 0.13; Right: fsw = 1 kHz, Ts/= 0.39
i q
(t)
in A
Time in ms Time in ms Time in ms
(a) (b) (c)
---: vqref(t) ─: iq(t)
CT FRFs for 2kHz switching frequency, 500Hz bandwidth - (a) discrete CVC,
(b)xw/xcontinuousxDCCSFb, (c) w/ discrete DCCSFb and MID.
DS FRFs for 2 kHz switching frequency, 500Hz bandwidth - (a) discrete CVC,
(b)xw/xcontinuousxDCCSFb, (c) w/ discrete DCCSFb and MID.
Response in q-axis current during a simultaneous step command on q- and d-axis
current of the studied control topologies @ e = 2500 rad/s, fsw = 2 kHz and est = 3(Lest = 1.5L, Rest = 0.5R); (a) CVC, (b) discrete DCCSFb w/ MID, (c) discrete full
DSFb w/ MID.
Control technique with full DSFb; (a) control structure, (b) CT, (c) DS @ 2 kHz
switching frequency, 500 Hz bandwidth.
Open-loop step response of various MID & DCCSFb techniques with parameter
estimation error for a 3 MW two-level inverter with 1Ts input delay. est = 1.5x(Lestx=x1.2L, Rest = 0.8xR) Step command: vq,ref(t) = 0V, vd,ref(t) = 50V, e = 250xrad/s,
w/ delayed parameters D1-D4.
• Discrete approaches show superior command tracking and disturbance rejection properties
• The discrete techniques show different behavior regarding robustness
• The advantages of discrete approaches are more pronounced at lower switching frequencies
• At low switching frequencies (depends on ratio of Ts and ), the advantages of discrete modeling
become very apparent, especially at high synchronous speed (method 2 is unstable for some o.p.)
• The examined discrete decoupling techniques differ in robustness attributes
• Discrete approaches provide enhanced decoupling properties compared to quasi-continuous (2)
• Technique (1) – high robustness, but can get oscillatory at high output frequencies
• Technique (3) – overall well-behaved. Medium sensitivity regarding delay and load estimation
• Technique (4) – well-behaved. Low parameter sensitivity regarding load but very sensitive to delay
1 2 3
4 4
1 2 3
1 3 4
Discrete plant model with one period input delay with delay compensation using a Discrete
Luenberger Style Observer (DLSO).
3 kHz 1 kHz
Output Frequency Parameter Estimation Error