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