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OBSERVER BASED ACTIVE DAMPING OF
LCL RESONANCE IN GRID CONNECTED
VOLTAGE SOURCE CONVERTERS
by
Vlatko Miskovic
A project submitted in partial fulfillment of the
requirements for the degree of
Master of Science
(Electrical Engineering)
at the
UNIVERSITY OF WISCONSIN-MADISON
2013
APPROVED
By
Adviser Signature: ______________________________________
Adviser Title: _________________________________________
Date: __________________
i
Abstract
Voltage source converters (VSC) with LCL filters are attractive in grid connected
power electronics because they greatly reduce pollution of the utility voltage due to
switching harmonics. However, the presence of the LCL network can cause stability
issues due to its inherent resonance behavior, therefore damping is necessary. This work
proposes novel current controller that uses Luenberger observer as a sensor replacement
and state predictor to predict filter capacitor current. The use of the observer alleviates
the impact of control delay and also eliminates the need for additional sensors. The
predicted filter capacitor current passed through virtual resistor creates damping effect,
while outer loop with feedforward terms ensures instantaneous current command tracking
with zero steady state error. This project with simulation results demonstrates true active
damping and the effectiveness of the virtual resistance in high power active front end
(AFE) drives.
iii
Table of Contents
Contents
Abstract ............................................................................................. i
Table of Contents ............................................................................ iii
Nomenclature.................................................................................. vi
Chapter 1 Introduction ................................................................. 1
1.1
Overview ......................................................................................................2
1.2
Research Contributions ................................................................................3
1.3
State of the Art Literature Review ............................................................... 4
1.4
Overview of Chapters ..................................................................................6
Chapter 2 Modeling of VSC with LCL Line Filters ..................... 7
2.1
Continuous Time Modeling .........................................................................8
2.2
Discrete Time Modeling ............................................................................14
2.3
Summary ....................................................................................................18
iv
Chapter 3 LCL Resonance Damping Methods ........................... 19
3.1
Passive Damping Methods.........................................................................20
3.2
Active Damping Methods ..........................................................................22
Chapter 4 Control of VSC with LCL Line Filter ........................ 26
4.1
Top Level Control Structure ......................................................................27
4.2
Grid Synchronization (Phase Locked Loop) .............................................28
4.3
DC Link Voltage Controller ......................................................................32
4.4
Current Controller Design .........................................................................36
4.5
Summary ....................................................................................................48
Chapter 5 Simulation Results ...................................................... 49
5.1
Simulation Settings .................................................................................... 50
5.2
Time Domain Observer Evaluation ........................................................... 51
5.3
Transient Response Evaluation with Stiff Grid (RSCE=120)...................... 56
5.4
Transient Response Evaluation with Soft Grid (RSCE=10) ........................ 66
5.5
High Frequency Grid Disturbance Rejection.............................................77
5.6
Power Factor Control ................................................................................. 89
5.7
Operation under Polluted and Unbalanced Grid ........................................94
5.8
Summary ..................................................................................................102
v
Chapter 6 Experimental Results ............................................... 103
Chapter 7 Conclusions and Future Work ................................. 106
7.1
Discussion of Results ...............................................................................107
7.2
Recommendations for Future Research ...................................................108
Appendix .......................................................................................... 1
vi
Nomenclature
Eg
Ideal grid voltage
Zg
Grid impedance
E
Measured grid voltage
Vf
Filter capacitor voltage
If
Filter capacitor current
V
Converter side voltage
Ic
Converter side current
Im
Mains side current
Lc
Converter side inductance
Lm
Mains side inductance
Rc
Converter side inductor equivalent resistance
Rm
Mains side inductor equivalent resistance
Cf
Filter capacitor capacitance
Rd
Damping resistor resistance
Rv
Virtual resistance
VDC
DC link voltage
CDC
DC link capacitor capacitance
IDC
DC link load current
vii
RLOAD
DC link load resistance
m
Modulation index
F_D
D-axis component of vector F_DQ
F_Q
Q-axis component of vector F_DQ
RSCE
Maximum short circuit current at PCC to maximum demand load current
ratio
PCC
Point of common coupling
VSC
Voltage source converter
AFE
Active front end
1
Chapter 1 Introduction
This chapter presents an overview of the project, main research contributions, and overview of
chapters.
Lm
Lc
CDC
RLOAD
Cf
Rd
Figure 1-1.
Power circuit of three-phase grid connected VSC
2
1.1
Overview
Active front end (AFE) drives (Figure 1-1) have advantage over regular diode rectifier drives
because of their ability to control DC link bus voltage to desired constant value, bi-directional
power flow, ability to control power factor, and “cleaner” (with less THD) input currents. Instead
of simple L (inductor) line filters, LCL line filters are more attractive because as a 3rd order filters
they provides 60dB per decade attenuation for high frequency harmonics (i.e. switching
harmonics), while L filters as a 1st order filters provide only 20 dB per decade attenuation. With
only L filter it is hard to meet IEEE519-1992 harmonic standard: very big inductor would be
needed, higher boost voltage would be needed to achieve stability, resulting in higher switching
losses. Because of those advantages and reduced size and weight, LCL filter is preferred solution,
but also LCL filter has a high inherent resonance which has to be properly damped to ensure stable
operation. Generally there are two ways of damping methods, passive and active. Passive damping
involves connecting resistors in series or parallel with capacitors of LCL filter, which is
unattractive because it causes extra losses. Active damping is done in control and therefore does
not require extra resistors and extra losses, and because of that is preferred solution. This project
deals with modeling, control, and complete discrete control implementation of proposed control
algorithm. Main emphasis of the project is observer based active damping of LCL resonance and
grid resonant harmonic disturbances rejection as a part of current controller where discrete
Luenberger style observer was used as sensor replacement as well as state predictor.
3
1.2
Research Contributions
The following list summarizes main research contributions in this project:
1)
Novel current controller structure is proposed that uses Luenberger observer as a
sensor replacement and state predictor to predict filter capacitor current which is
passed through virtual resistor to create damping effect. Predicted filter capacitor
through virtual resistor is inner fast loop, while outer loop with appropriate
feedforward terms ensures fast command tracking and zero steady-state error.
2)
Discrete time closed loop Luenberger observer of LCL filter states is designed
which is instrumental in enabling prosed current control scheme.
3)
High frequency (close to LCL resonance) grid voltage disturbance capability is
valuated to demonstrate the effects of true active damping, which is today
unexplored in the literature.
4)
Evaluation of optimal sensor choice selection is discussed.
4
1.3
State of the Art Literature Review
Control of grid connected voltage source converters has been a popular research topic in
the last 15 years. Early work in [22] suggest the use of phase locked loop on measured grid voltage
for grid synchronization, and control structure with outer DC link controller and inner current
controller loop, which became standard approach for AFE drives with L filters. In [17] alternative
approach was presented for control of AFE drives with L filter called Direct Power Control (DPC),
which is basically hysteresis based control that estimates grid voltage which involves
differentiation and the need to operate at much higher control frequencies.
Active damping of LCL filters proposed in [1] is achieved by passing filter capacitor
voltage feedback through a lead compensator, which is mathematically equivalent to low passed
(at cut off frequencies above resonance) filter capacitor voltage and current, which provides
effective damping. Use of filter capacitor current feedback to damp LCL resonance is suggested in
literature: [2], [4], [8], [9], [10], [11], [12], [13], [18] and [20]. In [18] all possible different
feedbacks are explored, and it is showed that only proportional feedback that effectively damps
LCL resonance is filter capacitor feedback. In [3] and [16] full set of state sensors is suggested for
control using state space methods, which is not feasible in the industry due to the cost of the
sensors.
In [6] filter based active damping is suggested which is basically a way of using discrete
filters on voltage command in order not to excite the resonance from control, and is not true active
damping that would damp high frequency grid disturbances as well. Several other approaches
5
suggest solutions that are not true active damping [5], [15], as the solution makes sure only not to
excite the resonance, and not truly damp it.
Improved method of active damping using filter capacitor feedback is presented in [10],
and uses lead network on sensed current to compensate for control delays. In [7], active damping is
achieved with multiple control loop using both main and converter side current feedbacks, which is
equivalent of having filter capacitor current feedback.
In [14] sensorless control (having only converter current sensors) with LCL filter is
suggested, and requires use of differentiation to estimate filter capacitor which requires much
higher control frequencies. Estimated capacitor current is than high passed to achieve active
damping, but effectiveness of sensorless approach regarding high frequency grid disturbance
damping is not explored. In [21] it is also suggested to use high passed filter capacitor voltage to
achieve active damping.
Use of observer to compensate for control delays is suggested in [19] for AFE control with
LCL filters, however, observer design is not presented and also high frequency grid disturbance
damping and transient response is not evaluated.
6
1.4
Overview of Chapters
Project is structured of 5 main chapters.
Chapter 1 is an introduction to the project, with short background, overview of the project,
main research contributions and literature review.
Chapter 2 is about modeling of AFE drives with 2 level VSC connected to the grid with LCL
filter. Detailed continuous and exact zero order hold discrete model are derived.
Chapter 3 describes basics of LCL resonance methods: passive and active.
Chapter 4 starts with overview of control and top level control block diagram. It then describes
design and topology of phase locked loop, DC link voltage regulator design. The main part of this
chapter is devoted to current control design, which starts with sensor choice evaluation and zero
lag state observer design, and then introduces detailed current controller with observer based active
damping.
Chapter 5 starts with an overview of a discrete time implementation of proposed controller. It
then follows by state observer time domain evaluation including effects of parameter mismatch.
Furthermore, controller performance is evaluated considering step load transients with both stiff
and soft grid, high frequency (at resonant frequency range) grid voltages disturbance rejection,
operation under polluted and unbalanced grid, power factor control.
Chapter 6 presents discussion of results, conclusions and suggestions for future work.
7
Chapter 2 Modeling of VSC with LCL Line
Filters
Having accurate mathematical model is crucial to any model based control design. This
chapter presents continuous and exact discrete zero order hold modeling of two level VSC
connected to the grid with LCL filter.
8
2.1
Continuous Time Modeling
A three phase mathematical model of the two level VSC with LCL filter in continuous domain is
derived in [1].
E
im
ic
Lm
Lc
Vf
VDC IDC
Q1
Q2
Q3
V
CDC
Q4
Cf
Q5
RLOAD
Q6
Figure 2.1-1. Two level grid connected VSC with LCL line filter
Equations (2.1.1) – (2.1.5) can be written from equivalent circuit of VSC with LCL line filter
depicted in Figures 2.1-1 and 2.1-2.
Lc
dic.i
 v f ,i  vi  Rc  ic ,i
dt
d v f ,i
Cf
Lm
dt
dim,i
Cdc
dt
 im ,i  ic ,i
(2.1.2)
 ei  v f ,i  Rm  im,i
dVDC
1

dt
VDC
3
v
i 1
i
(2.1.1)
 ic ,i  I DC
(2.1.3)
(2.1.4)
9
s  s2  s3 

vi  VDC   si  1

3


(2.1.5)
Where i  {1, 2,3} for each of three phases
si  1 , when switch Qi is closed and switch Qi 3 is open
si  0 , when switch
Qi 3 is closed and switch Qi is open
Rm
Zg

Eg
Lm
Rc
Vf
Ic
Im
E
Lc
Cf
If
V

Figure 2.1-2. Equivalent circuit of LCL filter
Transformation from abc to αβ (stationary) reference frame (32):



 fα   

 fβ 



1 2
3 2
1
0
 f 
 1 2   a
 3 2   fb 
 fc 
(2.1.6)
Transformation from αβ (stationary) to DQ (synchronous) reference frame rotating at speed ω:
 f  
 d    cos  

   sin 
 fq  


sin   
cos   




f 
 α
 
 fβ 
Where angle θ is rotating at speed ω:
(2.1.7)
10
   t
(2.1.8)
Vector in (2.1.6) can be represented in complex form:
f  f  j  f 
(2.1.9)
Also vector in (2.1.7) can be represented in complex form:
f DQ  f d  j  f q
(2.1.10)
Relationship between f and f DQ can be stated as:
f DQ  f  e  j
(2.1.11)

Eg
Lm
Rm
Zg
Vf
Rc

I LOAD
Ic
Im
E
Lc
2
(md icd mq icq)
V DC
3
Cf
If
CDC
RLOAD
(md  jmq ) VDC
Figure 2.1-3. DQ phasor equivalent circuit of three-phase VSC with LCL filter
Equations (2.1.1) – (2.1.5) can be transformed with (2.1.6) and (2.1.7) transformations to get
equations in DQ reference frame:
Lc 
dicd
 v fd  vd    Lc  icq  Rc  icd
dt
Lc 
dicq
dt
 v fq  vq    Lc  icd  Rc  icq
(2.1.12)
(2.1.13)
11
Cf 
dv fd
Cf 
dv fq
Lm 
dimd
 ed  v fd    Lm  imq  Rm  imd
dt
Lm 
dimq
dt
dt
Cdc 
 imd  icd    C f  v fq
(2.1.14)
 imq  icq    C f  v fd
(2.1.15)
dt
 eq  v fq    Lm  imd  Rm  imq
dVDC 2  vd  icd  vq  icq
 
dt
3
VDC

  I DC

(2.1.16)
(2.1.17)
(2.1.18)
Where we can define modulation index in DQ reference frame as follows:
vd  md  VDC
(2.1.19)
vq  mq  VDC
(2.1.20)
Equations (2.1.12) – (2.1.17) can be written in complex form using (2.1.10):
Lc
Cf
Lm
dic _ DQ
dt
dv f _ DQ
dt
dim _ DQ
dt
 v f _ DQ  vDQ  jLc  ic _ DQ
(2.1.21)
 im _ DQ  ic _ DQ  jC f  v f _ DQ
(2.1.22)
 eDQ  v f _ DQ  jLm  im _ DQ
(2.1.23)
Figure 2.1-3 represents equivalent circuit of VSC in DQ reference frame described in equations
(2.1.12) – (2.1.20).
12
Note that by setting ω=0 in (2.1.21) – (2.1.23) we get equations αβ (stationary) reference frame:
Lc
Cf
Lm
Cdc
dic _ 
dt
dv f _ 
dt
dim _ 
dt
 v f _   v
(2.1.24)
 im _   ic _ 
(2.1.25)
 e  v f _ 
(2.1.26)
dVDC 2  v  ic _   v  ic _ 
 
dt
3
VDC

  I DC

(2.1.27)
e
v



1
sLc
ic
Rc  jLc



im
vf
1
sC f
j C f



1
sLm
Rm  jLm
Figure 2.1-4. Complex state block diagram of VSC with LCL filter in ω ref frame
Figure 2.1-4 represents complex state block diagram described in (2.1.21) – (2.1.23), while figures
2.1-5 and 2.1-6 represent state block diagram of complete system described in (2.1.12) – (2.1.20).
13
ed
md
vd




icd
1
sLc


vfd
1
sC f





Rc
1
sLm
imd
Rm
UDC
Lc
C f
Lm
Lc
C f
Lm
Rm
Rc
U DC

mq
vq




i cq
1
sLc

1
sCf


v fq



1
sLm
eq
Figure 2.1-5. State block diagram of LCL filter in ω ref frame
i cd
I DC
md


mq
2
3


1
sC DC
U DC
i cq
Figure 2.1-6.
State block diagram of DC link circuit
imq
14
2.2
Discrete Time Modeling
Since control is implemented on digital microprocessors, accurate discrete model of the
system is required for any high bandwidth estimation and control.
In αβ reference frame model of LCL filter there is no cross-coupling between α and β
quantities, so equations (2.2.24) – (2.2.26) can be separated in α and β matrices:

 0

 ic 
v     1
 C
 f
f



i
 m i
 0


1
Lc

0
1
Lm


0 
 1 


 L 
0 
  ic 

c
1   





v

0
f

  vi   0   ei



Cf
1
 


 im 
i  0 


Lm 



0 




(2.2.1)
where i  { ,  }
Equation (2.2.1) can be written in compact state space form:

xi  A  xi  B  vi  D  ei

Where x  ic
vf
im
(2.2.2)

T
Exact zero order hold discretization of (2.2.2) is as follows:
Ad  e ATs
(2.2.3)
Bd  A 1  ( Ad  I )  B
(2.2.4)
Dd  A 1  ( Ad  I )  D
(2.2.5)
Which gives us the following discreet zero order hold model of LCL filter:
x(k  1)  Ad  x(k )  Bd  v(k )  Dd  e(k )
(2.2.6)
15
where
 ic (k ) 
 a11 a12


x(k )  v f (k ) Ad  a 21 a 22
 im (k ) 
a31 a32
a13 
a 23 
a33 
 b1 
Bd  b2 
b3 
 d1 
Dd  d 2 
 d 3 
For each α and β, there are two separate state space systems with no cross-coupling
xi (k  1)  Ad  xi (k )  Bd  vi (k )  Dd  ei (k )
(2.2.7)
where i  { ,  } .
Closed form coefficients in (2.2.6) are gotten by expanding
e ATs as infinite sum of Taylor series
coefficients, and recognizing appropriate infinite sum terms (i.e. cos(x) and sin(x)), also shown in
[8]:
Table 2.2-1 Closed form coefficients of discreet model of LCL filter
a11
Lc
Lm

 cos( resTs )
Lc  Lm Lc  Lm
a12
Ts sin( resTs )
Lc resTs
a13
Lm
Lm

 cos( resTs )
Lc  Lm Lc  Lm
a21

Ts sin( resTs )

Cf
resTs
a22
cos(resTs )
a23
Ts sin( resTs )

Cf
resTs
16
Lc
Lc

 cos( resTs )
Lc  Lm Lc  Lm
a31
a32

Lm
Lc

 cos( resTs )
Lc  Lm Lc  Lm
a33
b1
Ts sin( resTs )

Lm
resTs

Ts
L
Ts
sin(  resTs )
 m

Lc  Lm Lc Lc  Lm
 resTs
b2
Lm
Lm

 cos(resTs )
Lc  Lm Lc  Lm
b3

Ts
Ts
sin( resTs )


Lc  Lm Lc  Lm
resTs
d1
Ts
Ts
sin(  resTs )


Lc  Lm Lc  Lm
 resTs
d2
Lc
Lc

 cos( resTs )
Lc  Lm Lc  Lm
d3
Ts
L
Ts
sin(  resTs )
 c

Lc  Lm Lm Lc  Lm
 resTs
 res
Lc  Lm
Lc C f Lm
 res 
Lc  Lm
is the resonant frequency of LCL filter.
Lc C f Lm
Converter voltages from (2.1.5) in αβ reference frame using (2.1.6) transformation are:
17
1
1


v (k )  VDC (k )   s1 (k )  s2 (k )  s3 (k ) 
2
2


(2.2.8)
 3

3
v (k )  VDC (k )  
s2 ( k ) 
s3 (k ) 
2
 2

(2.2.9)
DC Link equation (2.1.4) can be discretized using Euler-forward approximation:
VDC (k  1)  VDC (k ) 
Ts  3

  ic ,n (k )  sn (k )  I DC (k ) 
C DC  n 1

(2.2.10)
18
2.3
Summary
In this chapter continuous models of LCL filter in both stationary and synchronous rotating
reference frame are derived. Exact closed form discreet zero order hold model of LCL filter in
stationary reference frame is derived, which will be instrumental in Luenberger state observer and
current control design.
19
Chapter 3 LCL Resonance Damping
Methods
As mentioned earlier LCL line filter have inherent resonance frequency. Figures 3-1 and 32 represent open loop frequency response of mains current to converter voltage and grid voltage
respectively. In both cases there is high resonant frequency.
Bode Diagram
150
Magnitude (dB)
100
50
0
-50
-100
-150
90
Phase (deg)
45
0
-45
-90
3
10
4
10
5
10
Frequency (rad/s)
Figure 3-1.
Frequency response of mains side current to converter side voltage
Bode Diagram
Magnitude (dB)
150
100
50
0
-50
90
Phase (deg)
45
0
-45
-90
3
10
4
10
5
10
Frequency (rad/s)
Figure 3-2.
Frequency response of mains side current to grid voltage
20
3.1
Passive Damping Methods
Passive damping methods are very reliable and they involve connecting a resistor in series
or parallel with filter capacitor. Figure 3.1-1 represents passive damping with resistor connected in
series with filter capacitor. Reliability and simplicity of passive damping solution come with the
increase of the cost, filter size, dissipative losses and need for additional cooling.
e
v


1
sLc
ic


1 
sC f
vf



1
sLm
im
Rd
Figure 3.1-1. Block diagram LCL filter with damping resistor in series with filter capacitor
Transfer functions of mains current to converter and grid voltage with passive damping are
represented in (3.1.1) and (3.1.2).
C f Rd s  1
im
1

 2
2
2
v
Lc C f Lm s s  Rd C f res
s  res
(3.1.1)
C f Lc s 2  sC f Rd s  1
im
1


2
2
e LcC f Lm s s 2  Rd C f res
s  res
(3.1.2)
21
 
Rd C f res
2
res

(3.1.3)
2
Lc  Lm
LcC f Lm
(3.1.4)
Both (3.1.1) and (3.1.2) have the same characteristic equation, from which damping coefficient ζ
can be related with Rd in (3.1.3) where  res is described in (3.1.4).
22
3.2
Active Damping Methods
Several techniques of active damping of LCL resonance have been claimed in the literature. In [6]
filter based active damping is proposed, which basically consists of having notch band-stop filter
on a voltage command. In this approach it is basically made sure that resonance is not excited from
the converter voltage command, but any voltage disturbance on the grid is not accounted for and
would excite the resonance. This approach therefore does not perform true active damping of LCL
resonance considering both converter side and grid voltage. In [2], [8]-[11] and [20] filter capacitor
feedback through the gain (i.e. virtual resistor) is used to achieve active damping. In [18] it is
shoved that filter capacitor current is the only feedback that could achieve damping with
proportional gain. Filter capacitor voltage passed through derivative [18] element or lead
compensator [1] can also be used to achieve damping. Both of approaches above involve direct or
indirect differentiation of capacitor voltage to gain the same information as from filter capacitor
current.
In case of derivative on capacitor voltage, it is equivalent to proportional filter capacitor current
feedback:
v f ( s)  K D  s  i f ( s) 
KD
Cf
(3.2.1)
In case of lead compensator on capacitor voltage, it is equivalent to low passed (at high frequency
above resonance) proportional filter capacitor current and filter capacitor voltage feedback:
v f ( s )  K ll
 K T
1  Tn  s
K ll
 v f ( s) 
 i f ( s )   ll n
 C
1  Td  s
Td  s  1
f


1

 T  s 1
 d
(3.2.2)
23
where
i f (s)  v f ( s)  C f  s
(3.2.3)
e
v



1
sLc
ic


1
sC f
vf


1
sLm
im
Rv
Figure 3.2-1. Block diagram LCL filter with capacitor current feedback through virtual resistor
Figure 3.2-1 shows active damping achieved by filter capacitor current feedback through virtual
resistor. Transfer functions of mains current to converter and grid voltage with virtual resistor
active damping are represented in (3.1.4) and (3.1.5).
im
1


v
Lc C f Lm s
1
R
2
s 2  v s   res
Lc
C f Lc s 2  sC f Rv s  1
im
1


R
e Lc C f Lm s
2
s 2  v s  res
Lc
 
Rv
2 Lcres
(3.2.4)
(3.2.5)
(3.2.6)
24
Both (3.2.4) and (3.2.5) have the same characteristic equation, from which damping coefficient ζ
can be related with virtual resistor Rv in (3.2.6). Note that in this approach true active damping is
achieved, considering both converter side and grid voltage.
Figures 3.2-2 and 3.2-3 represent frequency response of mains current to converter voltage and
gird voltage respectively, with un-damped LCL filter (blue), passively damped (green) and
actively damped (red) with damping coefficient ζ=1.
Bode Diagram
150
Magnitude (dB)
100
50
0
-50
-100
-150
90
Phase (deg)
45
0
-45
-90
2
3
10
4
10
5
10
6
10
7
10
10
Frequency (rad/s)
Figure 3.2-2. Bode plot of im / e with no damping, passive and active damping (ζ=1)
Bode Diagram
Magnitude (dB)
200
100
0
-100
-200
90
Phase (deg)
45
0
-45
-90
2
10
3
10
4
10
5
10
6
10
7
10
Frequency (rad/s)
Figure 3.2-3. Bode plot of im / v with no damping, passive and active damping (ζ=1)
25
Figures 3.2-4 and 3.2-5 represent frequency response of mains current to converter voltage and
gird voltage respectively, with un-damped LCL filter (blue), passively damped (green) and
actively damped (red) with damping coefficient ζ=0.2.
Bode Diagram
150
Magnitude (dB)
100
50
0
-50
-100
-150
90
Phase (deg)
45
0
-45
-90
3
4
10
5
10
6
10
10
Frequency (rad/s)
Figure 3.2-4. Bode plot of im / e with no damping, passive and active damping (ζ=0.2)
Bode Diagram
150
Magnitude (dB)
100
50
0
-50
-100
-150
90
Phase (deg)
45
0
-45
-90
3
10
4
5
10
10
6
10
Frequency (rad/s)
Figure 3.2-5. Bode plot of im / v with no damping, passive and active damping (ζ=0.2)
From the figures above it is obvious that even lightly damped (ζ=0.2) LCL filter greatly reduce
resonant frequency and that true active damping with virtual resistor can be as effective as passive
damping.
26
Chapter 4 Control of VSC with LCL Line
Filter
This chapter will present detailed proposed control structure of grid connected VSC with LCL line
filter. Controller will be designed to the following basic requirements:
1) Ideal command tracking (no phase and amplitude errors)
2) Fast dynamic response (ability to sustain load transients)
3) Good DC bus voltage utilization (low boost)
4) Limited (low) switching frequency
5) Power factor control
6) Low harmonic content (IEEE-519 compliancy)
7) Grid disturbance rejection around resonant frequency (true active damping)
8) Ability to operate on both soft and stiff grids
9) Ability to operate under polluted and unbalanced grid conditions
For verification purposes, 900kW Danfoss AFE drive is used with parameters in Table 4-1.
Resonant frequency of LCL filter is 1.4 kHz, switching frequency is 5 kHz and control task is
executed every 10 kHz (twice the switching frequency).
Grid Voltage
690V
Power
900kW
Table 4-1
Lc
100µH
(=6% @ f=50Hz)
System parameters
Cf
Lm
317µH
67µH
(=18.8% @f=50Hz)
(=4% @ f=50Hz)
Cdc
31.5mH
(=1872% @ f=50Hz)
27
4.1
Top Level Control Structure
Top level control structure can be seen in Figure 4.1-1. Basic control is classical voltage
oriented control as described in [22] and [1], with an inner current control loop (with active
damping) and outer voltage control loop that keeps DC link voltage constant and provides
reference for current controller. Grid synchronization is done via phase-locked loop (PLL) on
measured grid voltages to synchronize converter with the grid.
e abc
V
*
DC
PLL

DC Link
Voltage Controller
V DC
e abc
i m*
Current
Controller
_ DQ
V DC
e abc ic _ abc
Figure 4.1-1. Top level control structure
*
v abc
Q1 ...Q 6
SV-PWM
28
4.2
Grid Synchronization (Phase Locked Loop)
Accurate and fast detection of grid frequency, phase angle and voltage magnitude are
crucial in correct reference signals generation and therefore performance of the entire control
system. One of the best methods found in the literature ([1], [22]) to synchronize converter with a
grid is phase locked loop (PLL). Block diagram of PLL for grid connected converters
synchronization is presented in Figure 4.2-1. Measured grid voltages are transformed to αβ
reference frame via transformation (2.1.6) and to DQ synchronous reference frame via
transformation (2.1.7). The aim is to align synchronous (rotating) voltage vector with D axis such
that Q axis voltage vector is zero.
e
e
^
^
^
^
 e  sin(  )  e  cos(  )
e  e
2
Figure 4.2-1.
PI
2

1
s

Phase locked loop (PLL) for grid synchronization
Principle of PLL operation can be explained with (4.2.1) by using definition of Q-axis voltage and
trigonometric identities. Figure 4.2-2 represent equivalent PLL block diagram, which is simply
closed loop grid voltage angle and frequency observer.
29
^

 +
PI
-
Figure 4.2-2.
^
eq
e2  e2

e2  e2

Simplified PLL block diagram

^
 e  cos( )  sin(  )  e  sin(  )  cos( )
e2  e2
^

^
(4.2.1)
 cos( )  sin(   )  sin(  )  cos(   ) 
^
1
s
^
 e  sin(  )  e  cos( )
^

^
^
^
^
sin(    )  sin(    ) sin(    )  sin(    )



2
2
^
^
 sin(    )    
where e 
e2  e2
Using PI controller PI ( s)  K P 
KI
closed loop response is
s
^

s  KP  KI
 2
 s  s  KP  KI
(4.2.2)
Characteristic equation can be written in the form:
s2  s  KP 
where  
KP
KI
KP
 s 2  s  2   2

(4.2.3)
30
Equation (4.2.3) gives relationship between damping, proportional gain and time constant of PLL:
4  2    K P
(4.2.4)
Optimal damping is selected (  
1
) and proportional gain K P  160 which gives the time
2
constant of   12.5mS and eigenvalues 80±j·80 rad/sec. Figures 4.2-3 and 4.2-4 are bode plot and
step response of PLL for tuning above.
Bode Diagram
Magnitude (dB)
0
-20
-40
-60
-80
0
Phase (deg)
-45
-90
-135
-180
0
1
10
2
10
3
10
Frequency
4
10
10
(rad/s)
Figure 4.2-3. Bode plot of PLL frequency response
Step Response
1.4
1.2
Amplitude
1
0.8
0.6
0.4
0.2
0
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (seconds)
Figure 4.2-4. PLL step response
0.07
0.08
0.09
31
Figures 4.2-5 and 4.2-6 represent detected grid frequency and phase angle respectively.
400
350
300
250
200
150
100
50
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.18
0.2
Figure 4.2-5. PLL detected grid frequency
7
6
5
4
3
2
1
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Figure 4.2-6. PLL detected grid phase angle
32
4.3
DC Link Voltage Controller
DC link voltage controller is the most outer loop used to regulate DC link to a constant value. If
lossless line filter is considered for simplicity and grid voltage is aligned with D axis by PLL,
equation (4.3.1) represents balance of real power in DC link capacitor as a net power delivered by
the grid (represented in synchronous DQ reference frame) and consumed by the load. Relationship
in (4.3.1) is used as a basis for DC link controller to generate reference for D axis mains
*
current imd .
dV  2

VDC   Cdc DC   ed  imd  VDC  I DC
dt  3

(4.3.1)
Relation in (4.3.1) can be rearranged as:
 3 VDC
 dV
 3 VDC

 CDC   DC  imd  
 2 ed
 dt
 2 ed

  I DC

(4.3.2)
(4.3.2) can be parameterized as follows:
A(VDC )
dVDC
 imd  B(VDC )  I DC
dt
(4.3.3)
Since DC link voltage will be close to the operating point (DC link voltage reference),
A(VDC ) and B(VDC ) can be assumed to be a constant for analysis:
*
3 VDC
A
 C DC
2 ed
3V
B  DC
2 ed
(4.3.4)
*
(4.3.5)
33
Using that assumption, nonlinear relationship in (4.3.2) can be simplified to linear:
A
dVDC
 imd  B  I DC
dt
(4.3.6)
Figure 4.3-1 depicts simplified model of the system with DC link regulator, where low pass filter
(LPF) represents lumped dynamics of current controller and PWM block, and is much faster than
DC link controller outer loop such that it will be ignored in the analysis.
I DC
B
*
VDC
*
md
i md
i
+
PI
+
VDC
-
LPF
-
1
A
1
s
Figure 4.3-1. Simplified system block diagram of the system for VDC control
Using PI controller PI ( s)  K P 
KI
, simplified DC link closed loop response is
s
VDC
s  KP  KI
s  B  I DC
 2
 *
*
2
VDC s  A  s  K P  K I VDC  ( s  A  s  K P  K I )
(4.3.7)
From (4.3.7) it can be seen that steady state error is zero for any load.
Characteristic equation can be written in the form:
s2  s 
KP KP

 s 2  s  2   2
A A
(4.3.8)
34
where  
KP
KI
Equation (4.3.9) gives relationship between damping, proportional gain and time constant of DC
link regulator:
4  2   
KP
A
(4.3.9)
Optimal damping is selected (  
1
) and proportional gain K P  300 which gives the time
2
constant of   6.67mS and eigenvalues of 150±j·150 rad/sec. Figures 4.3-2 and 4.3-3 are bode plot
and step response respectively of DC link regulator for tuning above.
Voltage reference is calculated from the grid line voltage and low boost is added:
VDC  ed 
*
2
 3  K BOOST
3
(4.3.10)
To minimize losses, extremely low boost 3% is selected ( K BOOST  1.03 )
Bode Diagram
Magnitude (dB)
0
-20
-40
-60
-80
0
Phase (deg)
-45
-90
-135
-180
1
10
2
3
10
10
Frequency (rad/s)
Figure 4.3-2. Bode plot of DC link regulator frequency response
4
10
35
Step Response
1.4
1.2
Amplitude
1
0.8
0.6
0.4
0.2
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Time (seconds)
Figure 4.3-3. DC link regulator step response
0.04
0.045
36
4.4
Current Controller Design
Current controller is used to regulate current to a reference obtained from DC link controller
output, as well as to damp any oscillations of LCL resonance caused by high frequency component
grid voltage disturbances. Novel approach is presented here using observer based active damping.
4.4.1 Sensor Choice Evaluation and Observer Construction
In control engineering very important issue is the choice of sensors used for control. In this work it
is argued that optimal sensor choices are converter side current sensor ic and grid voltage sensor e
(Note that there will always be DC link voltage sensor for DC link regulation as well as
protections), in case there is choice to pick two sets of sensors. With this sensor choice LCL states
are completely observable with zero phase leg. If grid voltage was not measured, LCL states would
not be observable as grid voltage is (uncontrolled) input to the system, equally as important as
manipulated input converter voltage. Advantages of using converter side current sensors instead of
mains current sensors, is fast protections (of especial importance in high power drives), and also
converter side current is the first state that is affected by changing manipulated input, so feedback
would be fastest (i.e. it is not possible to control filter capacitor voltage and mains side current and
not in the first place controlling converter side current). Grid voltage sensors can also be used for
operation under faulted gird, anti-islanding detection, etc.
Using exact zero order hold model of LCL filter developed in (2.2.7) closed loop Luenberger state
observer can be constructed:



xi (k  1)  Ad  x i (k )  Bd  vi (k )  Dd  ei (k )  L  C  [ xi (k )  xi (k )]
(4.4.1.1)
37
where
^

 a11
 ^i c ,i ( k ) 
^

x i ( k )  v f ,i ( k )  ; Ad  a 21
^

a31
 i m ,i ( k ) 


a12
a 22
a32
a13 
 b1 
 d1 



a 23  ; Bd  b2  ; Dd  d 2 
b3 
 d 3 
a33 
For each i  { ,  }
Since only converter side current sensors will be used vector C is:
C  1 0 0
(4.4.1.2)
To confirm that with sensor choice selection (4.4.1.1) is observable, it is showed below that
observability matrix has a full rank:
 C 
rank  CAd   3
CAd 2 
(4.4.1.3)
Vector L defines the bandwidth of the observer, where n is design coefficient:
 L

L   c 0 0
 Ts  n

T
(4.4.1.4)
Roots of the closed loop Luenberger observer are determined from the following determinant:
z  I  Ad  L  C  0
(4.4.1.5)
Table 4.4.1-1 and Figure 4.4.1-1 show closed observer loop roots in z-domain for different choices
of n. For n   (L=0) we have open loop observer, roots on the unit circle, and as n increases
roots move inside unit circle. Optimal choice is n=1, as roots are well inside unit, observer has fast
dynamics, and roots are on the right side of unit circle, which is desirable to avoid forced
oscillations.
38
n
Table 4.4.1-1 Observer roots in z-domain for different feedback gain values
Observer Eigenvalues
∞
1.0000;
0.6319 ± 0.7750i
3
0.8076;
0.5615 ± 0.7558i
2
0.7079;
0.5280 ± 0.7292i
1
0.2450;
0.5095 ± 0.5858i
0.7
-0.3380;
0.5866 ± 0.5475i
0.5
-1.0000;
0.6319 ± 0.5526i
In Figure 4.4.1-1 closed loop roots are circled for n=1, as optimal choice for observer pole
placement.
Figure 4.4.1-1. Observer roots in z-plane for different observer gains
39
4.4.2 Current Controller with Observer Based Active Damping Design
Figures 4.4.2-1 and 4.4.2-2 represent detailed proposed current controller structures with
observer based active damping in z-domain and time domain respectively. It consists of inner
active damping loop in stationary reference frame and outer fundamental frequency loop in
synchronous reference frame.
^
Predicted (one step ahead) filter capacitor current i f _  (k  1) calculated from (4.4.1.1) and
(4.4.2.1) is passed through virtual resistor Rv to achieve active damping, as described in Section
3.2. Predicted value is used instead of current value to compensate for computational delay (Fig
4.4.2-1 and 4.4.2-2).
^
^
^
i f _  (k  1)  i m _  (k  1)  i c _  (k  1)
(4.4.2.1)
FF
v DQ
(z )
ic*_ DQ ( z ) +
DQ  
K
-
+
v* ( z )
    Ts

ic _ DQ(z)
Rv
z 1
ic _  ( z)
v (z)
Plant
z  i f _ (z)
Observer
e (z) v (z )
  DQ
Figure 4.4.2-1. Current Controller with observer based active damping and plant in z-domain
40
FF
vDQ (k)
ic*_ DQ (k )
+
K
-
+
+
*
vDQ
(k )
+
DQ  
  DQ
Gate Signals
PWM
-
ic _ DQ ( k )

*
v
(k )
    Ts
Rv
VDC (k )
^
i f _ (k 1)
Observer
ic _  ( k )
v (k)
e (k )
ic _ (k)
Figure 4.4.2-2. Current Controller with observer based active damping in time domain
Outer loop regulates converter side fundamental component current to a referenced value.
Reference for mains side current comes from DC link voltage regulator, and reference for
converter side current (4.4.2.5) is calculated from (4.4.2.2) – (4.4.2.3) which are steady state
solution of (2.1.21) – (2.1.22) in synchronous (at fundamental frequency ω) reference frame.
v*f _ DQ  eDQ  jLm  im* _ DQ
(4.4.2.2)
ic*_ DQ  im* _ DQ  jC f  v*f _ DQ
(4.4.2.3)
FF
vDQ
 v*f _ DQ  jLc  ic*_ DQ
(4.4.2.4)
ic*_ DQ (k )   jC f  eDQ (k )  (1   2C f Lm )  im* _ DQ (k )
(4.4.2.5)
Feedforward converter voltage term (4.4.2.6), for fast command tracking, is obtained from
(4.4.2.2) – (4.4.2.4), which are again steady state solutions of (2.1.21) – (2.1.23) in synchronous
reference frame.
vDQ (k )  (1   2 LcC f )  eDQ (k )  j  (Lc  Lm   3 LcC f Lm )  im* _ DQ (k )
FF
(4.4.2.6)
41
Proposed current controller can be summarized as follows: The measured currents are
transformed to a synchronous reference frame, and difference between it and the result in equation
(4.4.2.5) is passed through PI regulator. The feedforward term calculated in (4.4.2.6) is added and
the resulting converter voltage reference is transformed back in stationary reference frame along
^
with delay compensation. The active damping voltage term Rv  i f _  (k  1) is then added to a
fundamental voltage command and total voltage command is passed to a Space Vector PWM.
Equation (4.4.2.7) shows closed loop transfer function of mains current response to a grid
voltage. For simplicity, outer loop (synchronous reference frame loop) in current controller is
assumed to be a proportional controller, as integral control loop is much slower, used only to bring
steady state errors to zero. And if system parameters were accurate proportional controller would
suffice in proposed design.
K  Rv
1

Lc
LcC f
im
1


e Lm s 3  s 2  K  Rv  s   2  K   2
res
res
Lc
Lc  Lm
s2  s 
(4.4.2.7)
Proportional controller gain is selected to be 0.1 which makes current controller have
approximately 160 Hz bandwidth (4.4.2.8).
K  Lc  2  160  0.1
(4.4.2.8)
Figure 4.4.2-3 shows mains current to a grid voltage bode plots, open loop (green) and closed
loop (blue) with fundamental controller only, and without active damping ( Rv  0 ). Even with
fundamental current controller only, a stable system is achieved but very lightly damped.
42
Figure 4.4.2-4 shows that as virtual resistance increases Rv  {0.0;0.2;0.5;1.0}
damping of the system increases significantly.
Bode Diagram
150
Magnitude (dB)
100
50
0
-50
-100
-150
90
Phase (deg)
45
0
-45
-90
4
10
Frequency
(rad/s)
Figure 4.4.2-3. Bode plot of im / e with K P  0; Rv  0 (green) and K P  0.1; Rv  0 (blue)
Bode Diagram
30
Magnitude (dB)
20
10
0
-10
Phase (deg)
-20
90
45
0
-45
-90
3
10
4
10
5
10
Frequency (rad/s)
Figure 4.4.2-4. Bode plot of im / e with K P  0.1 and Rv  {0.0,0.2,0.5,1.0} blue, green, red, cyan
43
Bode Diagram
Magnitude (dB)
50
0
-50
Phase (deg)
-100
0
-90
-180
-270
2
3
10
4
10
5
10
10
Frequency (rad/s)
Figure 4.4.2-5. Bode plot of im / im with K P  0.1 and Rv  {0.0,0.2,0.5,1.0} blue, green, red, cyan
*
Command tracking bode plot (Figure 4.4.2-5) shows effects of active damping on command
tracking, while Table 4.4.2-1 shows eigenvalues and damping coefficient for difference values of
virtual resistor.
Table 4.4.2-1. Current Controller Eigenvalues for different virtual resistor values
K
Rv
Eigenvalues (Hz)
ζ
0.0
0.0
0, 0 ± j1409
0.0
0.1
0.0
-95, -32± j1406
0.02
0.1
0.2
-97, -189 ± j1383
0.14
0.1
0.5
-99, -425 ± j1311
0.32
0.1
1.0
-104, -818± j1070
0.61
44
Figures 4.4.2-6 through 4.4.2-8 show effectiveness of the observer and predicted states in delay
compensation. In each of the figures below green graph is currently observed state, blue graph is
predicted state and red graph is actual measured state at the end control task at which calculations
are performed. Note that measured values (in red) were not available (even measured converter
side current) at time instant when calculations are performed. Graphs below are obtained using
simulation described in Chapter 5, where observer is used only for estimation and prediction, and
not for control (active damping). 5% of 26th harmonic is superimposed on the grid, so that each of
the state would have significant high harmonic current to demonstrate effectiveness and high
bandwidth of the observer. For each of the observed states below, predicted state shows no phase
delay, while currently observed state has some phase delay (due to computational delay) which is
more significant at frequencies around resonant frequencies. Therefore using predicted values
instead of measured or observed can successfully compensate for computational delays. One other
thing to note in Figure 4.4.2-6 is that observed and predicted converter side currents contain less
high frequency switching ripple, due to limited bandwidth of the observer, which means that
predicted filter capacitor current will have less high frequency switching ripple, which is another
advantage in proposed approach.
45
2000
1500
1000
500
0
0.18
0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189
0.19
0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189
0.19
2000
1500
1000
500
0
0.18
Figure 4.4.2-6. Overlaid predicted (blue), observed (green) and measured (red) converter side
current, α (top) and β (bottom) axis
46
1000
800
600
400
200
0
0.18
0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189
0.19
0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189
0.19
1000
800
600
400
200
0
0.18
Figure 4.4.2-7. Overlaid predicted (blue), observed (green) and measured (red) filter capacitor
voltage, α (top) and β (bottom) axis
47
2000
1500
1000
500
0
0.18
0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189
0.19
0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189
0.19
2000
1500
1000
500
0
0.18
Figure 4.4.2-8. Overlaid predicted (blue), observed (green) and measured (red) mains side current,
α (top) and β (bottom) axis
48
4.5
Summary
In this chapter complete detailed control algorithm is proposed and described for gird
connected voltage source converters with LCL line filter. Grid synchronization with phase locked
loop is described, following by description of DC link controller used to regulate DC link to a
constant value. Finally, novel current controller, along with observer design and observer based
active damping is proposed.
49
Chapter 5 Simulation Results
This chapter presents summary of simulation results of AFE control proposed in Chapter 4. All
control requirements described in Chapter 4 will be verified in MATLAB simulation. The Plant is
modeled with SimPower systems and control is implemented in C++ code using Matlab Sfunctions (See Appendix).
50
5.1
Simulation Settings
Simulink simulation was executed with ode45 (Dormand-Prince) solver for ordinary
differential equations with variable time step, maximum tolerance 1e-4 and relative tolerance of
1e-4.
Simpower systems simulation of AFE circuit was done in discrete domain with Tustin
solver type and sample time of 1µs.
51
5.2
Time Domain Observer Evaluation
For the purpose of observer evaluation Rv is set to zero (i.e. observer is not used for control)
and harmonics are superimposed on the grid voltage such that THD of the voltage up to 25th
harmonic was 15%, and also 5% of 26th harmonic is added because 26th harmonic is close to LCL
resonant frequency. Figures below show externally measured (blue) and observed (green) filter
capacitor and mains current states in stationary αβ reference frame. It can be seen that observer
accurately estimates states with zero phase leg even at high frequencies (at resonant frequencies
range) and parameter mismatch up to 20%. Figures 5.2-1 through 5.2-9 show time domain
response with different parameters mismatch.
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-1. Observer performance, nominal parameters
52
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-2. Observer performance with Lc of +20% of nominal value
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-3. Observer performance with Lc of -20% of nominal value
53
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-4. Observer performance with Cf of +20% of nominal value
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-5. Observer performance with Cf of -20% of nominal value
54
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-6. Observer performance with Lm of +20% of nominal value
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-7. Observer performance with Lm of -20% of nominal value
55
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-8. Observer performance with all elements +20% of nominal values
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.2-9. Observer performance with all elements -20% of nominal values
56
Transient Response Evaluation with Stiff Grid (RSCE=120)
Six cases for transient responses are evaluated below under stiff grid condition. RSCE of 120 is
selected as the stiffest grid. For each test case there are graphs for measured state responses,
observer output states responses and mains and converter currents in DQ reference frame
responses. Transient responses below show fast and well behaved response even in toughest
conditions that would not easily be replicated in the field.
5.3.1 Zero to 100% Motoring Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
2000
Im
5.3
0
-2000
Figure 5.3.1-1. VDC, ic, vf and im measured states
57
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.3.2-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.3.3-3. im (left) and ic (right) with error in DQ ref. frame
58
5.3.2 Zero to 100% Generating Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.3.2-1. VDC, ic, vf and im measured states
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.3.2-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
59
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.3.2-3. im (left) and ic (right) with error in DQ ref. frame
5.3.3 100% Motoring to Zero Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
2000
Im
imQ
0
-2000
0
-2000
Figure 5.3.3-1. VDC, ic, vf and im measured states
60
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.3.3-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
2000
icD
3000
2000
imD
0
-2000
1000
0
icQ
-1000
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
2000
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
1000
0
icQerr
imQ
0.08
0
0.2
3000
-1000
-2000
-3000
0.06
-1000
icDerr
-3000
0.04
1000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.3.3-3. im (left) and ic (right) with error in DQ ref. frame
61
5.3.4 100% Generating to Zero Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.3.4-1. VDC, ic, vf and im measured states
62
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.3.4-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.3.4-3. im (left) and ic (right) with error in DQ ref. frame
63
5.3.5 100% Motoring to 100% Generating Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.3.5-1. VDC, ic, vf and im measured states
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.3.5-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
64
2000
icD
3000
2000
imD
0
-2000
1000
0
icQ
-2000
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
0.2
3000
2000
1000
imQ
0.06
-1000
0.04
icDerr
-3000
0.04
1000
-1000
1000
0
-1000
icQerr
0
-1000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
Figure 5.3.5-3.
0.14
0.16
0.18
1000
0
-1000
0.2
im (left) and ic (right) with error in DQ ref. frame
5.3.6 100% Generating to 100% Motoring Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.3.6-1. VDC, ic, vf and im measured states
65
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
Figure 5.3.6-2.
2000
icD
3000
2000
imD
0
-2000
1000
0
icQ
-2000
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
0.2
3000
2000
1000
0
-1000
1000
0
icQerr
imQ
0.06
-1000
0.04
icDerr
-3000
0.04
1000
-1000
-1000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.3.6-3. im (left) and ic (right) with error in DQ ref. frame
66
Transient Response Evaluation with Soft Grid (RSCE=10)
Six cases for transient responses are evaluated below under soft grid condition. RSCE of 10 is
selected as the softest grid. For each test case there are graphs for measured state responses,
observer output states responses and mains and converter currents in DQ reference frame
responses. Transient responses below show fast and well behaved response even in toughest
conditions that would not easily be replicated in the field.
5.4.1 Zero to 100% Motoring Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
2000
Im
5.4
0
-2000
Figure 5.4.1-1. VDC, ic, vf and im measured states
67
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.4.1-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
2000
icD
3000
2000
imD
0
-2000
1000
0
icQ
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
2000
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
1000
0
icQerr
imQ
0.08
0
0.2
3000
-1000
-2000
-3000
0.06
-1000
icDerr
-3000
0.04
1000
-1000
0.04
0.06
0.08
0.1
0.12
Figure 5.4.1-3.
0.14
0.16
0.18
0.2
1000
0
-1000
im (left) and ic (right) with error in DQ ref. frame
68
5.4.2 Zero to 100% Generating Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.4.2-1. VDC, ic, vf and im measured states
Vf
a
1000
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
Vf
b
1000
0
-1000
0.08
Im
a
2000
0
-2000
0.08
Im
b
2000
0
-2000
0.08
Figure 5.4.2-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
69
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
icDerr
3000
2000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.4.2-3. im (left) and ic (right) with error in DQ ref. frame
5.4.3 100% Motoring to Zero Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.4.3-1. VDC, ic, vf and im measured states
70
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
Figure 5.4.3-2.
2000
icD
3000
2000
imD
0
-2000
1000
0
icQ
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
2000
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
1000
0
icQerr
imQ
0.08
0
0.2
3000
-1000
-2000
-3000
0.06
-1000
icDerr
-3000
0.04
1000
-1000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.4.3-3. im (left) and ic (right) with error in DQ ref. frame
71
5.4.4 100% Generating to Zero Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.4.4-1.
VDC, ic, vf and im measured states
72
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.4.4-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.4.4-3. im (left) and ic (right) with error in DQ ref. frame
73
5.4.5 100% Motoring to 100% Generating Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.4.5-1. VDC, ic, vf and im measured states
74
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.4.5-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
Figure 5.4.5-3.
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
im (left) and ic (right) with error in DQ ref. frame
75
5.4.6 100% Generating to 100% Motoring Step Load Change
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.4.6-1. VDC, ic, vf and im measured states
76
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.4.6-2. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.4.6-3. im (left) and ic (right) with error in DQ ref. frame
77
5.5
High Frequency Grid Disturbance Rejection
In this section high frequency (around LCL resonance) grid voltage disturbance is injected to
verify effectiveness of proposed active damping algorithm. Two cases are considered, in the first
one 5% of 25th harmonic component (1250Hz) is superimposed on the fundamental component of
the grid voltage, and on the second one 5% of 29th harmonic component (1450Hz) is superimposed
on the grid.
5.5.1 Operation under Grid Voltage with Superimposed 5% of 25th
Harmonic
600
400
200
0
-200
-400
-600
0.155
0.16
0.165
0.17
0.175
0.18
0.185
0.19
0.195
0.2
0.205
Figure 5.5.1-1. Grid with superimposed 5% or 25th harmonic
Figure 5.5.1-1 shows grid voltage at PCC with 5% of 25th harmonic component. Figures
5.5.1-2 to 5.5.1-4 represent measured state responses, observer output states responses and mains
and converter currents in DQ reference frame with RV=0. High components of 25th harmonic in
converter and mains side current can be seen in Figure 5.5.1-5 which is spectrum of those currents.
78
Converter side current has 11% of 25th harmonic, while mains side current has 14% of 25th
harmonic. It shows low impedance of LCL filter at 25th harmonic when RV=0.
Figures 5.5.1-6 to 5.5.1-8 represent measured state responses, observer output states
responses and mains and converter currents in DQ reference frame with RV=0.5. In those figures it
can be seen that the presence of 25th harmonic is greatly reduced, showing that virtual resistor has
the same effect as passive resistor increasing impedance of the system. Harmonic content of
converter and mains side current can be seen in Figure 5.5.1-9, converter current having 5.4% and
mains current having only 3.2% of 25th harmonic.
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.5.1-2. VDC, ic, vf and im measured states
79
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.5.1-3. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
icD
2000
2000
imD
1000
0
-1000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icQ
1000
-2000
0
-1000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
3000
2000
1000
1000
0
-1000
0
-1000
icQerr
imQ
0
-2000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.5.1-4. im (left) and ic (right) with error in DQ ref. frame
80
FFT plot; THD = 14.5%
FFT plot; THD = 13.2%
14
12
12
10
10
8
8
6
6
4
4
2
0
2
0
1000
2000
3000
4000
5000
6000
7000
0
0
1000
2000
3000
4000
5000
6000
Figure 5.5.1-5. ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
7000
81
Figure 5.5.1-6. VDC, ic, vf and im measured states
a
1000
Vf
0
-1000
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
0.085
0.09
0.095
0.1
0.105
0.11
0.115
0.12
b
1000
Vf
0
-1000
0.08
a
2000
Im
0
-2000
0.08
b
2000
Im
0
-2000
0.08
Figure 5.5.1-7. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
icD
2000
2000
imD
0
icQ
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
-1000
0
-1000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
3000
2000
1000
1000
0
-1000
0
icQerr
imQ
0
-2000
1000
-1000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.5.1-8. im (left) and ic (right) with error in DQ ref. frame
82
FFT plot; THD = 11.3%
FFT plot; THD = 9.21%
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1000
2000
3000
4000
5000
6000
7000
0
0
1000
2000
3000
4000
5000
6000
Figure 5.5.1-9. ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
7000
83
5.5.2 Operation under Grid Voltage with Superimposed of 5% of 29th
Harmonic
600
400
200
0
-200
-400
-600
0.155
0.16
0.165
0.17
0.175
0.18
0.185
0.19
0.195
0.2
0.205
Figure 5.5.2-1. Grid with superimposed 5% of 29th harmonic
Figure 5.5.2-1 shows grid voltage at PCC with 5% of 29th harmonic component. Figures
5.5.2-2 to 5.5.2-4 represent measured state responses, observer output states responses and mains
and converter currents in DQ reference frame with RV=0. High components of 29th harmonic in
converter and mains side current can be seen in Figure 5.5.2-5 which is spectrum of those currents.
Converter side current has 10.8% of 29th harmonic, while mains side current has 16.1% of 29th
harmonic. It shows low impedance of LCL filter at 29th harmonic when RV=0.
Figures 5.5.2-6 to 5.5.2-8 represent measured state responses, observer output states
responses and mains and converter currents in DQ reference frame with RV=0.5. In those figures it
can be seen that the presence of 29th harmonic is greatly reduced, showing that virtual resistor has
the same effect as passive resistor increasing impedance of the system. Harmonic content of
converter and mains side current can be seen in Figure 5.5.2-9, converter current having 4.9% and
mains current having 5.7% of 29th harmonic.
84
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.5.2-2. VDC, ic, vf and im measured states
85
a
2000
Vf
0
b
-2000
0.1
1000
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.11
0.12
0.13
0.14
0.15
0.16
0.17
Vf
0
a
-1000
0.1
5000
Im
0
b
-5000
0.1
5000
Im
0
-5000
0.1
Figure 5.5.2-3. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.5.2-4. im (left) and ic (right) with error in DQ ref. frame
86
FFT plot; THD = 11.6%
FFT plot; THD = 16.3%
12
18
16
10
14
8
12
10
6
8
4
6
4
2
2
0
0
1000
2000
3000
4000
5000
6000
0
7000
0
1000
2000
3000
4000
5000
6000
7000
Figure 5.5.2-5. ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.5.2-6.
VDC, ic, vf and im measured states
87
a
1000
Vf
0
b
-1000
0.1
1000
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.11
0.12
0.13
0.14
0.15
0.16
0.17
Vf
0
a
-1000
0.1
5000
Im
0
b
-5000
0.1
5000
Im
0
-5000
0.1
Figure 5.5.2-7. Overlaid measured (blue) and observed (green) vf and im in αβ ref. frame
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.5.2-8. im (left) and ic (right) with error in DQ ref. frame
88
FFT plot; THD = 9.64%
FFT plot; THD = 10.1%
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1000
2000
3000
4000
5000
6000
7000
0
0
1000
2000
3000
4000
5000
6000
7000
Figure 5.5.2-9. ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
89
5.6
Power Factor Control
This section just shows that proposed controller can easily adjust power factor (PF). So far all
test cases had unity power factor. Four test cases are presented below respectively: motoring mode
with positive PF, motoring mode with negative PF, generating mode with positive PF and
generating mode with negative PF.
5.6.1 70% Motoring Load with +0.8pf
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.6.1-1. VDC, ic, vf and im measured states
90
2000
icD
3000
2000
imD
0
icQ
-2000
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
-3000
0.04
1000
-1000
3000
2000
1000
1000
0
-1000
0
icQerr
imQ
0
-2000
1000
-1000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.6.1-2. im (left) and ic (right) with error in DQ ref. frame
91
5.6.2 70% Motoring Load with -0.8pf
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.6.2-1. VDC, ic, vf and im measured states
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
Figure 5.6.2-2.
0.16
0.18
0.2
1000
0
-1000
im (left) and ic (right) with error in DQ ref. frame
92
5.6.3 70% Generating Load with -0.8pf
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.6.3-1. VDC, ic, vf and im measured states
3000
icD
2000
2000
imD
0
-1000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icQ
1000
-2000
0
-1000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
3000
2000
1000
1000
0
-1000
0
icQerr
imQ
0
-2000
1000
-1000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.6.3-2. im (left) and ic (right) with error in DQ ref. frame
93
5.6.4 70% Generating Load with +0.8pf
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.6.4-1.
VDC, ic, vf and im measured states
3000
2000
icD
2000
imD
1000
0
-1000
-3000
icQ
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
icDerr
2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0
-1000
0.2
3000
1000
1000
0
-1000
0
icQerr
-1000
-2000
-3000
0.04
1000
-2000
imQ
0
-2000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1000
0
-1000
Figure 5.6.4-2. im (left) and ic (right) with error in DQ ref. frame
94
5.7
Operation under Polluted and Unbalanced Grid
In this section controller performance is investigated under polluted and unbalanced grid.
Sections 5.7.1 and 5.7.4 shows controller operation and harmonic limits under full load with stiff
and soft grid respectively and no harmonic pre-distortion. With stiff grid (Figures 5.7.1-1 and
5.7.1-2), mains current THD is 3.76% with all individual harmonics complying with IEEE-519
standard. Same with the soft grid (Figures 5.7.4-1 and 5.7.4-2), mains current THD is 4.72% with
all individual harmonics complying with IEEE-519 standard.
With 4% grid voltage THD pre-distortion (Figures 5.7.2-1 and 5.7.2-2), mains current THD at
full load is 4.51%, still complying with IEEE-519 standard total THD and individual harmonics.
With extreme grid conditions, under 15% grid voltage THD pre-distortion (Figures 5.7.3-1 and
5.7.3-2), mains current THD at full load is 11.2%, still being close to compliance with IEEE-519
standard.
In case with unbalanced grid operation with 1.7% unbalance (phase b set to 95% of magnitudes
of phases a and c), there was insignificant deterioration in controller performance as can be seen in
Figures 5.7.5-1 through 5.7.5-3, with no significant negative sequence in currents.
In case with extreme unbalanced grid operation with 7.1% unbalance (phase b set to 80% of
magnitudes of phases a and c), there was deterioration in controller performance, having visible
negative sequence as can be seen in Figures 5.7.6-1 through 5.7.6-3, but controller was stable and
operation in that condition would not be dangerous to AFE hardware.
95
5.7.1 Clean Grid Operation at Full Load and RSCE=120
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.7.1-1. VDC, ic, vf and im measured states
FFT plot; THD = 3.76%
FFT plot; THD = 7.4%
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1000
2000
3000
4000
5000
6000
7000
0
0
1000
2000
3000
4000
5000
6000
7000
Figure 5.7.1-2. ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
96
5.7.2 4% Grid Voltage THD Pre-distortion at Full Load and Rsce=120
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.7.2-1. VDC, ic, vf and im measured states
FFT plot; THD = 8.57%
FFT plot; THD = 4.51%
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1000
Figure 5.7.2-2.
2000
3000
4000
5000
6000
7000
0
0
1000
2000
3000
4000
5000
6000
7000
ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
97
5.7.3 15% Grid Voltage THD Pre-distortion at Full Load and Rsce=120
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.7.3-1. VDC, ic, vf and im measured states
FFT plot; THD = 11.2%
FFT plot; THD = 14%
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1000
Figure 5.7.3-2.
2000
3000
4000
5000
6000
7000
0
0
1000
2000
3000
4000
5000
6000
7000
ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
98
5.7.4 Clean Grid at Full Load and Rsce=10
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.7.4-1. VDC, ic, vf and im measured states
FFT plot; THD = 4.72%
4
FFT plot; THD = 7.16%
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0
1000
2000
Figure 5.7.4-2.
3000
4000
5000
6000
7000
0
1000
2000
3000
4000
5000
6000
7000
ic (left) and im (right) spectrums along with IEEE-519 harmonic limits
99
5.7.5 Unbalanced Grid with 1.7% Unbalance
600
400
200
0
-200
-400
-600
0.155
0.16
0.165
Figure 5.7.5-1.
0.17
0.175
0.18
0.185
0.19
0.195
0.2
0.205
Grid phase b set to 95% of magnitude of phases a and c
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.7.5-2. VDC, ic, vf and im measured states
100
3000
2000
imD
1000
0
-1000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
3000
2000
imQ
1000
0
-1000
-2000
-3000
Figure 5.7.5-3.
im in DQ ref. frame
5.7.6 Unbalanced Grid with 7.1% Unbalance
600
400
200
0
-200
-400
-600
0.155
0.16
0.165
0.17
0.175
0.18
0.185
0.19
0.195
0.2
Figure 5.7.6-1. Grid phase b set to 80% of magnitude of phases a and c
0.205
101
Vdc
1200
1000
800
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Ic
2000
0
-2000
Vf
1000
0
-1000
Im
2000
0
-2000
Figure 5.7.6-2.
VDC, ic, vf and im measured states
3000
2000
imD
1000
0
-1000
-2000
-3000
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
3000
2000
imQ
1000
0
-1000
-2000
-3000
Figure 5.7.6-3.
im in DQ ref. frame
102
5.8
Summary
Through extensive simulations in section 5.3 to 5.7 controller requirements defined in Chapter
4 have been verified. Those requ
1) Ideal command tracking (no phase and amplitude errors)
2) Fast dynamic response (ability to sustain load transients)
3) Good DC bus voltage utilization (low boost)
4) Limited (low) switching frequency
5) Power factor control
6) Low harmonic content (IEEE-519 compliancy)
7) Grid disturbance rejection around resonant frequency (true active damping)
8) Ability to operate on both soft and stiff grids
9) Ability to operate under polluted and unbalanced grid conditions
103
Chapter 6 Experimental Results
Figure 6-1.
Experimental Setup
104
Figure 6-1 shows 900kW Danfoss AFE drive setup where proposed control algorithm was
loaded. Parameters of AFE drive in Figure 6-1 are listed in Table 4-1. AFE drive is connected to
the grid through 1MVA transformer. Grid voltage at PCC is 690V.
Step load transient test is created by placing 1.7Ω resistor in parallel with DC link. Resistor in
series with the contactor is placed in parallel with DC link with contactor initially being open. By
placing 1.7Ω resistor in parallel with DC link, about 530kW step load transient is created. That is
the absolute worst transient case that was possible to create in the lab.
Figures 6-2 to 6-4 represent DC link voltage, converter side phase a current and mains side
currents, respectively. DC link shows well damped and fast transient response. Converter and
mains currents also show fast (almost instantaneous) response, while there is no resonance
excitation. While it was not possible in the lab setup to inject grid disturbances at high frequencies,
step load transients showed excellent and well damped response in the line with simulation results.
1100
1050
1000
950
900
850
800
0
0.005
0.01
0.015
Figure 6-2.
0.02
0.025
0.03
0.035
DC link voltage
0.04
0.045
0.05
105
1000
800
600
400
200
0
-200
-400
-600
-800
-1000
0
0.005
0.01
Figure 6-2.
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Converter side current phase a
1000
800
600
400
200
0
-200
-400
-600
-800
-1000
0
0.005
0.01
Figure 6-3.
0.015
0.02
0.025
0.03
0.035
0.04
Mains side current (three phases)
0.045
0.05
106
Chapter 7 Conclusions and Future Work
Novel control is presented here and verified through simulation and experimental results.
Presented control algorithm with true active damping solution improves stability, performance,
cost and efficiency especially in high power AFE drives.
107
7.1
Discussion of Results
Observer is used as a sensor replacement and state predictor to achieve true active damping
of LCL resonance. Due to feedforward terms in outer synchronous reference frame loop,
instantaneous command tracking capability is achieved, while active damping loop in stationary
reference frame ensures well damped response as well as excellent high frequency grid harmonic
disturbance rejection. Also extensive simulation results as well as limited experimental results
verified all requirements defined in Chapter 4:
1) Ideal command tracking (no phase and amplitude errors)
2) Fast dynamic response (ability to sustain load transients)
3) Good DC bus voltage utilization (low boost)
4) Limited (low) switching frequency
5) Power factor control
6) Low harmonic content (IEEE-519 compliancy)
7) Grid disturbance rejection around resonant frequency (true active damping)
8) Ability to operate on both soft and stiff grids
9) Ability to under polluted and unbalanced grid conditions
108
7.2
Recommendations for Future Research
Future work recommendation is development of grid voltage estimators to replace grid voltage
sensors, and not to compromise greatly achieved performance with grid voltage sensors.
109
Bibliography
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[4]
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[9] C. Bao, X. Ruan, X. Wang, W. Li, D. Pan, K Weng, “Design of Injected Grid Current
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111
[12] P.C. Loh, D.G. Holmes, “Analysis of Multiloop Control Strategies for LC/CL/LCL-Filtered
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Industry
Applications,
vol.
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no.
5,
pp.
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September/October, 2007.
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1
Appendix
A
Matlab/Simulink Models
This appendix contains print diagrams and program listings of all the models used in
this project.
2
Figure A1. Top Level Simulink Model
3
Figure A2. AFE plant block diagram
4
Figure A3. Simulink model of AFE circuit
5
6:0
imbalanceVect
0:32
Constant6
imbalanceON
Constant4
5:0
(1 1 1)
0:35{6,5}
Constant5
Switch2
0:36
0:39
R
0:38
Product
S
2
T
0:40
0:82
0:37
V_ideal
0:41
R 2nd
0:45
0:42
S 2nd
Add
Switch3
T 2nd
0:43
harm2ON
Constant7
0:44
[0 0 0]
0:46
Constant8
0:47
R 5th
0:48
0:51
S 5th
Switch
T 5th
0:49
harm5ON
0:52
Constant
0:50
R 7th
[0 0 0]
0:54
Constant1
0:53
0:57
S 7th
Switch1
T 7th
0:55
harm7ON
Constant2
0:56
[0 0 0]
0:58
R 11th
0:60
Constant3
0:59
0:63
S 11th
Switch4
0:64
T 11th
0:61
R 13th
harm11ON
Constant9
0:66
0:62
0:65
0:69
S 13th
Switch5
[0 0 0]
T 13th
0:67
Constant10
harm13ON
0:70
Constant12
0:72
0:68
[0 0 0]
0:71
0:75
R 17th
Constant11
S 17th
Switch7
0:76
T 17th
0:73
R 19th
harm13ON
Constant16
0:78
0:74
0:77
0:81
S 19th
Switch6
[0 0 0]
T 193th
Constant15
0:79
harm13ON
Constant14
0:80
[0 0 0]
Constant13
6
Figure A4. Mains voltage simulator
f()
tCon1
2:2
2:1
1
1/2
Udc
1
UdcFilt
Gain
1 2:0
z
Unit Delay
2 2:3
ic
3 2:4
um
2
icFilt
3
umFilt
Figure A5. Measurement block
7
/*--------------------------------------------------------------------+
Filename: AngleRefGen.h
By:
Vlatko Miskovic
----------------------------------------------------------------------+
Purpose: C-mex s-function, header file
----------------------------------------------------------------------+
Date created: 1 May 2012
Revision history:
Date:
ID:
Description:
---------------------------------------------------------------------*/
// This macro converts an angle into the range 0 -> 2*pi
// Is only necessary when angle is represented as a float variable.
#define limAngle(A)
while((A)>=TWOPI) (A)-=TWOPI; while((A)<0) (A)+=TWOPI;
#define PI
((float)3.14159265359)
// PI
#define PIHALF
((float)1.57079632680)
// PI/2
#define TWOPI
((float)6.28318530718)
// 2*PI
#define SINPITHIRD
((float)0.86602540379)
// sin(PI/3)
#define SINPISIXTH
((float)0.5)
// sin(PI/6)
#define SQRT2
((float)1.41421356237)
// sqrt(2)
#define SQRT3
((float)1.73205080757)
// sqrt(3)
#define SQRT3HALF
((float)0.86602540379)
// sqrt(3.0) / 2
#define SQRT3RECIP
((float)0.57735026919)
// 1/sqrt(3)
#define ONETHIRD
((float)0.33333333333)
// 1.0/3.0
#define TWOTHIRD
((float)0.66666666667)
// 2.0/3.0
#define SQRTTWOTHIRD ((float)0.81649658093)
// sqrt(2/3)
void InitAngleRefGen
rho
0.5);
rho_1k
rho_2k
uM_a
uM_b
uM_d
uM_q
iLc_d
iLc_q
w
i_channel_pll
uM_d_fund
uM_q_fund
iLc_a = 0.0;
iLc_b = 0.0;
uC_a_ideal = 0.0;
uC_b_ideal = 0.0;
}
() {
= atan2(SQRT3HALF * (uM_s - uM_t),uM_r - (uM_s + uM_t) *
= 0.0;
= 0.0;
=
=
=
=
=
=
0.0;
0.0;
0.0;
0.0;
0.0;
0.0;
= 0.0;
= 0.0;
= uM_r - (uM_s + uM_t) * 0.5;
= SQRT3HALF * (uM_s - uM_t);
8
void AngleRefGen () {
double
double
double
double
kP, tI, tCon1, delta_rho;
a1_pf, b0_pf;
a1_fund, b0_fund;
K_norm;
tCon1
= 1 / (2.0 * FSW);
kP =KP_PLL;
tI =TAU_PLL;
b0_pf = tCon1*2*PI*PFBW_PLL;
a1_pf = 1.0 - b0_pf;
b0_fund = tCon1*2*PI*FUND_BW_PLL;
a1_fund = 1.0 - b0_fund;
uM_a = uM_r - (uM_s + uM_t) * 0.5;
uM_b = SQRT3HALF * (uM_s - uM_t);
uM_d = uM_a * cos(rho_1k) + uM_b * sin(rho_1k);
uM_q = -uM_a * sin(rho_1k) + uM_b * cos(rho_1k);
uM_d_fund_pll = b0_pf * uM_d + a1_pf * uM_d_fund_pll;
uM_q_fund_pll = b0_pf * uM_q + a1_pf * uM_q_fund_pll;
uM_d_fund = b0_fund * uM_d + a1_fund * uM_d_fund;
uM_q_fund = b0_fund * uM_q + a1_fund * uM_q_fund;
uM_a_fund= uM_d_fund_pll * cos(rho_1k) - uM_q_fund_pll * sin(rho_1k);
uM_b_fund= uM_d_fund_pll * sin(rho_1k) + uM_q_fund_pll * cos(rho_1k);
uM_d_harm= uM_d - uM_d_fund_pll;
uM_q_harm= uM_q - uM_q_fund_pll;
uM_a_harm= uM_d_harm* cos(rho_1k) - uM_q_harm* sin(rho_1k);
uM_b_harm= uM_d_harm* sin(rho_1k) + uM_q_harm* cos(rho_1k);
iLc_a = iLc_r - (iLc_s + iLc_t) * 0.5;
iLc_b = SQRT3HALF * (iLc_s - iLc_t);
iLc_d = iLc_a * cos(rho_1k) + iLc_b * sin(rho_1k);
iLc_q = -iLc_a * sin(rho_1k) + iLc_b * cos(rho_1k);
iLc_d_fund = b0_fund * iLc_d + a1_fund * iLc_d_fund;
iLc_q_fund = b0_fund * iLc_q + a1_fund * iLc_q_fund;
iLc_d_harm= iLc_d - iLc_d_fund;
iLc_q_harm= iLc_q - iLc_q_fund;
iLc_a_harm = iLc_d_harm* cos(rho_1k) - iLc_q_harm* sin(rho_1k);
iLc_b_harm = iLc_d_harm* sin(rho_1k) + iLc_q_harm* cos(rho_1k);
9
K_norm = uM_d_fund_pll;
delta_rho = uM_q_fund_pll / uM_d_fund_pll;
i_channel_pll = i_channel_pll + kP*tCon1*delta_rho/tI;
w = kP*delta_rho + i_channel_pll;
rho = rho + tCon1*w;
rho_1k = rho + tCon1*w;
rho_2k = rho_1k + tCon1*w*0.5;
limAngle(rho);
limAngle(rho_1k);
limAngle(rho_2k);
}
double
double
double
double
rho, rho_1k, rho_2k;
w, uM_d, uM_q;
iLc_d, iLc_q, iLc_d_fund, iLc_q_fund;
i_channel_pll;
double
double
double
double
double
double
double
double
double
double
uM_a, uM_b;
uM_d_fund, uM_q_fund;
uM_d_fund_pll, uM_q_fund_pll;
uM_d_harm, uM_q_harm;
uM_a_fund, uM_b_fund;
uM_a_harm, uM_b_harm;
iLc_d_harm, iLc_q_harm;
iLc_a_harm, iLc_b_harm;
iLc_a, iLc_b;
uC_a_ideal, uC_b_ideal;
Figure A6. PLL implementation code
10
/*--------------------------------------------------------------------+
Filename: DClinkVoltCtr.h
By:
Vlatko Miskovic
----------------------------------------------------------------------+
Purpose: C-mex s-function, header file
DC-link voltage controller
----------------------------------------------------------------------+
Inputs: uDC_filt, uM_d_fund, uM_q_fund, pf, i_ff
Block parameter input:
Outputs:
iLm_d_ref, iLm_q_ref
----------------------------------------------------------------------+
Date created: 1 May 2012
Revision history:::
Date:
ID:
Description:
---------------------------------------------------------------------*/
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
#define
PI
((float)3.14159265359)
// PI
PIHALF
((float)1.57079632680)
// PI/2
TWOPI
((float)6.28318530718)
// 2*PI
SINPITHIRD
((float)0.86602540379)
// sin(PI/3)
SINPISIXTH
((float)0.5)
// sin(PI/6)
SQRT2
((float)1.41421356237)
// sqrt(2)
SQRT3
((float)1.73205080757)
// sqrt(3)
SQRT3HALF
((float)0.86602540379)
// sqrt(3.0) / 2
SQRT3RECIP
((float)0.57735026919)
// 1/sqrt(3)
ONETHIRD
((float)0.33333333333)
// 1.0/3.0
TWOTHIRD
((float)0.66666666667)
// 2.0/3.0
SQRTTWOTHIRD ((float)0.81649658093)
// sqrt(2/3)
THREEOVERSQRT2 ((float)2.12132034356)
// 3/sqrt(2)
void InitDClinkVoltCtr () {
// Initializing variables
i_channel_DC = 0.0;
iLm_d_ref
= 0.0;
iLm_d_ref
= 0.0;
uDC_err = 0.0;
uDC_ref = uM_d_fund_pll * eeprom.BOOST_DEFAULT / SQRT3HALF;
}
void DClinkVoltCtr () {
//Local variables
11
double i_max, i_ff, kP, tI, p_channel_DC, PI_out, tCon1, pf, i_nom;
double a1, b0;
double ref_BW;
// Initializing constants
kP
= KP_VOLT_CTR * DC_LINK_C * SQRT3;
tI
= TAU_VOLT_CTR;
i_max
= I_MAX*THREEOVERSQRT2;
i_nom
= I_NOM*THREEOVERSQRT2;
tCon1 = 1 / (2.0 * FSW);
b0 = tCon1*2*PI*ref_BW;
a1 = 1.0 - b0;
DC_limit_factor = 0.95;
ref_BW = 1.0;
// Inputs from user (pf) and load feedforward
pf
= user.Cos_Phi;
i_ff
= i_load * BOOST_DEFAULT * SQRT3;
// Calculating DC link Voltage reference
uDC_ref = uM_d_fund_pll * eeprom.BOOST_DEFAULT / SQRT3HALF;
// Calculating DC link voltage error
uDC_err = uDC_ref - uDC_filt;
// PI regulator
p_channel_DC =
PI_out
iLm_d_ref
i_channel_DC +=
uDC_err * kP;
= p_channel_DC + i_channel_DC;
= PI_out;
(kP * tCon1 * uDC_err/tI);
// Adding feedforward term
iLm_d_ref = iLm_d_ref + i_ff;
iLm_q_ref = iLm_d_ref * sqrt(1 - pf * pf) / pf;
double iLm_d_ref, iLm_q_ref, i_channel_DC;
double DC_limit_flag;
double uDC_ref, uDC_ref_temp, uDC_err;
Figure A7. DC link voltage regulator implementation code
12
/*--------------------------------------------------------------------+
Filename: MainCurrCtrl.h
By:
Vlatko Miskovic
----------------------------------------------------------------------+
Purpose: C-mex s-function, header file
id and iq current controller
----------------------------------------------------------------------+
Input:
imdRef, imqRef, icd, icq, UdcFilt
Block parameter input:
Output:
ucdRef, ucqRef, ucdqRef, thetaRef
----------------------------------------------------------------------+
Date created: 1 May 2012
Revision history:::
Date:
ID:
Description:
---------------------------------------------------------------------*/
#define limAngle(A)
while((A)>=TWOPI) (A)-=TWOPI; while((A)<0) (A)+=TWOPI;
#define PI
((float)3.14159265359)
// PI
#define PIHALF
((float)1.57079632680)
// PI/2
#define TWOPI
((float)6.28318530718)
// 2*PI
#define SINPITHIRD
((float)0.86602540379)
// sin(PI/3)
#define SINPISIXTH
((float)0.5)
// sin(PI/6)
#define SQRT2
((float)1.41421356237)
// sqrt(2)
#define SQRT3
((float)1.73205080757)
// sqrt(3)
#define SQRT3HALF
((float)0.86602540379)
// sqrt(3.0) / 2
#define SQRT3RECIP
((float)0.57735026919)
// 1/sqrt(3)
#define ONETHIRD
((float)0.33333333333)
// 1.0/3.0
#define TWOTHIRD
((float)0.66666666667)
// 2.0/3.0
#define SQRTTWOTHIRD ((float)0.81649658093)
// sqrt(2/3)
void InitMainCurrCtr () {
// Initializing variables
iLm_d_ref = iLm_q_ref = uCf_d_ref = uCf_q_ref = iLc_d_ref = iLc_q_ref = 0.0;
i_channel_D = 0.0;
i_channel_Q = 0.0;
uC_d_ref = uC_q_ref = 0.0;
k_limit = 1.0;
k_max = 1.0;
theta = 0.0;
windup = 0.0;
iLc_a_OBS = iLc_a;
iLc_b_OBS = iLc_b;
uCf_a_OBS = 0.0;
uCf_b_OBS = 0.0;
13
iLm_a_OBS = 0.0;
iLm_b_OBS = 0.0;
iLc_a_OBS_NEW = 0.0;
iLc_b_OBS_NEW = 0.0;
uCf_a_OBS_NEW = 0.0;
uCf_b_OBS_NEW = 0.0;
iLm_a_OBS_NEW = 0.0;
iLm_b_OBS_NEW = 0.0;
uC_a = 0.0;
uC_b = 0.0;
}
void MainCurrCtr () {
//Local variables
double tCon1, kP, tI, kI, Lm, Rm, Cf, Lc, Rc, Lf;
double uC_dq_max, uC_d_max, uC_q_max;
double p_channel_D, p_channel_Q, PI_out_D, PI_out_Q;
double Lobsv, wres, cosWT, sinWT;
double Rv;
Rv = 0.0;
// Initializing constants
tCon1 = 1 / (2.0 * FSW);
kP
= - KP_CURR_CTR;
tI
= TAU_CURR_CTR;
Lm
= LM;
Rm
= RM;
Cf
= CF;
Lc
= LC;
Rc
= RC;
Lf
= Lm + Lc;
limit_BW = 0.1;
CC_limit_factor = 0.8;
wres = sqrt((Lm+Lc)/(Lm*Lc*Cf));
cosWT = cos(wres*tCon1);
sinWT = sin(wres*tCon1);
Lobsv = Lc*10000.0/2.0;
// Calculating maximum available voltage at the output
uC_dq_max = uDC_filt * SQRT3HALF;
//theta = rho_2k;
uC_a = uC_a_ref;
uC_b = uC_b_ref;
// Observer
iLc_a_OBS_NEW = iLc_a_OBS*((Lc/Lm+cosWT)*Lm/(Lc+Lm)) + uCf_a_OBS*(sinWT/(Lc*wres))
+ iLm_a_OBS*((1-cosWT)*Lm/(Lc+Lm)) + uC_a *(-tCon1/(Lc+Lm)-
14
sinWT*Lm/(Lc*(Lc+Lm)*wres)) + uM_a*(tCon1/(Lc+Lm)-sinWT/((Lc+Lm)*wres)) +
Lobsv*(iLc_a - iLc_a_OBS);
iLc_b_OBS_NEW = iLc_b_OBS*((Lc/Lm+cosWT)*Lm/(Lc+Lm)) + uCf_b_OBS*(sinWT/(Lc*wres))
+ iLm_b_OBS*((1-cosWT)*Lm/(Lc+Lm)) + uC_b *(-tCon1/(Lc+Lm)sinWT*Lm/(Lc*(Lc+Lm)*wres)) + uM_b*(tCon1/(Lc+Lm)-sinWT/((Lc+Lm)*wres)) +
Lobsv*(iLc_b - iLc_b_OBS);
uCf_a_OBS_NEW = iLc_a_OBS*(-sinWT/(Cf*wres)) + uCf_a_OBS*(cosWT) +
iLm_a_OBS*(sinWT/(Cf*wres)) + uC_a *((1-cosWT)*Lm/(Lc+Lm)) + uM_a*((1cosWT)*Lc/(Lc+Lm));
uCf_b_OBS_NEW = iLc_b_OBS*(-sinWT/(Cf*wres)) + uCf_b_OBS*(cosWT) +
iLm_b_OBS*(sinWT/(Cf*wres)) + uC_b *((1-cosWT)*Lm/(Lc+Lm)) + uM_b*((1cosWT)*Lc/(Lc+Lm));
iLm_a_OBS_NEW = iLc_a_OBS*((1-cosWT)*Lc/(Lc+Lm)) + uCf_a_OBS*(-sinWT/(Lm*wres)) +
iLm_a_OBS*((Lm/Lc+cosWT)*Lc/(Lc+Lm)) + uC_a *(-tCon1/(Lc+Lm)+sinWT/((Lc+Lm)*wres))
+ uM_a*(tCon1/(Lc+Lm)+sinWT*Lc/(Lm*(Lc+Lm)*wres));
iLm_b_OBS_NEW = iLc_b_OBS*((1-cosWT)*Lc/(Lc+Lm)) + uCf_b_OBS*(-sinWT/(Lm*wres)) +
iLm_b_OBS*((Lm/Lc+cosWT)*Lc/(Lc+Lm)) + uC_b *(-tCon1/(Lc+Lm)+sinWT/((Lc+Lm)*wres))
+ uM_b*(tCon1/(Lc+Lm)+sinWT*Lc/(Lm*(Lc+Lm)*wres));
iCf_a_OBS_NEW = iLm_a_OBS_NEW- iLc_a_OBS_NEW;
iCf_b_OBS_NEW = iLm_b_OBS_NEW- iLc_b_OBS_NEW;
iLc_a_OBS = iLc_a_OBS_NEW;
iLc_b_OBS = iLc_b_OBS_NEW;
uCf_a_OBS = uCf_a_OBS_NEW;
uCf_b_OBS = uCf_b_OBS_NEW;
iLm_a_OBS = iLm_a_OBS_NEW;
iLm_b_OBS = iLm_b_OBS_NEW;
// Calculating Correct References
uCf_d_ref = uM_d + w * Lm * iLm_q_ref;
uCf_q_ref = uM_q - w * Lm * iLm_d_ref;
iLc_d_ref = iLm_d_ref + w * Cf * uCf_q_ref;
iLc_q_ref = iLm_q_ref - w * Cf * uCf_d_ref;
// Calculating error
iLc_d_err = iLc_d_ref - iLc_d;
iLc_q_err = iLc_q_ref - iLc_q;
// PI
p_channel_Q = iLc_q_err * kP;
PI_out_Q
= p_channel_Q + i_channel_Q;
p_channel_D = iLc_d_err * kP;
PI_out_D
= p_channel_D + i_channel_D;
15
i_channel_D += (kI*tCon1*iLc_d_err);
i_channel_Q += (kI*tCon1*iLc_q_err);
// Add feedforward terms
uC_d_ref = PI_out_D + uCf_d_ref + w * Lc * iLc_q_ref; //Commanded ic used
uC_q_ref = PI_out_Q + uCf_q_ref - w * Lc * iLc_d_ref; //Commanded ic used
// DQ to AB and Active Damping Addition
theta = rho_2k;
uC_a_ref = uC_d_ref* cos(theta) - uC_q_ref* sin(theta) - Rv * iCf_a_OBS_NEW;
uC_b_ref = uC_d_ref* sin(theta) + uC_q_ref* cos(theta) - Rv * iCf_b_OBS_NEW;
}
double
double
double
double
uCf_d_ref, uCf_q_ref, iLc_d_ref, iLc_q_ref;
i_channel_D, i_channel_Q;
uC_d_ref, uC_q_ref;
uC_a_fund_ref, uC_b_fund_ref;
double
double
double
double
CC_limit_flag;
theta;
iLc_d_err, iLc_q_err;
windup;
double
double
double
double
iLc_a_OBS, iLc_b_OBS, iLc_a_OBS_NEW, iLc_b_OBS_NEW;
uCf_a_OBS, uCf_b_OBS, uCf_a_OBS_NEW, uCf_b_OBS_NEW;
iLm_a_OBS, iLm_b_OBS, iLm_a_OBS_NEW, iLm_b_OBS_NEW;
uC_a, uC_b;
double iLc_d_OBS, iLc_q_OBS;
double uCf_d_OBS, uCf_q_OBS;
double iLm_d_OBS, iLm_q_OBS;
Figure A8. Observer and current regulator implementation code
16
I_NOM=730;
UM_NOM= 690;
I_MAX=I_NOM*1.85;
SAMP_NO= 15;
BOOST_DEFAULT=1.03;
LM=67.0e-6;
RM=0.01e-3;
CF=317.3e-6;
RD=0.0;
LC=100.6e-6;
RC=0.01e-3;
DC_LINK_C=31500e-6;
FSW=5000;
UDC_MAX=0;
UDC_MIN=0;
UM_MAX=0;
UM_MIN=0;
UM_THD_MAX=0;
UM_IMBALANCE_MAX=0;
KP_CURR_CTR=(eeprom.LC)*2*pi*150.0;
TAU_CURR_CTR=4*eeprom.LC/eeprom.KP_CURR_CTR;
KP_VOLT_CTR=80.0;
TAU_VOLT_CTR=0.04;
KP_PLL=200;
TAU_PLL=0.04;
PFBW_PLL=20.0;
FUND_BW_PLL=1591.0;
KP_RES_CTR=0;
TAU_RES_CTR=0;
Figure A9. The control parameters initialization
17
%% Initialization File
clc
clear all;
close all;
AFE_P630T7;
grid.sc_ratio=1;
grid.XtRt_ratio=1;
grid.um=UM_NOM;
% line to line RMS
grid.Wm=2*pi*50;
%grid.Lt=10e-6;
%function of grid.sc_ratio and grid.XtRt_ratio
%grid.Rt=5.0e-3;
%function of grid.sc_ratio and grid.XtRt_ratio
Rsce = 120; % 10 for weak grid, 120 for strong grid
grid.Lt = (grid.um/sqrt(3))/(I_NOM*2*pi*50*Rsce);
grid.Rt = grid.Lt*2*pi*50*0.05;
grid.kTHDv=0.035*5;
% Put 8 for 8% THD (0.035 is multiplier)
grid.imbalance=1.0;
grid.harm_2nd=0;
grid.harm_5th=grid.kTHDv/5;
grid.harm_7th=grid.kTHDv/7;
grid.harm_11th=grid.kTHDv/11*1;
grid.harm_13th=grid.kTHDv/13*1;
grid.harm_17th=grid.kTHDv/17*1;
grid.harm_19th=grid.kTHDv/19*1;
grid.harm_res=0.0;%1*grid.kTHDv/25; % resonant harmonic amplitude
grid.freq_res=29;
% 27 for 27th harmonic, i.e. 1350Hz
%% lcp
umNom = UM_NOM; % line to line
WmNom = 2*pi*50;
% in radians
Udc_Reference = 0;
Reactive_Power = 0;
Cos_Phi = 1.0;
Regen_Current_Limit = I_NOM * 1.0;
%% Choose LCL
(SimPowerSystems Parameters)
Lm=LM*1.0;
Rm=RM*1.0;
Cf=CF*1.0;
Rd=RD*1.0;
Lc=LC*1.0;
Rc=RC*1.0;
DClinkC=DC_LINK_C*1.0;
Lt=grid.Lt;
Rt=grid.Rt;
18
w_res=sqrt((lcl.Lc+lcl.Lm+lcl.Lt)/(lcl.Lc*(lcl.Lm+lcl.Lt)*lcl.Cf))/(2*p
i)
%% Load
load.time_vector = [0.05 0.1 0.5 0.7];
load.initial_value = [0 0 0 0];
load.final_value = [1 -2 0 0]* 1.0
*sqrt(3/2.)*eeprom.I_NOM/eeprom.BOOST_DEFAULT;
sim('AFE_LCL_SimPower_v0.mdl',0.16);
t=MAIN_DATA.time;
DC_link_V=MAIN_DATA.signals(1,1).values(:,:);
i_c=MAIN_DATA.signals(1,2).values(:,:);
i_f=MAIN_DATA.signals(1,3).values(:,:);
i_m=MAIN_DATA.signals(1,4).values(:,:);
v_f=MAIN_DATA.signals(1,5).values(:,:);
vf_a_OBS=OBSERVER_DATA.signals(1,1).values(:,:);
vf_b_OBS=OBSERVER_DATA.signals(1,2).values(:,:);
im_a_OBS=OBSERVER_DATA.signals(1,3).values(:,:);
im_b_OBS=OBSERVER_DATA.signals(1,4).values(:,:);
u_m=GRID_VOLTAGE.signals(1,1).values(:,:);
kk=10000;
figure(1),plot(t(kk:end,:),DC_link_V(kk:end,:));
figure(2),plot(t(kk:end,:),i_c(kk:end,:));
figure(3),plot(t(kk:end,:),i_f(kk:end,:));
figure(4),plot(t(kk:end,:),i_m(kk:end,:));
figure(5),plot(t(kk:end,:),v_f(kk:end,:));
figure(6),plot(t(kk:end,:),vf_a_OBS(kk:end,:));
figure(7),plot(t(kk:end,:),vf_b_OBS(kk:end,:));
figure(8),plot(t(kk:end,:),im_a_OBS(kk:end,:));
figure(9),plot(t(kk:end,:),im_b_OBS(kk:end,:));
figure(10),plot(t(kk:end,:),u_m(kk:end,:));
Figure A10. Main data initialization and plotting file