Control and Stability Analysis of Offshore Meshed HVDC
Grids
Modeling HVDC grids as a feedback control system
Ali Bidadfar
October 13, 2017
Denmark Technical University
Wind Energy Department
© PROMOTioN - Progress on Meshed HVDC Offshore Transmission NetworksThis project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 691714
Table of contents
1. Introduction
2. Feedback Control System Model and its Benefits
3. Developing Feedback Control System Model for an HVDC Grid
4. Simulation Results
5. Conclusions
1
Introduction
Specifications of DC grids:
• Low impedance of transmission lines (higher short circuit current)
• Faster dynamics (small time delays play significant role in system dynamic)
• Lower tolerance to faulty situations
• Higher and faster interaction between converters
• The grid control systems must satisfy grid code requirements
• It connects different system operators who may not the same control paradigm
• Control paradigm depends on wind farm production
2
Specifications of DC grids:
• Low impedance of transmission lines (higher short circuit current)
• Faster dynamics (small time delays play significant role in system dynamic)
• Lower tolerance to faulty situations
• Higher and faster interaction between converters
• The grid control systems must satisfy grid code requirements
• It connects different system operators who may not the same control paradigm
• Control paradigm depends on wind farm production
2
Specifications of DC grids:
• Low impedance of transmission lines (higher short circuit current)
• Faster dynamics (small time delays play significant role in system dynamic)
• Lower tolerance to faulty situations
• Higher and faster interaction between converters
• The grid control systems must satisfy grid code requirements
• It connects different system operators who may not the same control paradigm
• Control paradigm depends on wind farm production
2
Specifications of DC grids:
• Low impedance of transmission lines (higher short circuit current)
• Faster dynamics (small time delays play significant role in system dynamic)
• Lower tolerance to faulty situations
• Higher and faster interaction between converters
• The grid control systems must satisfy grid code requirements
• It connects different system operators who may not the same control paradigm
• Control paradigm depends on wind farm production
2
Specifications of DC grids:
• Low impedance of transmission lines (higher short circuit current)
• Faster dynamics (small time delays play significant role in system dynamic)
• Lower tolerance to faulty situations
• Higher and faster interaction between converters
• The grid control systems must satisfy grid code requirements
• It connects different system operators who may not the same control paradigm
• Control paradigm depends on wind farm production
2
Specifications of DC grids:
• Low impedance of transmission lines (higher short circuit current)
• Faster dynamics (small time delays play significant role in system dynamic)
• Lower tolerance to faulty situations
• Higher and faster interaction between converters
• The grid control systems must satisfy grid code requirements
• It connects different system operators who may not the same control paradigm
• Control paradigm depends on wind farm production
2
Specifications of DC grids:
• Low impedance of transmission lines (higher short circuit current)
• Faster dynamics (small time delays play significant role in system dynamic)
• Lower tolerance to faulty situations
• Higher and faster interaction between converters
• The grid control systems must satisfy grid code requirements
• It connects different system operators who may not the same control paradigm
• Control paradigm depends on wind farm production
2
Research Questions Related to DC Grids:
• How DC and AC systems interact with each other?
• How this interaction is analysed? (quantified and qualified)
• How droop controllers impact the system stability?
• Can voltage and frequency droop be implemented on one converter?
• Can conventional tools be used for DC grid stability analysis?
• more possible questions!
3
Research Questions Related to DC Grids:
• How DC and AC systems interact with each other?
• How this interaction is analysed? (quantified and qualified)
• How droop controllers impact the system stability?
• Can voltage and frequency droop be implemented on one converter?
• Can conventional tools be used for DC grid stability analysis?
• more possible questions!
3
Research Questions Related to DC Grids:
• How DC and AC systems interact with each other?
• How this interaction is analysed? (quantified and qualified)
• How droop controllers impact the system stability?
• Can voltage and frequency droop be implemented on one converter?
• Can conventional tools be used for DC grid stability analysis?
• more possible questions!
3
Research Questions Related to DC Grids:
• How DC and AC systems interact with each other?
• How this interaction is analysed? (quantified and qualified)
• How droop controllers impact the system stability?
• Can voltage and frequency droop be implemented on one converter?
• Can conventional tools be used for DC grid stability analysis?
• more possible questions!
3
Research Questions Related to DC Grids:
• How DC and AC systems interact with each other?
• How this interaction is analysed? (quantified and qualified)
• How droop controllers impact the system stability?
• Can voltage and frequency droop be implemented on one converter?
• Can conventional tools be used for DC grid stability analysis?
• more possible questions!
3
Research Questions Related to DC Grids:
• How DC and AC systems interact with each other?
• How this interaction is analysed? (quantified and qualified)
• How droop controllers impact the system stability?
• Can voltage and frequency droop be implemented on one converter?
• Can conventional tools be used for DC grid stability analysis?
• more possible questions!
3
Feedback Control System Model
and its Benefits
An appropriate model (a tool) to answer the research questions:
Modeling entire system as a linear, time invariant, multi-input multi-output Feedback Control
System (FCS)
+_C J
The FCS model is a basic concept in control engineering!
J and C are respectively plant (Jacobian) and controller system model in Laplas domain.
4
Why FSC model?
• System dynamic can be studied in both time and frequency domain.
• Provides more insight into system dynamics.
• An appropriate model for controller design (Many controller design methods are based on
the open loop transfer function).
• The Grid Code Requirements can be taken into account when the limits for the system
stability and performance are determined.
• The interaction between ac and dc systems, and also between converters can be quantified
and qualified.
5
Why FSC model?
• System dynamic can be studied in both time and frequency domain.
• Provides more insight into system dynamics.
• An appropriate model for controller design (Many controller design methods are based on
the open loop transfer function).
• The Grid Code Requirements can be taken into account when the limits for the system
stability and performance are determined.
• The interaction between ac and dc systems, and also between converters can be quantified
and qualified.
5
Why FSC model?
• System dynamic can be studied in both time and frequency domain.
• Provides more insight into system dynamics.
• An appropriate model for controller design (Many controller design methods are based on
the open loop transfer function).
• The Grid Code Requirements can be taken into account when the limits for the system
stability and performance are determined.
• The interaction between ac and dc systems, and also between converters can be quantified
and qualified.
5
Why FSC model?
• System dynamic can be studied in both time and frequency domain.
• Provides more insight into system dynamics.
• An appropriate model for controller design (Many controller design methods are based on
the open loop transfer function).
• The Grid Code Requirements can be taken into account when the limits for the system
stability and performance are determined.
• The interaction between ac and dc systems, and also between converters can be quantified
and qualified.
5
Why FSC model?
• System dynamic can be studied in both time and frequency domain.
• Provides more insight into system dynamics.
• An appropriate model for controller design (Many controller design methods are based on
the open loop transfer function).
• The Grid Code Requirements can be taken into account when the limits for the system
stability and performance are determined.
• The interaction between ac and dc systems, and also between converters can be quantified
and qualified.
5
Example 1: Stability of Current Control Loop of a Grid Connected VSC
A VSC connected to strong DC and AC grids at both sides.
• Does this control loop ever go to
instability?
• If yes, what is the cause?
• And how it can be identified and
taken into account in controller
design?
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
6
Example 1: Stability of Current Control Loop of a Grid Connected VSC
A VSC connected to strong DC and AC grids at both sides.
• Does this control loop ever go to
instability?
• If yes, what is the cause?
• And how it can be identified and
taken into account in controller
design?
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
6
Example 1: Stability of Current Control Loop of a Grid Connected VSC
A VSC connected to strong DC and AC grids at both sides.
• Does this control loop ever go to
instability?
• If yes, what is the cause?
• And how it can be identified and
taken into account in controller
design?
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
6
Example 1: Stability of Current Control Loop of a Grid Connected VSC
• System becomes unstable when the controller
gain has a large value.
• Transport and sampling delay caused by the
PWM process and digital controller
sampling/computation can lead to instability
[Holmes et al., 2009].
• With modal analysis stability and its cause is
not identified.
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
7
Example 1: Stability of Current Control Loop of a Grid Connected VSC
• System becomes unstable when the controller
gain has a large value.
• Transport and sampling delay caused by the
PWM process and digital controller
sampling/computation can lead to instability
[Holmes et al., 2009].
• With modal analysis stability and its cause is
not identified.
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
7
Example 1: Stability of Current Control Loop of a Grid Connected VSC
• System becomes unstable when the controller
gain has a large value.
• Transport and sampling delay caused by the
PWM process and digital controller
sampling/computation can lead to instability
[Holmes et al., 2009].
• With modal analysis stability and its cause is
not identified.
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
7
Example 1: Stability of Current Control Loop of a Grid Connected VSC
For stability analysis the frequency response of FCS open loop model is used.
+_JCCCCC
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
JCC is the AC system model and CCC current controller model.
8
Example 1: Stability of Current Control Loop of a Grid Connected VSC
The frequency response of the system indicates that the system is unstable!
-20
0
20
40
60
80
Ma
gn
itu
de
(d
B)
From: eid1 To: Id1
10-1
100
101
102
103
104
105
-540
-360
-180
0
180
Ph
ase
(d
eg
)
Frequency (rad/s)
Negative Gain Margine
+_JCCCCC
• The negative gain margin in open-loop transfer function indicate the instability.
• How to detect the cause of instability?
9
Example 1: Stability of Current Control Loop of a Grid Connected VSC
The frequency response of the system indicates that the system is unstable!
-20
0
20
40
60
80
Ma
gn
itu
de
(d
B)
From: eid1 To: Id1
10-1
100
101
102
103
104
105
-540
-360
-180
0
180
Ph
ase
(d
eg
)
Frequency (rad/s)
Negative Gain Margine
+_JCCCCC
• The negative gain margin in open-loop transfer function indicate the instability.
• How to detect the cause of instability?
9
Example 1: Stability of Current Control Loop of a Grid Connected VSC
The frequency response of the plant model with and without time delay!
-40
-20
0
20
40
60
Ma
gn
itu
de
(d
B)
Without Time Delay
With Time Dela
100
101
102
103
104
105
-540
-450
-360
-270
-180
-90
0
90
180
Ph
ase
(d
eg
)
Frequency (rad/s)
+_JCCCCC
Time delay changes the phase of the plant model, J, at high frequency.
10
Example 1: Stability of Current Control Loop of a Grid Connected VSC
The controller must have low gain at high frequency.
-50
0
50
100
Magnitude (
dB
)
Plant with time delay
Controller
Open loop
100
101
102
103
104
105
-360
-270
-180
-90
0
90
180
Phase (
deg)
Frequency (rad/s)
Negative Gain Margin
+_JCCCCC
In controller design the time delay must be taken into account!
11
Example 2: Stability of Power Control Loop of a Weak Grid Connected VSC
A VSC connected to a weak AC grid.
-4
-2
0
2
To: P
1
From: Pref1
Strong AC System
Weak AC Syetem
0 1 2-4
-2
0
2
To: Q
1
From: Qref1
0 1 2
Step Response
Time (seconds)
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
The system is unstable when AC grid is weak!
12
Example 2: Stability of Power Control Loop of a Weak Grid Connected VSC
The FCS model for power control loop!
CPQJPQ
+_ +_JCCCCC
PLL CC
L
dv+
_
+
_
+
_
+
_s
vsE
sgv
si
srefv
srefiθ
)(ssZ
JPQ is the plant model ( AC system and current controller model).
CPQ is the power loop controller model ( usually a pair of PI controller).
13
Example 2: Stability of Power Control Loop of a Weak Grid Connected VSC
The accessibility of the plant, JPQ , model help to understand the cause of instability!
-1
0
1
2
3
To
: P
1
From: Idref1
Strong AC System
Weak AC System
0 0.05 0.1-2
0
2
To
: Q
1
From: Iqref1
0 0.05 0.1
Step Response
Time (seconds)
CPQJPQ
+_ +_JCCCCC
There are severe interactions between P and Q control loops when AC grid is weak.
The plant is ill-condition at low frequencies!
14
Developing Feedback Control
System Model for an HVDC Grid
FCS Model of an HVDC Grid:
One of the possible DC grid topologies considered for North Sea
Con1
Con2
Coff1
Coff2Onshore Offshore
==
==
==
==
15
FCS Model of an HVDC Grid:
FCS Model for Converters Current Control Loop:
+_JCCCCC
• The model is block-diagonal i.e. DC grid dynamic can be neglected and CC can be design
independently for each converter!
• Each AC system is represented by a Thevenin equivalent.
16
FCS Model of an HVDC Grid:
FCS Model for Converters Current Control Loop:
+_JCCCCC
• The model is block-diagonal i.e. DC grid dynamic can be neglected and CC can be design
independently for each converter!
• Each AC system is represented by a Thevenin equivalent.
16
FCS Model of an HVDC Grid:
FSC model for Power (Active and Reactive) and Voltage (AC and DC) Contrl
CPVJPV+
_ +_JCCCCC JDC
PVREF
• The DC grid dynamic, JDC , is included in the plant model, JPV .
• Each AC system is represented by a Thevenin equivalent (detailed model can be regarded
of a fast dynamic device like FACTS devices is in nearby).
17
FCS Model of an HVDC Grid:
FSC model for Power (Active and Reactive) and Voltage (AC and DC) Contrl
CPVJPV+
_ +_JCCCCC JDC
PVREF
• The DC grid dynamic, JDC , is included in the plant model, JPV .
• Each AC system is represented by a Thevenin equivalent (detailed model can be regarded
of a fast dynamic device like FACTS devices is in nearby).
17
FCS Model of an HVDC Grid:
FSC model for Direct Voltage Droop Control
CPVJPV
+_ +_JCCCCC
+_RV
JV
JDC
PVREF
• The direct voltage controller gain, RV , is the inverse of power-voltage droop!
18
FCS Model of an HVDC Grid:
FSC model for Providing Frequency Support to Onshore Grids
CPVJPV
+_ +_JCCCCC
+_RV
JV
+_RF CMC
JF
JDC
PVREFVREF
• Electromechanical dynamics, CMC , of onshore AC systems are included in the plant model,
JF .
• There are different schemes of implementing frequency support control (with or without
communication, converter pairing, etc.).
19
FCS Model of an HVDC Grid:
FSC model for Providing Frequency Support to Onshore Grids
CPVJPV
+_ +_JCCCCC
+_RV
JV
+_RF CMC
JF
JDC
PVREFVREF
• Electromechanical dynamics, CMC , of onshore AC systems are included in the plant model,
JF .
• There are different schemes of implementing frequency support control (with or without
communication, converter pairing, etc.).
19
FCS Model of an HVDC Grid:
Simplification:
When studying a slow dynamic phenomenon, faster dynamic control loops can be simplified.
E.g., in frequency support modeling the converter current control loop can be ignored or
simplified by a first order dynamic as:
I = TCC Iref , TCC =ωc
s + ωc, ωc ≈ 1000→ 5000 rad/sec
CPVJPV
+_ +_JCCCCC
+_RV
JV
+_RF CMC
JF
JDC
PVREFVREF
20
Simulation Results
Simulation Results:
Considerations:
• Dynamics of wind farms are not included (YET) in the FCS model.
• Both of onshore converters participate in direct voltage control.
• Frequency of onshore system one is supported by first offshore wind farm through a
communication link.
Con1
Con2
Coff1
Coff2Onshore Offshore
==
==
==
==
21
Simulation Results:
Considerations:
• Dynamics of wind farms are not included (YET) in the FCS model.
• Both of onshore converters participate in direct voltage control.
• Frequency of onshore system one is supported by first offshore wind farm through a
communication link.
Con1
Con2
Coff1
Coff2Onshore Offshore
==
==
==
==
21
Simulation Results:
Considerations:
• Dynamics of wind farms are not included (YET) in the FCS model.
• Both of onshore converters participate in direct voltage control.
• Frequency of onshore system one is supported by first offshore wind farm through a
communication link.
Con1
Con2
Coff1
Coff2Onshore Offshore
==
==
==
==
21
Simulation Results:
Frequency support from offshore one to onshore one
There is 100 ms communication time delay in control loop!
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
0.2
0.4
0.6
0.8
1
f1 to ∆P
3
f1 to f
1,ref with communication delay
f1 to f
1,ref without communication delay
Time (seconds)
Am
plit
ude (
pu)
Con1
Con2
Coff1
Coff2Onshore Offshore
==
==
==
==
22
Simulation Results:
Frequency support from offshore one (C3) to onshore one (C1)
There is 100 ms communication time delay in control loop!
-30
-25
-20
-15
-10
-5
Magnitude (
dB
)
100
101
102
-720
-540
-360
-180
0
Phase (
deg)
Frequency (rad/s)
Con1
Con2
Coff1
Coff2Onshore Offshore
==
==
==
==
23
Simulation Results:
Point-to-point connection between Con.1 and Con.3————————————
Frequency control creates more
interactions between converters.
Some overshoots in active power
of Con3 must be limited by a
proper controllers/limiters.0
1
2
To
: V
DC
1
From: Vdcref1
-1
0
1
To
: W
1
0 0.5-1
0
1
To
: P
3
From: Pmech1
0 0.5
From: Wref1
0 0.5
From: Pref3
0 0.5
Time (seconds)
With frequency control; Without frequency control24
Simulation Results:
Point-to-point connection between Con.1 and Con.3
0 0.2 0.4 0.6 0.8-1
-0.8
-0.6
-0.4
-0.2
0
0.2
To
: W
1
From: Vdcref1
Strong AC system
Weak AC system
0 0.2 0.4 0.6 0.8
From: Wref1
Time (seconds)
100
102
-70
-60
-50
-40
-30
-20
-10
0
10
To
: W
1
From: Vdcref1
100
102
From: Wref1
Frequency (rad/s)
Ma
gn
itu
de
(d
B)
25
Simulation Results:
Meshed HVDC grid with master-slave control: Con.1 in onshore side controls the
direct voltage.
——————————-
In this control scheme the
Con2 and Con4 have not
been impacted by frequency
control.0
1
2
To: V
DC
1
From: Vdcref1
-2
0
2
To: W
1
0
1
2
To: V
DC
2
-2
0
2
To: P
3
0 0.50
1
2
To: P
4
From: Wref1
0 0.5
From: Vdcref2
0 0.5
From: Pref3
0 0.5
From: Pref4
0 0.5
Time (seconds)
26
Simulation Results:
Meshed HVDC grid with voltage droop control: onshore converters (Con1 and Con2)
control the direct voltage.
——————————-
With communication based
frequency control the
operation of non-relevant
converters is not impacted
significantly!
0
0.5
1
To
: V
DC
1
From: Vdcref1
-5
0
5
To
: W
10
0.5
1
To
: V
DC
2
-2
0
2
To
: P
3
0 0.50
1
2
To
: P
4
From: Wref1
0 0.5
From: Vdcref2
0 0.5
From: Pref3
0 0.5
From: Pref4
0 0.5
Time (seconds)
27
Conclusions
Conclusions:
• FCS model is an appropriate tool for dealing with time delays in fast dynamic systems.
• Interactions between different inputs and outputs can be quantified.
• Frequency and voltage droop controls create complicated interactions between converters
28
Conclusions:
• FCS model is an appropriate tool for dealing with time delays in fast dynamic systems.
• Interactions between different inputs and outputs can be quantified.
• Frequency and voltage droop controls create complicated interactions between converters
28
Conclusions:
• FCS model is an appropriate tool for dealing with time delays in fast dynamic systems.
• Interactions between different inputs and outputs can be quantified.
• Frequency and voltage droop controls create complicated interactions between converters
28
Conclusions:
More inputs to FCS model:
• Wind turbine model
• Communication less method for frequency support
• Offshore wind farm with diode rectifier
• Detailed model of AC systems to study power oscillation damping and complicated
interactions between AC and DC grids
29
Conclusions:
More inputs to FCS model:
• Wind turbine model
• Communication less method for frequency support
• Offshore wind farm with diode rectifier
• Detailed model of AC systems to study power oscillation damping and complicated
interactions between AC and DC grids
29
Conclusions:
More inputs to FCS model:
• Wind turbine model
• Communication less method for frequency support
• Offshore wind farm with diode rectifier
• Detailed model of AC systems to study power oscillation damping and complicated
interactions between AC and DC grids
29
Conclusions:
More inputs to FCS model:
• Wind turbine model
• Communication less method for frequency support
• Offshore wind farm with diode rectifier
• Detailed model of AC systems to study power oscillation damping and complicated
interactions between AC and DC grids
29
Questions?
29
References i
Holmes, D. G., Lipo, T. A., McGrath, B. P., and Kong, W. Y. (2009).
Optimized design of stationary frame three phase ac current regulators.
IEEE Transactions on Power Electronics, 24(11):2417–2426.