Stability Control by FACTS
Xiao-Ping ZhangInstitute for Energy Research and Policy
University of BirminghamUK
Seminario Internacional Bienal CIGRE 2007“Innovación en parques de generación y redes eléctricas
de transmisión”2-4 Dec 2007
2
Contents
• Overview of FACTS Applications
• Design Approaches for Power System Damping Control using FACTS
• Formulation of a Multi-Model System for System Damping Control
• A Two-Step LMI Optimization Approach For the Multi-Model System for System Damping Control
• Two Control Design Strategies
• Modeling of STATCOM into A Multi-machine System
• Numerical Examples
• Conclusions
3
Overview of FACTS Applications
Source: Monograph – Flexible AC Transmission Systems: Modelling and Control by Zhang, Rehtanz & Pal
conventional(switched)
Thyristorvalve
Static VarCompensator
(SVC)
Thyristor ControlledSeries Compensator
(TCSC)
Dynamic FlowController
(DFC)
Voltage Source Converter (VSC)
Static SynchronousSeries Compensator
(SSSC)
Static SynchronousCompensator(STATCOM)
Unified / Interline Power Flow Controller
(UPFC/ IPFC)
R, L, C, Transformer
Switched Shunt-Compensation (L,C)
(Switched) Series-Compensation (L,C)
Phase ShiftingTransformer
FACTS-Devices(fast, static)
Shunt-Devices
Series-Devices
Shunt &Series-Devices
Shunt &Series-Devices
HVDC Back to Back(HVDC B2B)
HVDC VSCBack to Back
(HVDC VSC B2B)
4
Overview of FACTS Applications
• Power flow control
• Increase of transmission capability
• Voltage control
• Reactive power compensation
• Stability control
• Power quality improvement
• Power conditioning
• Flicker mitigation
• Interconnection of renewable and distributed generation and storages.
5
Design Approaches for System Damping Control using FACTS
• Fixed parameter and fixed structure damping controller: The idea from PSS (Power System Stabilizer) design
• Damping Torque Analysis based on Phillips-Heffron model
• H∞∞∞∞ Robust Control Approaches
• LMI (Linear Matrix Inequalities) based Approaches for nominal model
6
Linear Matrix Inequality (LMI) Techniques for nominal model
• H∞∞∞∞ mixed-sensitivity
• Mixed H2/H∞∞∞∞ with pole placement
• Normalized H∞∞∞∞ loop-shaping
7
System model with multiple operating points
where L is the total number of operating points consideredi is the index of different operating points and i = 1, 2, 3,…, L. The plant output y is the feedback signal while u is the controller input.
Formulation of a Multi-Model System for System Damping Control
uDxCy
uBxAx
ii
ii
+=+=�
8
• The design objective for the problem is to find an output feedback controller u(s) = K(s)y(s) for the multi-model system that will place the eigenvalues of all the linearized models in a specified region
• The output feedback controller can be designed via the state output feedback controller:
• Control requirements can be described by nonlinear matrix inequalities (NMI)
State Output Feedback Controller
c c c c
c
x A x B y
u Kx
= +=
�
9
• Nonlinear matrix inequalities (NMI): No-convex problem, no unique solution, difficult to solve
• NMI can be transformed into LMI using a two-step optimization approach through suitable parameterization and transformation�First step: determination of matrix variable K via LMI
optimization�Second step: Determination of matrix variables Ac,
Bc via LMI optimization
A Two-Step LMI Optimization Approach for the Multi-Model System
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• Linear time invariant (LTI) system
where i = 1, 2, … , L. L is the number of operating points
• Output feedback controller
• LMI formulation with the feedback controller considering closed-loop pole clustering in desired LMI region is given by
where i = 1, 2, … , L. L is the number of operating points
• The optimal output feedback controller gain
First Step: Determination of Matrix Variable K
uBxAx ii +=�
Kxu =
0)()( <+⊗++⊗+⊗ Tii
Tii YBXAYBXAX ββα
0>X
1** )( −= XYK
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• Multi-model system
• Ouput feedback controller for the multi-model system in the first step
• Determination of output feedback controller u(s)=K(s)y(s)to replace
• Output state feedback controller
Second Step: Determination of Matrix Variable Ac, Bc
uDxCy
uBxAx
ii
ii
+=+=�
Kxu =
c c c c
c
x Ax B y
u Kx
= +=
�
Kxu =
12
• The LMI formulation for the multi-model with all closed-loop pole clustering in desired LMI region
where • The controller matrices of the output feedback
controller are
Second Step: Determination of Matrix Variable Ac, Bc (continued)
��
���
�
−+−+−+−+
⊗+��
���
�⊗
KYBKGDZZKDCGKBAY
KXBKBAX
Y
X
iiiiii
iii
)()()(
00
βα
0)()()(
)()()( <���
�
���
�
−+−−+−++⊗+
YKBGKDZXKB
ZGKDCYKBAXKBAT
iTT
iTT
i
TTTii
Tii
TiiTβ
0>X 0>YLi ,,2,1 �= TXX = TYY =
*1*)( ZYAc−= *1*)( GYBc
−=
13
Two Control Design Strategies• The first control design strategy: a single damping
controller is determined and used for all operating points.
• The second control strategy: multiple damping controllers are designed and utilized. Each of the multiple damping controllers corresponds to a few operating points.
• A FACTS damping controller is normally designed based on different operating points which correspond to different power transfer load levels. The load levels are grouped into load segments, each of which covers a few to several load levels (operating points).
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The Second Control Design Strategy
• Multiple damping controllers are designed and utilized. Each of the multiple damping controllers corresponds to a few operating points
• Each damping controller is triggered by the power transfer levelconstraint via the SCADA/EMS system while other damping controllers are off
15
Energy control center (ECC) – Brain of energy network
Substation
Remote terminal unit
SCADA Master StationEnergy control center with EMS
EMS one-line diagram
EMS alarm display
16
Modeling of STATCOM into A Multi-machine System
STATCOM (Source: ABB)
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Modeling of STATCOM into A Multi-machine System
STATCOM d-q decoupling control
d axis
q axis
Kp3 + Ki3 /s Kp1 + Ki1 /s
Lsh
+ –
+
+
+ – –
Vdc,ref
Vdc Ishd
Ishd, ref
Vac
Ishq
Vshd
Kp4 + Ki4 /s Kp2 + Ki2 /s
Lsh
+
–
+ –
– Vac,ref
Vmod
Ishq
Ishq, ref
Ishd
+
Vac
small signal damping controller feedback signal
–
Vshq
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Two-area Four-Machine Test System with STATCOM
Area 1 Area 2
G1
Load
STATCOM ±100 MVar
G2 G4
G3
B1 B5 B6 B8 B7 B9 B10 B3
B2 B4 Load
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Description of the Multiple Operating Points
• Multiple operating points were obtained by changing active powertransfer from area 1 to area 2.
• In the studies, four different power transfer levels (100MW, 200MW, 300MW, and 400MW) are created, which are corresponding to four operating points.
• For control strategy 1, four operating points are considered together.
• For control strategy 2, the power transfer levels are classified as two groups. Power transfer levels 100 MW and 200MW belong to Group 1, and power transfer levels 300MW and 400MW belong to Group 2
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STATCOM Damping Controller Using the Two-step LMI Approach
• Damping Controller using the first control design strategy (including all 4 operating points)
• Damping Controller using the second control design strategy
for transfer levels 100 and 200 MW
for power transfer levels 300 and 400 MW
)29.0s)(48.31+ s 1.69 + s)(215735 + s 8895 s(0.23)47.92)(s + s 1.10 + )(s75.73)(s524240.004(s
)s(22
2
+++++=K
)05.2s)(57.74 + s 89.3 s)(76.145)(28.933(
0.68)47.78)(s + s 2.99 + )(s35.57)(s1716600.0012(s)s(
2
2
+++++++=
ssK
)62.0s)(72.40 + s 85.1 s)(669595.437 s(0.25)71.06)(s + s 2.77 + )(s64.33)(s157810.0013(s
)s(22
2
+++++++=
sK
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Comparison of Two Control Strategies at Operating Point of 300MW
Solid line – Control Strategy 2 Dotted line – Control Strategy 1
0 2 4 6 8 10 12 14 16 18 2017.5
18
18.5
19
19.5
20
20.5
t (s )
Ang
le(G
1-G
3) (d
eg)
0 2 4 6 8 10 12 1 4 1 6 18 2 02 90
2 95
3 00
3 05
3 10
3 15
3 20
t (s )
Tie
line
flow
(MW
)
0 2 4 6 8 10 12 14 16 18 200 .992
0 .994
0 .996
0 .998
1
1 .002
1 .004
1 .006
1 .008
t (s )
VB
7 (p
.u)
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0-8
-6
-4
-2
0
2
4
6
8x 1 0
-3
t (s )
Vm
od (p
.u)
22
Comparison of Two Control Strategies at Operating Point of 400MW
Solid line – Control Strategy 2 Dotted line – Control Strategy 1
0 2 4 6 8 10 12 14 16 18 2024 .5
25
25 .5
26
26 .5
27
t (s )
Ang
le(G
1-G
3) (d
eg)
0 2 4 6 8 10 12 14 16 18 20385
390
395
400
405
410
415
t (s )
Tie
line
flow
(MW
)
0 2 4 6 8 10 12 14 16 18 200.994
0.996
0.998
1
1.002
1.004
1.006
1.008
t (s )
VB
7 (p
.u)
0 2 4 6 8 10 12 14 16 18 20-6
-4
-2
0
2
4
6
8x 10
-3
t (s )
Vm
od (p
.u)
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Conclusions
• A novel design approach for damping control of FACTS with multiple operating points has been presented.
• The problem of such a damping control design is actually the problem of designing optimal output-feedback controllers for a multi-model system, of which control requirements can be described by the nonlinear matrix inequalities (NMI).
• The two-step LMI design approach can transfer the original NMI into the linear matrix inequalities (LMI), which can be applicable to the design of FACTS damping control that can guarantee the satisfactory performance over a wide range of operating conditions rather than one operating condition.
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Conclusions• Two control design strategies have been proposed to apply the two-
step LMI approach.
• The first control design strategy is that a single damping controller is determined and used for all operating points.
• The second control strategy is that instead of using a single damping controller for all operating points, multiple damping controllers are designed and utilized. Each of the multiple damping controllers is corresponding to a few operating points.
• The advantage of the second control design strategy is that the LMI design problem is relatively small and easy to solve.
• It has also been found the controller designed is robust in the presence of transmission delay of feedback signal
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Comments may be sent to,
Application of NMI to the Design of FACTS Damping Control with Multiple
Operating Points
