3.4 Small-Signal Stability
Enhancement
Kai Sun
Spring 2016
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References
[1] P. Kundur, Power System Stability and Control, McGraw-Hill, 1994
[2] Joe H. Chow, “Power System Coherency and Model Reduction,” Springer,
2013
[3] S. Zhang, V. Vittal, Design of Wide-Area Power System Dampling
Controllers Resilient to Communication Failures, IEEE Trans. Power
Systems, v.28, Nov. 2013
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Objective and Methods
•The problem of small-signal stability is usually associated with
insufficient damping of system oscillations
– The use of power system stabilizers (PSS) to control generator
excitation systems is the most cost-effective method, whose
idea is to modulate the generator excitation so as to develop a
component of electrical torque (i.e. damping torque
component) in phase with rotor speed deviation
– Additionally, supplemental stabilizing signals may be used to
modulate HVDC converter controls and FACTS devices, e.g.
SVCs, to enhance damping
•The controls used for small-signal stability enhancement should
also perform satisfactorily under severe transient disturbances.
Therefore, while the controls are designed using linear system
techniques, their overall performance is assessed by considering
small- as well as large-signal responses
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Types of PSS (by selection of the input signal)
1. Delta-omega PSS (Shaft speed)
– Successfully used on hydraulic units since the mid-1960s
– Minimizing the noise from shaft run-out is an important consideration
in the design of measurement equipment.
– For thermal units, it requires a careful consideration of the effects on
oscillations or even instability of torsional modes (typically, >10Hz).
Thus, a torsional filter is needed, which has to be customized for each
type of generators.
2. Delta-P-omega PSS
Torsional
filter
Advantage:
No filter on this
main path.
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3. Frequency based PSS:
– It either directly uses the terminal frequency or derive the approximate
rotor speed using the terminal voltage and current
– The frequency signal is more sensitive to inter-area oscillations, so it is
possible to obtain greater damping contributions to inter-area modes of
oscillation than would be obtainable with the speed input signal.
– Shortcomings include
• During a rapid transient, the terminal frequency signal will undergo a
sudden phase shift. This results in a spike in the filed voltage.
• The frequency signal often contains power system noise caused by
large industrial loads such as furnaces.
• The same basic limitation as the delta-omega PSS: torsional filtering is
still required
4. Digital PSS:
– one of the programs of a digital excitation control system
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Excitation Control and PSS Design [1]
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Selection of the Excitation System: Tyristor exciter
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Selection of the Excitation System: Rotating exciter
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Small-signal stability performance
• PSS with the Tyristor exciter
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Performance under a large disturbance
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Supplementary Control of SVCs
• By rapidly controlling the voltage and reactive power, an SVC (Static Var
Compensator) can contribute to the enhancement of the power system
dynamic performance.
• Normally, voltage regulation is the primary mode of control to improve voltage
stability and transient stability
• Supplementary control with an SVC has the effectiveness in enhancing smallsignal stability depending on the location, input signals and controller design
• Placement of an SVC for small-signal stability enhancement
– Usually, an SVC may be placed on the dominant oscillation path near the
center of oscillation (at the middle of the interconnection between two
areas, where voltage swings are the greatest)
– For large complex systems, the SVC should be placed at the bus most
sensitive to susceptance change (with the highest voltage participation
factor)
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Dominant Inter-area Oscillation Path and Center [2]
• About a specific inter-area oscillation
mode, the path and center of
oscillation are important for
monitoring and control purposes
– line currents on the dominant
oscillation path have the largest
values of |PSD| about the mode
– The center of oscillation on the
path is the bus where the voltage
magnitude has the largest |PSD|
and the phase angle has the
smallest |PSD| about the mode
1
E Y * ( )Y ( ) 
T  T
PSD: S y ( )  lim
For details, see Chapter 10 (by Vanfretti, Chompoobutrgool and Chow) of Ref. [2]
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Example on the WECC System
•Identify the oscillation path and
center on the 0.25Hz mode
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Effect of SVC on an Inter-area mode [1]
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Using a supplementary control
Modal
observability
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Phase-Lead Compensation
G (s) 
Verr ( s )
I (s)
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Effect of SVC Supplementary Control
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Wide-area damping controller resilient to communication failures [3]
SVC
Both the local and wide-area control
signals are fed into the Washout filter
as supplementary control signals
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• Consider Td=100ms communication delay
and solve the optimal wide-area and local
controllers K1 and K2
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