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©International society of academic and industrial research
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International Journal of Academic Research in Applied Science
IJARAS 1(4): 16-23, 2012
ijaras.isair.org
Robust Stabilizer Design by Using QFT
Ahmad Memaripour
Department of Electrical Engineering, Boroujen Branch, Islamic Azad University, Boroujen, Iran
Email: [email protected]
Abstract
Static Synchronous Series Compensator (SSSC) is a voltage-sourced converter-based series
compensator and was proposed within the concept of using converter-based technology
uniformly for shunt and series compensation, as well as for transmission angle control. It has
been successfully applied in power systems. This paper presents the application of
supplementary stabilizer based on SSSC in order to stability enhancement. The ability of the
proposed method is evaluated in an electric power system. Quantitative feedback theory
(QFT) is used to design the proposed stabilizer.
Keywords
Quantitative Feedback Theory, Static Synchronous Series Compensator, Low Frequency
Oscillations, Stabilizer
Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012
1. Introduction
With the practical applications of converter-based flexible AC transmission system (FACTS)
controllers [1] such as the static synchronous compensator (STATCOM) [2], static
synchronous series compensator (SSSC) [3] and unified power- flow controller (UPFC) [4],
modeling and analysis of these FACTS controllers in power-system operation and control is
of great interest. Power-flow calculations are fundamental to the operation, planning and
control of power systems. In recent years, significant work has been done in the modeling of
the FACTS controllers in and optimal-power-flow studies [3, 5-16].
SSSC is a voltage-sourced converter-based series compensator and was proposed within the
concept of using converter-based technology uniformly for shunt and series compensation, as
well as for transmission angle control. It has been successfully applied in power systems. In
this paper, SSSC is used to increase power system stability. A supplementary stabilizer is
equipped based on SSSC. The proposed stabilizer is designed by using QFT.
2. QFT method
Quantitative Feedback Theory (QFT) is a unified theory that emphasizes to use of feedback
for achieving the desired system performance tolerances despite plant uncertainty and plant
disturbances. QFT quantitatively formulates these two factors as following form:
(i)- Sets τR = {TR} of acceptable command or tracking input-output relations and sets τD =
{TD} of acceptable disturbance input-output relations.
(ii)- Sets ρ = {P} of possible plants.
The object is to guarantee that the control ratio (system transfer function) TR =Y/R is a
member of τR and TD=Y/D is a member of τD for all P(S) in ρ. QFT is essentially a
frequency-domain technique and in this paper is used for multiple input – single output
(MISO) systems. It is possible to convert the MIMO system into its equivalent sets of MISO
systems to which the QFT design technique is applied. The objective is to solve the MISO
problems, i.e., to find compensation functions which guarantee that the performance
tolerance of each MISO problem is satisfied for all P in ρ. The detailed step-by-step
procedure to design controllers using QFT technique is given in [17].
3. Static Synchronous Series Compensator (SSSC)
SSSC is one of the most important FACTS devices. It is installed in series with transmission
line. This device has a voltage source converter serially connected to a transmission line
through a transformer. It is necessary an energy source to provide a continuous voltage
through a condenser and to compensate the losses of the VSC. A SSSC is able to exchange
active and reactive power with the transmission system. But if our only aim is to balance the
reactive power, the energy source could be quite small. The injected voltage can be controlled
in phase and magnitude if we have an energy source that is big enough for the purpose. With
reactive power compensation only the voltage is controllable, because the voltage vector
forms 90º degrees with the line intensity. In this case the serial injected voltage can delay or
advanced the line current. This means that the SSSC can be uniformly controlled in any
value, in the VSC working slot.
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Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012
The Static Synchronous Series Compensator (SSSC) uses a VSC interfaced in series to a
transmission line, as shown in the Figure 1. Again, the active power exchanged with the line
has to be maintained at zero hence, in steady state operation, SSSC is a functional equivalent
of an infinitely variable series connected capacitor. The SSSC offers fast control and it is
inherently neutral to sub-synchronous resonance.
Figure 1: SSSC - A VSC interfaced in series to a transmission line
As mentioned, Static Synchronous Series Compensator (SSSC) is placed in the group of
series connected FACTS devices. As shown in Figure 2, SSSC consists of a voltage source
inverter connected in series through a coupling transformer to the transmission line. A source
of energy is required for providing and maintaining the DC voltage across the DC capacitor
and compensation of SSSC losses. Figure 3 shows the model of SSSC which consists of a
series connected voltage source in series with impedance. This impedance represents the
impedance of coupling transformer.
Figure 2: basic configuration of SSSC
Figure 3: equivalent circuit of SSSC
The SSSC when operated with an appropriate DC supply (an energy source and/or sink, or
suitable energy storage) can inject a component of voltage in anti-phase with the voltage
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Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012
developed across the line resistance, to counteract the effect of the resistive voltage drop on
the power transmission.
4. Power system stabilizer
An AVR (without supplementary control loops) can weaken the damping provided by the
damper and field windings. This reduction in the damping torque is primarily due to the
voltage regulation effects inducing additional currents in the rotor circuits that oppose the
currents induced by the rotor speed deviation Δω. Adding supplementary control loops to the
generator AVR or FACTS devices is one of the most common ways of enhancing both smallsignal (steady-state) stability and large-signal (transient) stability. The Stabilizer can be used
to add damping signal to the SSSC, where the output signal of the stabilizer is used as an
additional input (vstab) to the SSSC. The stabilizer input signal can be either the machine
speed deviation, Δω, or its acceleration power. The stabilizer is modeled by the nonlinear
system depicted in Figure 4.
Figure 4: Conventional stabilizer
The model consists of a low-pass filter, a general gain, a washout high-pass filter, a phasecompensation system, and an output limiter. The general gain K determines the amount of
damping produced by the stabilizer. The washout high-pass filter eliminates low frequencies
that are present in the Δω signal and allows the stabilizer to respond only to speed changes.
The phase-compensation system is represented by a cascade of two first-order lead-lag
transfer functions used to compensate the phase lag between the excitation voltage and the
electrical torque of the synchronous machine.
5. Test system
Figure 5 shows a two area system installed with SSSC. Bus 4 is aggregation of a large
number of generators and it can be modeled as an infinite bus. The SSSC is installed in one
of two parallel lines. The system data are given in [18].
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Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012
Figure 5: power system installed with SSSC
6. Stabilizer design
In this section the SSSC supplementary stabilizer is designed by using QFT method. QFT
method leads to a controller which satisfies system performance over all operating conditions
and plants. The topology of control loop in the QFT method is depicted in figure 6. The
uncertain plant is obtained by using system model presented and then the controller is
designed to satisfy the output under all uncertainties in the plant.
disturbance
Input
+
Controller
+
+
Uncertain Plant
output
-
Figure 6: control loop in the QFT method
The controller is design by using QFT toolbox of MATLB software. In order to obtain a good
response, minimum damping ratios ζ for the dominant roots of the closed-loop system is
considered as ζ=1.2, this amount, on the Nichols chart establishes a region which must not be
penetrated by the template of loop shaping for all frequencies. The boundary of this region is
referred to as U-contour. The resulted controller is as follows:
Controller=192.5 ×
.
.
×
.
.
7. Simulation result
The proposed stabilizer is evaluated based on the test system given in section 4.1. Large
disturbance is considered to show ability of the proposed stabilizer. The simulation results are
depicted in figures 7-8. It is seen that the system without stabilizer contains insufficient
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Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012
damping and the responses are pendulous. But the stabilizer can greatly enhance power
system stability and damp out the oscillations and the advantages of the proposed stabilizer
are visibly seen.
1.015
1.01
Speed(pu)
1.005
1
0.995
0.99
0.985
0
5
10
15
Time(s)
Figure 7: speed following 6 cycle three phase short circuit in bus 2
Solid: with stabilizer dashed: without stabilizer
1.015
1.01
Speed(pu)
1.005
1
0.995
0.99
0.985
0
5
10
15
Time(s)
Figure 8: speed following 10 cycle three phase short circuit in bus 3
Solid: with stabilizer dashed: without stabilizer
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Int. J. Acad. Res. Appl. Sci., 1(4): 16-23, 2012
8. Conclusion
In this paper a supplementary stabilizer has been successfully applied based SSSC. A power
system installed with a SSSC has been assumed to demonstrate the ability of the proposed
stabilizer. Nonlinear simulation results demonstrated that the designed stabilizer capable to
guarantee the robust stability and robust performance under disturbances. Also, simulation
results show that the QFT is a suitable tool to design stabilizer parameters.
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