Course material

1. Answer: Introduction System stability analysis represents one of the
common
Answer:
Introduction
System stability analysis represents one of the common problems in the fields of control,
systems and signal processing. It is the part of systems and control theory that is adopted in
predicting and studying the stability or instability features of a system through the
Knowledge Of Mathematical Models. The analysis illustrates how a model reacts to changes
and perturbations. In electrical systems, stability analysis involves determining the system
capacity that allows it to continue in a position of functional equilibrium when exposed to
normal functional settings and also to recover a suitable position of equilibrium following a
disturbance.
When considering the design and analysis of electrical systems, stability analysis is always
looked into with great significance. Stability of the electrical system would imply its ability
to attain stable or normal operation following a disturbance [3]. On the contrary, instability
would imply falling out of step or synchronization. One common concept in electrical
systems is voltage stability. Enhancement of voltage stability can be attained by adding
FACTS devices. A perfect opportunity is presented by FACTS controllers to regulate (AC)
transmission, lowering or raising the flow of power in distinct lines and instantaneously
responding to the stability concerns. This technology provides the ability to control the
direction of power flow and capacity to link networks not properly interconnected and
offering the likelihood of exchanging energy between detached agents. The AC electrical
energy transmission is carried out through static FACTS equipment. [1]
Flexible AC Transmission System (Facts)
(FACTS) possess the control features for reliability, flexibility, stability and efficiency.
FACTS devices represent a group of power electronic-founded devices increasingly used in
the power system transmission grid. Such equipment can be used to provide various
functionalities including increased grid stability, improved power transfer capacity, and
great reactive voltage or power support. They are thus installed in AC transmission lines to

2. enhance the power transfer ability, controllability, and stability of the lines through shunt
and series compensation [4]. The addition of FACTS into a power system makes it greater
than other existing control techniques. Various FACTS equipment has various features. They
also enhance power transfer controllability and capability. The basic concept of FACTS is to
allow the system electric structures including impedance, phase angle and voltage, to
charge flexibly and quick within the context of ensuring security, reliability, and stability of
the power system. This ensures it makes the optimum of the available efforts for reasonably
dispensing transmission power, lowering cost and loss of power, and enhancing the
effectiveness of the power grid activities [6].
The FACTS devises can be categorized into three groups regarding their switching
technology. There are those that are fast switched, thyristor switched or mechanically
switched. Depending on the means of connection within the power system, we can
categorize these devices into the following three groups;
Shunt devices that are mostly adopted for reactive voltage and power flow control. Under
these we have the “Static Synchronous Compensator” (STATCOM) and the “Static Var
Compensator” (SVC).
Series devices that are mostly adopted for the prevention of power oscillator, enhancement
of the transient ability, and active power flow control. Under here we have the “Thyristor-
Controlled Series Capacitor” (TCSC), the “Thyristor-Controlled Phase Shifting Transformer”
(TCPST) and the “Static Synchronous Series Compensator” (SSSC).
Comprehensive device that is a combination of 1 and 2, the “Unified Power Flow Controller”
(UPFC)
UPFC is often the most powerful FACT equipment and has wide applications ability. The
device can efficiently enhance the distribution of power flow and equally enhance the
stability of the power system.
Mathematical Modelling Of The Facts Devices
UPFC Model
Overall, the back-to-back source of voltage model is implemented to represent the UPFC.
UPFC comprises of a variable and shunt voltage source VE together with the impedance ZE,
and a variable series
origin of voltage VB with the impedance ZB. It is often considered that UPFC can be fitted
within the s-side of the line s-m. it is also possible to add a dummy bus r to the UPFC end,
making the UPFC an independent outlet for calculation [2]. It is capable of adjusting the
control aspects including the phase angle and magnitude of the shunt and series input
voltage origins concurrently, or autonomously to regulate the flow of power and voltage
profile within the transmission line.
Figure 1: Model of the sources of UPFC Dual Voltage

3. Figure 2: the branch equivalent for the UPFC
During the derivations, the responsibility of UPFC is similar to its input power at every
branch adjacency and is often presented by Ps, upfc + jQs, upfc and Pr, upfc + jQr, upfc
The equivalent injected power is given by
Statacom Model
STATCOM represents the shunt type reactive compensation device that focuses on
supporting the voltage magnitude profile. Thus, it is possible to operate the STATCOM as an
inductive or capacitive compensation by absorbing or injecting power from the system to
control the voltage [11]. It is referred to as a reactive power input Qe.
Figure 3: STATCOM Branch equivalent
TCSC Static Model
The TCSC is often used to regulate the line flow as a desired constant in the coherent action
area by altering the corresponding line reactance continuously and fast. It is possible to
adjust the series variable reactance Xe in the figure below. Its maximum value depends on
the TCSC capacity [8]. Nonetheless, the reactive and active of the lines are often
independent. Thus, active flow of power can be controlled.
Figure 4: Branch equivalent of the TCSC
TCPST Model
The TCPST attains quick alteration of the phase shifter via thyristor mechanical switch. It
enhances the improved usage of this device. This enhances the extensive usage of the PCPST
[9]. The equivalent circuit is presented below;
It is related as a source of shunt current and series voltage. The flow of power can be
managed by adjusting the complex ratio. Equally, it is not conceivable to dependently
regulate the reactive and active power, thus, active power line cab can be referred to as
controllable [12].
Figure 5: Branch equivalent of the TCPST
SVC Model
The static var compensator can be handled at both capacitive and inductive compensation.

4. Within the dynamic and steady state evaluation, the inserted power at bus i during the
period t ? Qi = Q(t)svc that is the measured variable, can be moved to the inserted current at
bus I as shown in the equation below;
which represents the SVC terminal voltage during the time t. the mathematical model is
presented in the diagram below;
Figure 6: SVC model
Provide Power Flow Controllable Region For Tcsc, Tcpst And Upfc
TCSC. TCPST and UPFC have the capacity to control power flow and we will compare them
for the power flow controllable region. From the diagram below, the equivalent electric line
is connected with the FACTS equioment [15]. There is control of power flow through the
series voltage source Upq. In simpler form, we can assume that
Ui = Ui ∠ 0, jUj = jUj ∠ (- θ), Z = R + jX.
Figure 7: The installed equivalent electric line within the FACTS equipment
The apparent line flow is the provided as;
Whenever Upq = o, the electric line will not be managed by the FSCTS devices. Thus, the
above equation will be presented as;
It can also be written as
Depending on the formulations of the equations, the power flow controllable region will be
presented as shown in the figure below;
The point of connection represents the point of initial flow of power.
The controllable area of the TCSC represents a portion of an arc passing through the initial
spot, whereas for the TCPST, it is a section (negative slope) passing via the initial point. In
the case of the UPFC, the controllable area represents a filled circle, with the original spot
being the center spot [11].
Figure 8: Power flow controllable region
The region for the three controllable regions can be quantitatively compared. There is
similar capacity for each of the three devices. It is often considered that the TCSC control
region represents the arc area, whereas for the TCPST rectangular area. The control area
for the UPFC represents the whole circle.

5. Transient Ability Of Facts Devices
Transient ability represents the system ability to uphold a synchronous operation in the
occurrence of a large disturbances like switching of lines or multi-phase short circuit faults.
The analysis of transient stability often focuses on the duration of about three to five
seconds after a disruption. It can often extend to 10 or 20 seconds especially in big systems
that have overriding inter-area swings. In recent activities, the SVC and TSCS FACTS devices
are always adopted in reducing the losses and improving power flow within long distance
transmission lines [3]. Comparison between SSSC, TCSC, and SVC for enhancement of power
system stability following large disturbances for inter-area power system indicates that the
SSSC settling duration for line power within the post fault period is about 1.5 seconds, SVC
at 7 seconds and TCSC at 3 seconds. In determining the STATCOM transient characteristics
and summary of the switch strategy, the simulation outcomes indicated that STATCOM has
the ability to efficiently damp power oscillations. FACTS equipment possess the capacity to
regulate the reactive and active power control and the adaptive to voltage-magnitude
control concurrently due to their quick management and flexibility features. Considering
FACTS devices are made up of solid-state controllers, they tend to have accurate and fast
response [5]. The devices can therefore be used in improving the system voltage profile,
improving the transmission capability, and augmenting the system stability.
SVC Device- an SVC device has the ability to control the voltage at the desired bus thus
enhancing the system voltage ability. It can also offer the improved damping to power the
oscillations and improve flow of power within a line through auxiliary signal like line
reactive power, line active power, computed internal frequency and line current [4].
TCSC- they offer powerful mode of improving and controlling the level of power transfer for
a system through achieved by varying the apparent impedance of a given transmission line.
It can be adopted in desirable means for contingencies to enhance the power system
stability. The device enables stable operation at power limits above those for which the
system was initially desired without endangering its stability [16]. The device can also be
used to resolve sub synchronous resonance (SSR). A TCSC module is made up a series
capacitor, a metal-oxide varistor (MOV), a pair of anti-parallel thyristors with inductor in
parallel path that enables protection from over voltage and acts as a bypass breaker.
STATCOM- it is dependent on a synchronous source of voltage that produces a stable set of
3 sinusoidal voltages at the essential frequency with phase angle and swiftly controllable
amplitude. It generally comprises of a dc capacitor, coupling transformer, and voltage
source converter.
UPFC- the UPFC is considered the most versatile device that is often adopted in improving
the transient stability, dynamic stability, and steady state stability. The device has the ability
to absorb and supply reactive and real power. it is made up of two AC/ DC converters [9].

6. References
Purumala, R. R., Sinha, A. K., & Kishore, N. K. (2002). Incorporation of FACTS Devices in a
Transient Stability Analysis Programme. In National Power Systems Conference (NPSC) (pp.
519-524).
BEKRI, O., & FELLAH, M. THEORY, Modelling and Control of FACTS devices.
Liu, J., Chen, J., & Qian, Z. (2017). Comparative analysis of FACTS devices based on the
comprehensive evaluation index system. In MATEC Web of Conferences (Vol. 95, p. 15002).
EDP Sciences.
Murali, D., Rajaram, M., & Reka, N. (2010). Comparison of FACTS devices for power system
stability enhancement. International Journal of Computer Applications, 8(4), 30-35.
Damor, K. G., Patel, D. M., Agrawal, V., & Patel, H. G. (2014). Improving power system
transient stability by using facts devices. International Journal of Engineering Research &
Technology (IJERT), 3(7), 2278-0181.
Panda, S., & Patel, R. N. (2006). Improving power system transient stability with an off-
centre location of shunt FACTS devices. JOURNAL OF ELECTRICAL ENGINEERING-
BRATISLAVA-, 57(6), 365.
Esmaili, M., Shayanfar, H. A., & Moslemi, R. (2014). Locating series FACTS devices for multi-
objective congestion management improving voltage and transient stability. European
journal of operational research, 236(2), 763-773.
Damor, K. G., Patel, D. M., Agrawal, V., & Patel, H. G. (2014). Improving power system
transient stability by using facts devices. International Journal of Engineering Research &
Technology (IJERT), 3(7), 2278-0181.
Nelson, R. J., Bian, J., Ramey, D. G., Lemak, T. A., Rietman, T. R., & Hill, J. E. (1996). Transient
stability enhancement with FACTS control.
Praing, C., Tran-Quoc, T., Feuillet, R., Sabonnadiere, J. C., Nicolas, J., Nguyen-Boi, K., &
Nguyen-Van, L. (2000, July). Impact of FACTS devices on voltage and transient stability of a
power system including long transmission lines. In 2000 Power Engineering Society
Summer Meeting (Cat. No. 00CH37134) (Vol. 3, pp. 1906-1911). IEEE.
Bergen, A. R., & Hill, D. J. (1981). A structure preserving model for power system stability
analysis. IEEE transactions on power apparatus and systems, (1), 25-35.
Paserba, J. J., Miller, N. W., Larsen, E. V., & Piwko, R. J. (1995). A thyristor-controlled series
compensation model for power system stability analysis. IEEE Transactions on Power
Delivery, 10(3), 1471-1478.
Remon, D., Cantarellas, A. M., Mauricio, J. M., & Rodriguez, P. (2017). Power system stability
analysis under increasing penetration of photovoltaic power plants with synchronous
power controllers. IET Renewable Power Generation, 11(6), 733-741.
Hingorani, N. G. (1991, September). FACTS-flexible AC transmission system. In International
Conference on AC and DC Power Transmission (pp. 1-7). IET.
Georgilakis, P. S., & Vernados, P. G. (2011). Flexible AC transmission system controllers: An
evaluation. In Materials Science Forum (Vol. 670, pp. 399-406). Trans Tech Publications Ltd.
Song, Y. H., & Johns, A. (Eds.). (1999). Flexible ac transmission systems (FACTS) (No. 30).
IET.

7. Hingorani, N. G. (1996). Flexible AC transmission system (FACTS). In Electricity
Transmission Pricing and Technology (pp. 239-257). Springer, Dordrecht.