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]
(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 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;
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.
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
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
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
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
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
The static var compensator can be handled at both capacitive and inductive compensation. 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
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.
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].
References
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