Installation and Benefits of FACTS Controllers and Voltage Stability in Electrical Power Systems

Installation and Benefits of FACTS Controllers and Voltage Stability in Electrical Power Systems Sajid Ali 1, Sanjiv Kumar 2, Vipin Jain 2 1 Electrical Department, MIT Meerut (UP),India 2 Research Scholar, Delhi Technological University, Delhi Email: sajidali.ali01@gmail.com, activesanjiv007@rediffmail.com Abstract Flexible AC Transmission Systems (FACTS) devices have been used in power systems since the 1970s for the improvement of its dynamic performance. In this paper various facts related to the benefits and applications of FACTS controllers in electric utilities are presented. Increased electric power consumption causes transmission lines to be driven close to or even beyond their transfer capacities resulting in overloaded lines and congestions. FACTS technology encompasses a collection of controllers, which can be applied individually or in coordination with others to control one or more of the interrelated system parameters. This paper describes FACT controller used in electrical power system. An Unified power flow controller is FACTS controller used to control of active and reactive power and the interline power flow controller is use for series compensation with the unique capability of power management among multiline of a substation. FACTS controllers can control series impendence, shunt impedance,, voltage and phase angle. The overall process for system studies and analysis associated with FACTS installation projects and the need for FACTS controller models is also discussed.ipfc is used to improve the power flow and to provide a power balance of a transmission system. In this paper FACTS installations have been highlighted and performance comparison of different FACTS controllers has been discussed.various FACTS controllers and several devices in FACTS family are also discussed. By installing FACTS equipments at optimal sites the overall system benefits is sought. Keywords Flexible AC Transmission Systems,voltage stability, Power System Control, IPFC, STATCOM, SSSC, SVC, TCSC, Unified Power Flow Controller. I. INTRODUCTION Flexible devices have become more and more popular in power systems. Their primary application is to enhance power transfer capabilities, allow more flexible control of power flows, as well as provide reactive power support. Besides, they can also provide additional oscillation damping control, which improves power system small signal stability. The use of FACTS devices to improve power system stability has long been recognized. The concept of how an SVC adds damping to electromechanical oscillations was presented in some early publications [1] [3] for single machine infinite bus systems.the objective of a FACTS installation in a power system is usually not to perform one single task, but rather multiple tasks are trying to be optimally combined; for example power flow control, voltage control, minimising the losses, damping of oscillations etc. The location of the FACTS device has a large impact on its performance with regard to the objective to be fulfilled. A location being the best for one objective may be less suitable for another objective. If the objective of the Thyristor Controlled Series Capacitor (TCSC), for example, is the power flow control, the most effective location is often in highly loaded lines [1]. Located in highly loaded line, the TCSC can have a larger effect on another lightly loaded line. Applying the power flow control or any other objective of FACTS devices in general, it is often desirable to have a control design which enables the operation of the controlled transmission path without affecting the rest of the system. So far there is no FACTS controller that is able to satisfy the control objective without affecting the rest of the system, but it is possible to minimise its negative influence. Utilization of the existing power system is provided through the application of advanced control technologies. Power electronics based equipment, or Flexible AC Transmission Systems (FACTS), provide proven technical solutions to address these new operating challenges being presented today. FACTS technologies allow for improved transmission system operation with minimal infrastructure investment, environmental impact, and implementation time compared to the construction of new transmission lines The FACTS controllers offer a great opportunity to regulate the transmission of alternating (AC), increasing or diminishing the power flow in specific lines and responding almost instantaneously to the stability problems. The potential of this technology is based on the possibility of controlling the route of the power flow and the ability of connecting networks that are not adequately interconnected, giving the possibility of trading energy between distant agents.[3] Flexible Alternating Current Transmission System (FACTS) is a static equipment used for the AC transmission of electrical energy. It is meant to enhance controllability and increase power transfer capability. It is generally power electronics based device. FACTS is defined by the IEEE as "a power electronic based system and other static equipment that provide Proc. of the International Conference on Science and Engineering (ICSE 2011) Copyright 2011 RG Education Society ISBN: 978-981-08-7931-0 6

control of one or more AC transmission system and [2] The FACTS devices can be divided in three groups, dependent on their switching technology: mechanically switched (such as phase shifting transformers), thyristor switched or fast switched, using IGBTs [4]. While some types of FACTS, such as the phase shifting transformer (PST) and the static var compensator (SVC) are already well known and used in power systems, new developments in power electronics and control have extended the application range of FACTS. Furthermore, intermittent renewable energy sources and increasing international power flows provide new applications for FACTS. The additional flexibility and controllability of FACTS allow to mitigate the problems associated with the unreliable of supply issues of renewable.svcs and STATCOM devices are well suited to provide ancillary services (such as voltage control) to the grid and fault ride through capabilities which standard wind farms. Furthermore, FACTS reduce oscillations in the grid, which is especially interesting when dealing with the stochastic behavior of renewable. II. FACTS HISTORY IN ELECTRICAL POWER SYSTEM The concept of FACTS devices was presented in 1979, but the practical implementation and development of new analytical procedures are still in evolution. One of the objectives of the paper is to present the state-of-the-art technology and analysis of FACTS devices. Since the field FACTS controller, namely Sent Transformer (ST), has been proposed. In contrast to the UPFC, which uses a large number of solid-state switching devices, the ST uses time-tested components, such as transformer and load tap changers, but provides the same independent active and reactive power flow control as the UPFC at a much lower cost. The FACTS devices are installed on electric power (high voltage AC) transmission lines to stabilize and regulate power flow for the dynamic control of voltage impedance and phase angle. Power lines protected by FACTS devices can support greater because anomalies frequency excursions, voltage drop, phase mismatch, malformed wave shape, power spikes, etc. that would otherwise cause breakers to trip are removed or greatly reduced by FACTS conditioning. A FACTS device can also limit the amount of that flows on a line by effectively greater degree of flow control than provided by a switch or breaker. In particular, when applied to a FACTSprotected line is greater than the device will allow, the power merely flows elsewhere rather than tripping a breaker, and power continues to flow on the protected line. Essentially, lines can be run closer to their theoretical capacities when they are protected by FACTS devices. For a large line, that can mean substantial additional power. High voltage, high-power FACTS devices are buildingsized and expensive, but they are lower cost and have less impact per added unit of electric power than new transmission lines. This is the essential benefit of operating standalone FACTS devices on individual lines. In addition to the several successful installations of the first generation, the second generation of FACTS controllers which uses GTO-based VSC configurations is expected to evolve into another mature family of FACTS controllers as several power utilities worldwide have started installing such controllers.. III. GENERATIONS OF THE FACTS DEVICES Depending on technological features, the FACTS devices can divided into two generations - first generation: used thyristors with ignition controlled by gate(scr). - second generation: semiconductors with ignition and extinction controlled by gate (GTO s, MCTS,IGBTS,IGCTS, etc). FACTS devices Attributes of control First Generation Static Var Compensator Voltage control and SVC, (TCR,TCS,TRS) stability, compensation of VAR s. muffling of oscillations Thyristor Controlled Series Compensations (TCSC,TSSC) Thyristor Reactor (TCSR,TSSC) Controlled Series Thyristor Controlled Phase Shifting Transformer (TCPST,TCPR) Thyristor Controlled Voltage Regulator (TCVR) of of Control of active power, muffling of oscillations, transitory, dynamics and of voltage stability Control of reactive power, voltage control, muffling of namics and voltage stability Thyristor Controlled Limits of transitory and Voltage Limited (TCVL) dynamic voltage Thyristor Controlled Control of reactive power, Voltage Regulator voltage control, muffling of (TCVR) dynamics and voltage stability. Second Generation Synchronous Static Voltage control and with storage) stability, compensation of VAR s, muffling of oscillations, transitory, dynamics and of tension stability Synchronous Static without storage) Voltage control, compensation of VAR s, muffling of oscillations, 7

Static Synchronous Series without storage) Static Synchronous Series with storage) Unified Power Flow Controller(UPFC) Interline Power Flow Controller (IPFC) stability of voltage of of stability Control of active and reactive power, voltage control, compensation of VAR s, muffling of Control of reactive power, voltage control, muffling of stability Fig.1(d), in which series controllers Provide independent series reactive compensation for each line but also transfer real power among the lines via the power link. The real power transfer capability of the unified series-series Controller, referred to a Interline Power Flow controller, makes it possible to balance both the real and relative power flow in the lines and thereby maximize the utilization of the transmission system. Note that the term converters are all connected together for real power transfer. IV. BASIC TYPES OF FACTS CONTROLLERS In general, depending on the type of connection to the network FACTS devices can differentiate four categories Series controllers Shunt controllers Combined series-series controllers Combined series shunt controllers Series Controllers: [Fig. 1(b)]. The Series Controller could be variable impedance, such as capacitor, reactor, etc., or power electronics based variable source of main frequency, sub synchronous and harmonic frequencies (or a combination) to series the desired need. In principal, all series Controllers inject voltage in series with the line. Even variable impedance multiplied by the flow through it, represent an injected series voltage in the line. As long as the voltage is in phase quadrature with the line, the series controller only supplies or consumes variable reactive power. Another phase relationship will involve handle or real power as well. Shunt controller: [Fig.1(c)] as in the case of series controllers, the shunt controllers may be variable impedance, variable source, or a combination of these. In principle, all shunt controllers inject into the system at the point of connection. Even a variable shunt impedance connected to the line voltage causes a variable flow and hence represents injection of into the line. As long as the injected is in phase quadrature with the line voltage, the shunt controller only supplies or consumes variable reactive power. Any other phase relationship will involve handling of real power as well. Combined series-series controller: [Fig. 1(b)] This could be a combination of separate series controllers, which are controlled in a coordinated manner, in a multiline transmission system. Or it could be a unified Controller, Fig.1 Combined series-shunt Controller: [Fig. 1(e) and 1 (f)] This could be a combination of separate shunt and series controllers, which are controlled in a coordinated manner [Fig. 1(e)], or a Unified Power Flow controller with series and shunt elements [Fig.1(f)]. In principle, combined shunt and series controllers inject into the system with the hunt part of the controller and voltage in series in the line with the series part of the Controller. However, when the shunt and series controllers are unified, there can be a real power exchange between the series and shunt Controllers via the power link. V. RELATIVE IMPORTANCE OF DIFFERENT TYPES OF CONTROLLERS It is important to appreciate that the series- connected controller impacts the driving Voltage and hence the and power flow directly. Therefore, if the purpose of eh application is to control the /power flow and damp oscillations, the series Controller for a given MVA size is several times more powerful than the shunt Controller. As mentioned, the shunt controller, on the other hand, is like a source which draws from or injects into the line. The shunt Controller is therefore a good way to control voltage at and around the point of connection though injection of reactive (leading or lagging), alone or a combination of active and relative for more effective voltage control and damping of voltage oscillations. This is not to say that the 8

series Controller cannot be used to keep the line Controller within the specified range. After all, the voltage fluctuations are largely a consequence of the voltage drop in series impedances of lines, transformers, and generators. Therefore, adding or subtracting the FACTS Controller voltage in series (main frequency, sub synchronous or harmonic Voltage ad combination thereof) can be the most cost-effective way of improving the voltage profile. Nevertheless, a shunt controller is much more effective in maintaining a required voltage profile at a substation bus. One important advantage of the shunt Controller is that is serves the bus node independently of the individual lines connected to the bus. Series controller Solution May require, but not necessarily, a separate series controller for several lines connected to the substation, particularly if the application calls for contingency outage of any one line. However, this should not be a decisive reason for choosing a shunt connected controller, because the required MVA size of the series Controller is small compared to the shunt controller, and any case, the shunt controller does not provide control over the power flow in the lines. On the other hand, seriesconnected controllers have to be designed to ride through contingency and dynamic overloads, and ride through or bypass short circuit s. They can be protected by metal oxide arresters or temporarily bypassed by solidstate devices when the fault is too high, but they have to be rated to handle dynamic and contingency overload. For the combination of series and shunt controllers, the shunt controller can be single unit serving in coordination with individual line Controllers[ Figure 1(g)] This arrangement can provide additional benefits (reactive power flow control) with unified controllers. Static synchronous ): A static synchronous generator operated as a shunt connected static var compensator whose capacitive or inductive out can be controlled independent of the ac system voltage. STATCOM is one of the key FACTS controllers. It can be based on a voltage sourced or -sourced converter. As mentioned before, from and overall cost point of view, the voltage-sourced converters seem to be preferred, and will be the basis for presentations of most converter-based FACTS Controllers. The SVC as a compensation device operates similar to STATCOM. The STATCOM, however, performs much better than the SVC at very low voltages. Fig. 2. V-I characteristic of the SVC and STATCOM. For the voltage-sourced converter, its ac output voltage is controlled such that it is just right for the required reactive flow for any ac bus voltage de capacitor voltage is automatically adjusted as required to serve as a voltage source for that converter. STATCOM can be designed to also act as can active filter to absorb system harmonics. STATCOM ad defined above by IEEE is a subset of the broad based shunt connected Controller which includes the possibility of an active power source or storage on the dc side so that the injected may include active power. Such a controller is defined as. Static Synchronous Generator(SSG): A static self commutated switching power converter supplied form an appropriate electric energy source and operated to produce a set of adjustable multiphase output voltages, which may be coupled to an ac power system for the purpose of exchanging independently controllable real and reactive power. Clearly SSG is a combination of STATCOM and any energy source to supply or absorb power. The terms, SSG, generalizes connecting any source of energy including a battery, fly wheel, superconducting magnet, large dc storage capacitor, another rectifier/inverter, etc. An electronic interface known as a "Chopper" is generally needed between the energy source and the converter. For a voltage sourced converter the energy source serves to appropriately compensate the capacitor charge through the electronic interface and maintain the required capacitor voltage. Series connected controllers: Static synchronous Series Compensator (SSSC): A static synchronous generator operated without an external electric energy source as a series compensator hose output voltage is in quadrature with, and controllable independently of, the line for the purpose of increasing or decreasing the overall reactive voltage drop across the line and thereby controlling the transmitted eclectic power. The SSSC may include transiently rated energy storage or energy observing devices to enhance the dynamic behavior of the power system by additional temporary real power compensation, to increase or decrease momentarily, the overall real (resistive) voltage drop across the line. SSSC is one the most important FACTS Controllers. It is like a STATCOM except that the output ac voltage is in series with the line. It can be based on a voltage-sourced converter or -coerced converter. Usually the injected voltage in series would be quite small compared to the line voltage, and the insulation to ground would be quit high. With an appropriate insulation between the primary and the secondary of the transformer, the converter equipment is located at the ground potential unless the entire converter equipment is located on a platform duly insulated from ground. The transformer ratio is tailored to the most economical converter design. Without an extra energy source, SSSC can only inject a variable voltage, which is 90 degrees leading or lagging the. The primary of the transformer and hence the secondary as well as the converter has to carry full line including the fault unless the converter is temporarily bypassed during severe line faults. Batterystorage or superconducting magnetic storage can also be connected to a series Controller to inject a voltage vector of variable angle in series with the line. Combined Shunt and Series connected controllers Unified Power flow Controller (UPFC): A combination of static synchronous compensator (STATCOM) and a static series compensator (SSSC) which are coupled via a 9

common dc link, to allow bidirectional flow of real power between the series output terminals of the SSSC and the shunt output terminals of the STATCOM, and are controlled to provide con real and reactive, series line compensation without a external electric energy source. UNIFIED POWER FLOW CONTROLLER UPFC has been proved beneficial to provide adequate control of important parameters of power network [1-3]. UPFC may be a versatile and emerge as a strong candidate for power control. It combines features of Static Synchronous ) and Static Synchronous Series Compensator (SSSC) [5, 6]. UPFC is multifunctional FACTS device with capability of controlling all three parameters that dictate power flow over power transmission line, i.e., line voltage, impedance and phase angle, sequentially or conly, with internal reactive power generation in real time, it can be used for effective and efficient power flow control, enhancement of transient stability, mitigation of low frequency power system oscillations and voltage (reactive power) regulation. This section presents model development in state space framework. The system comprising of multi machines can be conceptualized as shown in Fig 3 Figure 5: UPFC Link in Transmission Line In UPFC, which combines a STATCOM and an SSSC, the active power for the series unit (SSSC) is obtained form the line itself via the shunt unit STATCOM; the latter is also used for voltage control with control of its reactive power. This is a complete Controller for controlling active and reactive power control through the line, as well as line voltage control. Additional storage such as a superconducting magnet connected to the dc link via an electronic interface would provide the means of further enhancing the effectiveness of the UPFC. AS mentioned before, the controlled exchange of real power with an external source, such as storage, is much more effective in control of system dynamics than modulation of the power transfer within a system. VI. BENEFITS OF UTILIZING FACTS DEVICES Fig. 3. Multi-machine representation in power network Multiple Generators of respective end may be grouped as area and thus a two-area power system with UPFC can be represented as shown in Fig.4 and Fig 5. Fig. 4. UPFC installed in a two area system Initially, an UPFC installed in two-area power network connected via an intertie has been modelled. The UPFC, be means of angularly unconstrained series voltage injection, is able to control, conly or selectively, the transmission line voltage impedance, and angle or, alternatively, the real and reactive power flow in the line. The UPFC may also provide independently controllable shunt reactive compensation. A basic UPFC functional scheme is shown in Fig.3. The benefits of utilizing FACTS devices in electrical transmission systems can be summarized as follows [4]: Better utilization of existing transmission system assets Increased transmission system reliability and availability Increased dynamic and transient grid stability and reduction of loop flows Increased quality of supply for sensitive industries Environmental benefits Better utilization of existing transmission system assets. In many countries, increasing the energy transfer capacity and controlling the load flow of transmission lines are of vital importance, especially in de-regulated markets, where the locations of generation and the bulk load centers can change rapidly. Frequently, adding new transmission lines to meet increasing electricity demand is limited by economical and environmental constraints. FACTS devices help to meet these requirements with the existing transmission systems. BENEFITS WITH THE APPLICATION OF FACTS CONTROLLERS: The benefits due to FACTS controllers are listed below: 1. They contribute to optimal system operation by reducing power losses and improving voltage profile. 2. The transient stability limit is increased thereby improving dynamic security of the system and reducing the incidence of blackouts caused by cascading outages. 3. The steady state or small signal stability region can be increased by providing auxiliary stabilizing controllers to damp low frequency oscillations. 4. The problem of voltage fluctuations and in particular, dynamic over- voltages can be overcome by FACTS controllers. 10

Table II describe the technical benefits of the main FACTS devices. TABLE II TECHNICAL BENEFITS OF MAIN FACTS DEVICES Continuous and discontinuous controls of FACTS devices are very commonly used to improve the dynamic performance of a power system. For small disturbances, continuous control is usually enough to improve damping of the system. VII. FACTS INSTALLATION ISSUES For the maximum effectiveness of the controllers, the selection of installing locations and feedback signals of FACTS-based stabilizers must be investigated. On the other hand, the robustness of the stabilizers to the variations of power system operation conditions is equally important factor to be considered. Also, the coordination among different stabilizers is a vital issue to avoid the adverse effects. Additionally, performance comparison is an important factor that helps in selection of a specific FACTS device. INSTALLING FACTS DEVICES FACTORS There are three factors to be considered before installing a FACTS device: 1. The type of device. 2. The capacity required. 3. The location that optimize the functioning of the device. All these three factors, the last one is of great importance, because the desired effect and the proper features of the system depend of the location of FACTS. Steps for the identification of FACTS Projects: 1. The first step should always be to conduct a detailed network study to investigate the critical conditions of a uld include: risks of voltage problems or even voltage collapse, undesired power flows, as well as the potential for power swings or sub synchronous resonances; 2. For a stable grid, the optimized utilization of the transmission lines e.g. increasing the energy transfer capability could be investigated; 3. If there is a potential for improving the transmission system, either through enhanced stability or energy transfer capability, the appropriate FACTS device and its required rating can be determined; 4. Based on this technical information, an economical study can be performed to compare costs of FACTS devices or conventional solutions with the achievable benefits. VIII.VOLTAGE STABILITY IN POWER SYSTEM Voltage stability is one of the biggest problems in power systems. The series and shunt compensation are able to increase the maximum transfer capabilities of power network [19]. Concerning to voltage stability, such compensation has the purpose of injecting reactive power to maintain the voltage magnitude in the nodes close to the nominal values, besides, to reduce line s and therefore the total system losses [2]. At the present time, thanks to the development of sophisticated and versatile power electronic devices named Flexible AC Transmission Systems (FACTS), which are used to adjust the magnitude of voltage in power system with proper control. A. Principal Causes of Voltage Stability Problems Some of the main causes for occurrence of voltage instability are i. Due to unsuitable locations of FACTS controllers. ii. High Reactive Power Consumption at Heavy Loads. iii. Occurrence of Contingencies. iv. Reverse Operation of ON Load Tap-Changer (OLTC). v. Voltage sources are too far from load centers. vi. Poor coordination between multiple FACTS controllers. vii. Presence of Constant Power Loads. viii. Difference in Transmission of Reactive Power under Heavy Loads. B. Prevention of Voltage Instability Some of the prevention of voltage instability by following: i. Placement of Series and Shunt Capacitors. ii. Generation Rescheduling. iii. Placement of FACTS Controllers. iv. Under-Voltage Load Shedding. v. Blocking of Tap-Changer under Reverse Operation. vi. Coordination of Multiple FACTS Controllers. vii. Installation of Synchronous Condensers. IX. CONCLUSIONS Facts controllers are able to control, simultaneously or selectively, all the parameters affecting power flow in the transmission line (i.e. voltage, impedance and phase angle). FACTS is one of the most important tool for the operational flexibility and controllability in system operator. In view of the various power system limits, FACTS provides the most reliable and efficient solution. FACTS also helps to better utilize the existing transmission resources, where the utilities are facing the problem of transmission expansion because of the strict environmental constraints. Due to changes in the energy situation and electricity industry structure, planning for the introduction of new facilities. FACTS technology can do a better job. For tie-line control, perhaps FACTS or HVDC can also do a better job, depending on what is required. Deregulation and privatization is posing new challenges on the high voltage transmission systems. System elements are going to be loaded up to their limits, widearea power trading with fast varying load patterns will cause congestion, because the systems are not designed for such conditions. System enhancement will be essential to keep the supply reliable and safe. The benefit for each type of FACTS can be associated with its particularities and 11

properties. They control the interrelated parameters that rule the operation of the transmission systems, including the series impedance, the shunt impedance, the, the voltage, the phase angle and the muffling of oscillations to different frequencies under the nominal frequency. X. REFERENCES [1] Understanding FACTS: concepts and technology of flexible AC transmission system 2000. [2] A. Edris, et.al Proposed Terms and Definitions for Flexible AC Transmission System (FACTS) IEEE Trans. Power Delivery, Vol. 12, No.4, pp. 1848-1853, Oct. 1997. [3] R.M. Mathur and R.K. Varma. Thyristor-based FACTS controllers for electrical transmission systems. IEEE Press,Piscataway,2002. [4 How FACTS Controllers Benefit AC Transmission Systems-Phases of Power System Studies Engineering Society General Meeting,2009. [5] B.A. Renz, A. Keri, A.S. Mehraban, C. Schauder, E. Stacey, L. AEP Unified Power Flow, IEEE Trans. PD, Vol. 14, No. 4,pp. 1374-1381, 1999. [6 Optimal Location of FACTS Devices for Congestion Management c Power System Research 58 (2001) pp. 71-79. [7 Location of Unified Power Flow Controller for Congestion Management System Research 58 (2001) 89-96. [8 Available Transfer Capability Enhancement Using FACTS Devices [9 Using FACTS Controllers to Maximize Available Transfer Capability Power System Dynamcis and Control IV Restructuring,August 24-28, 1998, Santorini,Greece. [10 STATCOM Control for Power System Voltage Control Applications Delivery,2000. [11 Strategies for Handling UPFC Constraints in Steady-State Power Flow and Voltage Control IEEE Trans.Power System, 2000. [12 Analysis of SVC and TCSC IEEE Trans. onpower system. Vol. 14, No. 1, pp. 158-165,Feb 1998 [13 Dynamic Compensation of AC Transmission Lines by Solid-State Synchronous Voltage Sources No.2, pp. 757-763, April 1994. [14] N. Mithulananthan, C. A. Canizares, J. Reeve and G. J. Rogers, Comparison of PSS, SVC,and STATCOM Controllers for Damping Power System Oscillations 2, pp. 786-792, May 2003. [15 TCSC Controler Design for Damping Interarea Oscillation - 946,April-1997. [16] N.G. Hingoran High Power Electronics and Flexible AC Transmission System 8, no.7, pp.3-4. [17] K.R.Padiyar, FACTS Controllers in Power Transmission & Distribution, New Age Pub. New Delhi. [18] M. Noroozian, L. Angquist, M. Gandhari, G. Andersson, "Improving Power System Dynamics by Series Connected FACTS devices", IEEE Transaction on Power Delivery, Vol. 12, No. 4, Oct. 1997,pp.1635-1641. [19] P. Kundur, Power System Stability and Control. New York: McGraw-Hill,1994. 12