Adaptive Control of Controlled Series Compensators for ... - CiteSeerX

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Paper ID: 74

Adaptive Control of Controlled Series Compensators for Power System Stability Improvement Nicklas P. Johansson, Student Member, IEEE, Lennart Ängquist, Member IEEE, Hans-Peter Nee, Senior Member, IEEE

Abstract— This paper describes the design and verification of a time-discrete adaptive controller for damping of inter-area power oscillations, power flow control, and transient stability improvement. Only locally measured signals are used as inputs to the controller. The controller may be used with any FACTS device which operates as a variable series reactance in the power grid, such as for example the TCSC. The controller is based on a reduced system model which relies on the assumption of one dominating inter-area oscillation mode in the power system where the FACTS device is placed. Verification of the controller is performed by means of digital simulations of a four-machine system commonly used to study inter-area oscillations. Index Terms—Control, FACTS, Power Oscillation, TCSC, TSSC, Transient stability

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I. INTRODUCTION

OWER utilities of today use a variety of technologies to reduce the impact of disturbances in the power grid, lowering the risk of blackouts. Many of these are commonly referred to as Flexible AC Transmission Systems (FACTS) devices. Two well known FACTS devices are the Thyristor Controlled Series Compensator (TCSC) and the Thyristor Switched Series Compensator (TSSC) belonging to the group of Controlled Series Compensators (CSC). CSC are based on the principle of varying of the power line series reactance in order to control power flows and enhance system stability. The most important phenomena which threaten the stability of power systems are poorly damped low frequency electromechanical oscillations, first-swing instabilities and voltage instabilities. This paper will focus on mitigation of electromechanical oscillations and improvement of the power system transient stability by means of CSC. Power oscillation damping is traditionally improved by the use of Power System Stabilizers (PSS) that act on the Automatic Voltage Regulators (AVR) controlling the generators in the power system. The structure of the power system determines the effectiveness of

Manuscript received November 29, 2006. This work was supported in part by the ELFORSK Elektra foundation. N.Johansson (phone: +46 (0)730-268404, [email protected]) and H.-P.Nee ([email protected]) are with the Royal Institute of Technology, Teknikringen 33, 100 44 Stockholm, Sweden L.Angquist ([email protected]) is with ABB AB, FACTS, 721 64 Västerås, Sweden

the PSS. In some cases, the damping of inter-area modes may be inadequate, and supplementary damping may be added to the power system by installing a CSC at a proper location. The design of an effective damping controller for such a device is complicated by the fact that the equations governing the oscillations in a power system are non-linear and that the power system parameters often change dramatically during the contingencies causing the power oscillations. A controller which shows a good performance in one operating point and one system configuration may be inadequate in another resulting ultimately in power system failure. Many approaches for damping control of CSC have been described [4]: traditional pole-placement techniques as well as robust controllers, non-linear approaches and adaptive controllers [5]. Controllers for improvement of transient stability are described in [4] and [7]. In this paper, an adaptive controller based on a model predictive approach to power oscillation damping is proposed. The controller is equipped with a function to improve transient stability as well as with a power flow control functionality. The goal of this paper is to demonstrate an easyto-use controller based on a simple generic grid model. II. REDUCED GRID MODEL In order to design a damping controller for inter-area power oscillations, a system model is required. The nature of interarea oscillations is often such that there is a dominant mode of oscillation which may be poorly damped. With this in mind, a simple way to reduce the total power grid is to approximate the grid as a system of the form seen in Fig. 1. The reduced model of the power system using a Center Of Inertia (COI) reference frame consists of two synchronous machines with interconnecting transmission lines. In this work, the model parameters are updated continuously by the controller using the locally measured responses in the CSC line active power (Pline) to changes in the variable series reactance.

Fig. 1: The reduced grid model used by the controller

The line where the CSC is installed is represented by a variable, known reactance X. The model is characterized by

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Paper ID: 74 four additional parameters: one series reactance Xi, one parallel reactance Xeq, the dominant angular frequency of the power oscillation ω and the damping exponent of this oscillation mode - σ. The machine terminal voltage phasors θ characterized by the magnitudes U1,2 and the phase angles 1,2 are assumed to be well controlled and thus constant in magnitude. When applied to real power systems, the model may represent two different grid areas with lumped moments of inertia and their interconnecting power lines. The load in each of these areas is modeled as constant voltage-independent loads. The reduced model was presented and verified in [1]. III. THEORY A. Estimation of the reduced model parameters Since an adaptive control approach is used, the parameters of the grid where the FACTS device is placed are estimated continuously by the controller according to the model of Fig. 1. The controller is time-discrete in nature making it possible for the estimation routines to be developed based on the step response of the reduced system in Fig. 1 to changes in the CSC reactance. In [1], equations governing the step response in active power on the reactance controlled line when a step in the line reactance is applied to a system at rest were derived. It is also possible to derive relations for the step response of the system when it is initially subject to an electro-mechanical oscillation. Such relations are used by the controller proposed here to estimate the grid parameters in real-time. B. Estimation of the CSC line power frequency content In order to use the estimation techniques outlined above and to determine the input and timing for the damping controller it is necessary to separate the average and oscillative components of the line active power in real-time. This is done using a Recursive Least Squares (RLS) algorithm [9]. In this paper, the algorithm is used based on the assumption that the line power is composed of a zero frequency component (the average value) and a component which has a known frequency range (the power oscillation frequency). The algorithm utilizes an expected oscillation frequency when no oscillations are at hand. At any event that causes power oscillations, the frequency parameter is adapted to the actual oscillation frequency by a PI-controller. The algorithm gives a real-time estimation of the line average power (Pav), oscillation amplitude (Posc), frequency (ω) and phase (φosc). C. Power oscillation damping The controller developed here is based on a time-discrete approach to power oscillation damping. The approach is somewhat similar to that of [6]. In [2] it was shown that a power oscillation in a power system characterized by one dominant mode of oscillation can be damped by changing a selected line series reactance in one step of a certain magnitude at a carefully selected time instant. The necessary reactance magnitude can be determined knowing the system parameters according to the model of Fig.1. It was also shown

that a more realistic controller can be built on the principle of (ideally) eliminating the power oscillation in two discrete reactance steps separated in time. This objective can also be met simultaneously as the active power flow on the reactance controlled line is changed to a pre-defined new set-point as shown in [3]. The time instants of the steps must be chosen such that they coincide with peaks (positive and negative) in the power oscillation. This gives a controller with a timediscretization determined by the oscillation frequency. D. Transient stability improvement strategy A severe contingency such as a three-phase short circuit in a two-area power system with an interconnection CSC may lead to a case such as the one depicted in Fig. 2. The horizontal line δ Pm( ) in the figure represents the initial power delivered from the sending to the receiving area which equals the excess mechanical power delivered to the generators in the sending area. This power is assumed to be constant during the event. The sinusoidal curves represent the transmitted power over the inter-tie for different values of the tie reactance as a function of the voltage phase angle separation between the areas.

Fig. 2: Illustration of the first-swing controller operation after a fault

Assume that the system starts from a stationary state at A δ δ and that the P- relationship is described by Ppre( ). Then a severe fault interrupts the transmission and the transmitted δ power drops to a small value on the curve Pfault( ) at B. The generators in the sending end are now accelerated with respect to the machines in the receiving end and the angle separation increases. At C, the breakers have isolated the faulted line and δ the system resumes transmitting power according to Ppost( ). With no action of the CSC, the system will move C-D-E and δ then towards I on Ppost( ). Since the area bounded by D-E-I is smaller than the area A-B-C-D, the system exhibits transient instability and it will fall out of phase. If on the other hand, the CSC is engaged at point C, maximizing the compensation, the δ system will move on the path C-D-E-F-G on PpostFC( ). and then turn back since the areas A-B-C-D and D-F-G-H are equal. At this point, the system has survived the first-swing and a power oscillation is initiated. It is important to note that the system may still be transiently unstable if the compensation level is reduced. Since the system parameters are unknown

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Paper ID: 74 immediately after a contingency, the control strategy for transient stability improvement cannot be based on the system model used for the damping controller. Instead, a preprogrammed response during the first swing is used. The transient (first-swing) strategy proposed here is the following: 1. The transient controller is engaged if a fast positive time derivative of the line power magnitude (at the CSC location) leading to a significant rapid change in line power is detected. The reactance of the CSC is set to its minimum XTCSC=XTCSCmin. It should be noted that fault cases which risk transient instability can be better detected using remote signals estimating the COI-values of the generator angles and speeds in each of the areas as in [6]. 2. To provide positive damping to the system, the level of compensation should be decreased at some point provided that the system has survived the first swing. This should ideally be done at the turning point G provided that the level of transmitted power after the change in compensation is larger than the mechanical power level in order to avoid instability. To reduce the risk of instability, the proposed controller decreases the δ compensation level after turning at G at the point J ( = 90 °) where the transmitted power for all tie reactances is maximized. If the faultδ case is such that the angle difference never = 90 °, the transition is made at the point where δexceeds reaches its maximum value (this case is not illustrated). 3. The choice of the level of compensation after the change at point J is not trivial. If the level chosen is too low it mayδ push the power curve under the mechanical level Pm( ) resulting in instability. If the level chosen is too high it will provide insufficient damping to the system in the following damping reactance steps. As a compromise, the proposed controller reduces the compensation level to XTCSC=XTCSCmin/2 δ at point J. Subsequently, the system follows PpostHC( ) and the new decelerating area G-J-K-AH is significantly reduced from the area G-J-F-L-H which would be the case if no change in compensation is applied. This provides positive damping to the system. Since the angle separation between the areas is not available in real-time at the FACTS device location, the time instant for the change in compensation is determined from measurements of the FACTS line current (which is monotonously increasing with angle separation) and estimation the line active power peaks by RLS. 4. Following the transient controller operation, the damping controller is commonly initiated. In order to maximize the system stability improvement, the controller operates to damp the oscillation at the same time as it controls the average level of line power (Pxsp) to a pre-determined short-term thermal overload limit Plimit (or the maximum power possible if the overload level cannot be reached). This limit is the active power level on the CSC line which can be allowed for the time it takes for the Transmission System Operator to re-dispatch the system to comply with the N-1 criteria of the new conditions (15-30 min.). This strategy will help the system to remain transiently stable in the subsequent swings after the first swing provided that the first swing does not give rise to instability by

δ

δ

δ

maximizing the decelerating area when Pe( )>Pm( ) and < 90 °. It will also enable the system to operate in cases with δ δ high tie reactance (Pm > Pe( ) for all ) by increasing the series compensation after the contingency so that a portion of the δ curve Pe( ) is pushed above Pm. Additionally, a higher average compensation level during the power oscillation damping scheme reduces the risk of the system oscillating in δ the range where > 90 ° since the average angle separation during the power oscillation is reduced. This enhances the effectiveness of damping schemes relying on linearization of the system equations, such as the one used in this work. Finally, the strategy will reduce the risk of voltage instability since a raised compensation level lowers the total line reactance between the grid areas, thus decreasing the voltage magnitude change across the inter-tie. IV. MULTI-OBJECTIVE CONTROLLER Now, a controller for power oscillation damping (POD), first-swing stability improvement (FSW) and active power flow control can be designed. The first-swing controller has the highest priority and inhibits the other controller parts if initiated. Generally, a fault in the system first leads to a risk of transient instability which initiates the first-swing controller. When the first-swing controller has performed its sequence there is commonly a power oscillation in the system which is detected by the RLS algorithm. This oscillation triggers the damping controller which has a built-in power flow control feature for fast control of the power on the line after a fault. Since the damping controller/fast power flow controller is only active when power oscillations are present, a separate slow PIcontroller is necessary for long-term power flow control. These controllers contribute the terms XPOD, XFSW and XPI to the reactance of the CSC - XTCSC (see Fig. 3). All controllers use the CSC line active power (Pline) or estimations of it as input signals. The first swing controller also uses the CSC line current (Iline) as an input signal.

Fig. 3: Principal schematic of the CSC controller

The damping controller used here is a dead-beat controller designed to ideally stabilize the oscillation in two discrete reactance steps. This objective is rarely met in reality since the estimated system parameters have errors and there are model errors between the reduced model and the actual system. Also, the control signal, in this case the variable series reactance of the CSC, is limited. One challenge for the controller is to determine the system parameters after a contingency when grid parameters commonly change dramatically due to line disconnections at fault clearance. Since the estimation routines are dependent on step response data, the parameters cannot be

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Paper ID: 74 estimated prior to the the first reactance step in a damping sequence. Therefore, a starting guess for the parameters is necessary to determine the first steps in a damping sequence. This starting guess is chosen as the set of parameters which corresponds to the grid (N-1) configuration case where the controllability of the inter-area oscillation mode from the FACTS device is the largest. This approach leads to a controller which generally is sub-optimal initially in order for it to maintain stability in all system configurations. Once the first step in a damping sequence has been executed, step response data is collected and the actual parameters are estimated. The input to the estimation routine is both the instantaneous and the average change in line power resulting from the change in reactance. Since the estimation of the average power on the line requires time to stabilize, the parameters are not updated until slightly before the next step is taken by the controller. This procedure is repeated after each new step in line reactance. To improve the robustness of the system to measurement errors, a forgetting factor is introduced which determines the weight of the previous parameter values to the new values obtained at each reactance step.

MW). During the damping controller operation, the line power changes in discrete steps. In order for the high time-derivative of these steps not to trigger the transient controller, it is blocked for a short time period after each step.

Fig. 4: Four machine test system (p.u. base power is 100 MW)

V. CONTROLLER VERIFICATION The controller is verified by means of digital simulations of a four-machine system (see Fig. 4) starting from a commonly used 230 kV/60 Hz system for studies of inter-area oscillations [10]. Some changes are made from original system: one tie line is added and the length of the lines interconnecting the two areas is stretched to 300 km. Shunt compensation in node 8 is also inserted to maintain a good voltage profile. The generators are equipped with fast exciters and Power System Stabilizers (PSS) with a low gain in order to give a system with a small positive damping ratio. A. Controller operation example In order to illustrate the operation of the controller in a fault case, the system in Fig. 4 was simulated in the case of a 3phase short circuit at node 8 cleared after 200 ms (which is a worst case scenario) by a disconnection of one of the lines N8N9 in parallel to the CSC. The CSC line short term overload capability was assumed to be 400 MW and this value was used as the post-contingency set-point of the fast power flow controller. Gaussian pseudo-random (simulated measurement) noise with a standard deviation of 1% of the input signal (Pline) stationary value was added to the controller input. From Fig. 5 it can be seen that the damping of the inter-area mode is greatly improved by the CSC operation. Fig. 6 shows the controller action in more detail. The first-swing controller is activated by the high positive time derivative of the line power at fault clearance (at t=1.2 s) and disengaged (at t=1.7 s). The damping controller is engaged at t=2.3 s. At first, the grid parameters are unknown and the parameters are reset to a safe state. As the system parameters are estimated with better accuracy, the damping is more and more effective. The damping of the oscillation is completed at t=7.3 s and the power flow on the line is stabilized close to the set-point (400

Fig. 5: Generator speed of G1(dotted), G2 (dash-dotted), G3 (dashed) and G4 (solid) for the system with the TCSC engaged and disengaged

Fig. 6: FACTS line active power, RMS current and connected series reactance for the system contingency with and without the TCSC engaged. The TCSC series reactance is limited to ± 0.075 p.u.

Fig. 7 shows the evolution of the system identification parameters Xi, Xeq and ω. The system exhibits a dominant inter-area mode of oscillation in the range of 0.52-0.75 Hz depending on configuration. The starting guess of ω is chosen to be 3.77 rad/s (0.6 Hz). The parameters Xi and Xeq are updated whenever a reactance step response in the CSC line active power above a certain magnitude is detected. It can be seen that the parameters stabilize close to Xi=0.21 p.u and Xeq=0.15 p.u after a few steps in CSC reactance.

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Paper ID: 74 studied for both load characteristics. 600 MW N7-N9

180 MW N7-N9

A

B

C

D

Oscpp=210 fi=0.65 σi=-0.001 σTCSC=-0.69 Ti=3700 TTCSC=5.4 Oscpp=120 f =0.72 σii =-0.12 σTCSC=-0.50 Ti =26 TTCSC=6.3

Oscpp=200 f =0.55 σi i=-0.045 σTCSC=-0.68 Ti =82 TTCSC=5.4 Oscpp=160 f =0.68 σi i=-0.097 σTCSC=-0.69 Ti =36 TTCSC=5.0

Oscpp=135 f =0.54 σi i=-0.059 σTCSC=-0.51 Ti =56 TTCSC=6.5 Oscpp=120 f =0.68 σii =-0.10 σTCSC=-0.60 Ti =32 TTCSC=5.3

Oscpp=30 f =0.63 σi i=-0.040 σTCSC(=-0.58 Ti =45 TTCSC=3.1 Oscpp=40 f =0.70 σii =-0.16 σTCSC=-0.69 Ti =13 TTCSC=3.0

Table I: Simulation results of system damping with TCSC controller engaged/disengaged in contingencies A-D. Voltage-dependent load, P=P0*U/U0, Q=Q0*(U/U0)2. Fig. 7: Estimated parameters Xi (dashed), Xeq (solid) and ω

The PI-controller tuning ω is continuously active as long as the (detected) power oscillation exceeds 10 MW in amplitude. Since no reliable method to continuously estimate the damping exponent σ has yet been developed, this parameter is set to zero. This has a minor effect on the controller performance. B. Power oscillation damping performance In order to demonstrate the damping performance of the controller, the system was simulated in four different severe contingencies for a high (200 MW/line) and a low (60 MW/line) loading situation of the tie lines between the areas. The loads used for the loading cases (high/low) were PL7=967/1367 MW QL7=100/200 MVAr and PL9=1967/1367 MW QL9=100/200 MVAr and the active power generation of generators 1 and 2 was 1600 MW in total. Simulated measurement noise of 1% was added to the controller input. Two cases of load characteristics were studied: (1) All loads are voltage dependent with constant current characteristics for the active power and constant impedance characteristics for the reactive power load; (2) All reactive and active power loads are voltage independent. The studied cases were: A. A 3-phase short circuit (SC) in node 8 cleared with no line disconnection after 200 ms B. A 3-phase SC in node 8 cleared by disconnection of one N8-N9 line in parallel to the CSC after 200 ms C. A 3-phase SC in node 8 cleared by disconnecting one of the N7-N8 lines after 200 ms D. A disconnection of load in node 7. ∆P=-250 MW ∆Q=50 MVAr in the high load case and ∆P=-250 MW ∆Q=-100 MVAr in the low load case. The results are shown in tables I and II. The power oscillation maximum peak-to-peak value is given as Oscpp (MW) and the damping exponents with the damping controller disengaged and engaged are given as σi and σTCSC respectively. The inter-area mode oscillation frequency fi for each case is given in Hz. The time it takes for the power oscillation amplitude to settle below 5 MW is given for the undamped system as Ti (s) and for the damped system as TTCSC (s). It can be seen from the tables that the damping of the system is significantly improved to satisfactory values in all the cases

A

B

C

D

Oscpp=135 Oscpp=145 Oscpp=90 Oscpp=30 600 fi =0.66 fi = 0.53 fi =0.52 f =0.65 σi =-0.003 σi =-0.002 σi =-0.005 σii =-0.05 MW σTCSC=-0.50 σTCSC=-0.64 σTCSC=-0.32 σTCSC=-0.20 N7-N9 Ti =1100 Ti =1600 Ti =580 Ti =36 TTCSC=6.7 TTCSC=5.1 TTCSC=9.0 TTCSC=8.8 Oscpp=105 Oscpp=130 Oscpp=100 Oscpp=40 180 MW fi =0.75 fi = 0.70 fi =0.70 f =0.75 σi =-0.18 σi =-0.17 σi =-0.17 σii =-0.28 N7-N9 σTCSC=-0.51 σTCSC=-0.65 σTCSC=-0.58 σTCSC=-0.36 Ti =17 Ti =19 Ti =18 Ti =7.5 TTCSC=6.0 TTCSC=5.0 TTCSC=5.2 TTCSC=5.7 Table II: Simulation results of system damping with TCSC controller engaged/disengaged in contingencies A-D. Constant power load P=P0, Q=Q0.

C. Transient stability improvement potential In order to investigate the performance of the proposed transient stability controller, simulations were made of the four-machine system described above. It was assumed that the system transfer capacity is limited by the transient stability in the worst case contingency B in the last paragraph. The system was investigated with the TCSC in five different configurations: (1): No first swing controller is used. The TCSC operates only to damp oscillations. (2): A first swing controller which operates like the one described in this paper except that the compensation is set to zero when it is reduced from the maximum value. The TCSC compensation base level is maintained at zero during the damping event. This approach is similar to the one of [8]. (3): The first swing controller proposed in this paper is used. The controller post contingency power set-point (the TCSC line short-term thermal limit) is set to 400 MW. (4): As in (3) but with a limit of 450 MW on the TCSC line. (5): As in (3) but with a limit of 500 MW on the TCSC line. Repetitive simulation of contingency B was performed in order to determine the maximum limit of the transmitted power demanding maintained transient stability and system damping (damping of all oscillations within 10 s). The results are summarized in Table III. It can be seen that the maximum transfer capacity of the tie-lines between the areas is significantly improved by application of the transient controller described in this paper.

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Paper ID: 74 CASE # 1 2 3 4 5

Max. total transfer capacity (MW) 690 720 760 780 820

improved to satisfactory values for all the contingencies studied at two operating power levels and two different load characteristics. The transient stability controller was shown to increase the maximum transfer capacity of the system significantly, especially in the case of a large short-term thermal overload limit on the CSC line.

Table III: Maximum transfer capacities for cases 1-5:

The short-term thermal overload limit of the TCSC line is seen to be a major determining factor for the total transfer capacity provided that the transient controller described here is used. It should be noted that the transfer capacity was in all cases limited by unsatisfactory oscillation damping. This degradation is due to the fact that the system is operating in the δ non-linear range ( >90°) where the assumptions made in the derivation of the damping controller are no longer valid. VI. LIMITATIONS OF THE PROPOSED CONTROLLER Since the proposed CSC controller relies only on locally measured signals, it is not dependent on any communication for its function, which is advantageous. One potential cause of damping controller instability is inadequate parameter estimation. This may be due to measurement noise in combination with a small magnitude of the change in line power following a performed reactance step. To reduce the risk of this, a low limit for the step response in line power is introduced. This limit must be exceeded for an estimation to take place. A sensitivity analysis indicates that the nonsystematic errors in the estimations of the instantaneous and average power step response required in the estimation process must be in the range of ± 25% of the step magnitudes to cause instability. Systematic errors have little effect on the parameter estimation. In this analysis, it was assumed that the forgetting factor was 100%, that is, the controller uses the currently estimated parameters with no regard to their previous values. A careful selection of the forgetting factor based on the noise level in the system allows for a significantly higher error tolerance if necessary. Another potential cause of instability is model errors, i.e. influence of other modes of oscillation, violation of the assumptions of a unity power factor, voltage independence of loads and the neglect of generator excitation system dynamics. These issues will be investigated in future work which includes scaling up the test system. The numerical stability of the damping algorithm has been studied and the cases where instability can occur have been identified. These are generally cases which are easily identified as not allowing a certain oscillation to be damped in two discrete reactance steps due to limitations in the control signal. To ensure the stability of the algorithm, these limitations have been included in the controller implementation. VII. CONCLUSIONS The CSC controller proposed in this paper has been verified by means of digital simulations of a four-machine power system with a poorly damped inter-area mode. The damping of the critical oscillation mode of the system was shown to be

VIII. REFERENCES [1]

Johansson, N P, Nee H-P and Ängquist L, “Estimation of Grid Parameters for The Control of Variable Series Reactance FACTS Devices” , Proceedings of 2006 IEEE PES General Meeting [2] Johansson, N P, Nee H-P and Ängquist L, “Discrete Open Loop Control for Power Oscillation damping utilizing Variable Series Reactance FACTS Devices”, Proceedings of the Universities Power Engineering Conference, Newcastle, UK, September 2006 [3] Johansson, N P, Nee H-P and Ängquist L, “An Adaptive Model Predictive Approach to Power Oscillation Damping utilizing Variable Series Reactance FACTS Devices”, Proceedings of the Universities Power Engineering Conference, Newcastle, UK, September 2006 [4] Zhou, X , Liang, J, “Overview of control schemes for TCSC to enhance the stability of power systems”, IEE Proc.- Gener. Transm. Distrib. Vol 146 No. 2, March 1999 [5] Sadikovic, R, Korba, P and Andersson, G, “Self-tuning Controller for Damping of Power System Oscillations with FACTS devices”, Proceedings of 2006 IEEE PES General Meeting [6] Kosterev, D. N, Kolodziej, W. J, ”Bang-Bang Series Capacitor Transient stability Control”, IEEE Trans. on Power Systems, vol. 10, No. 2, May 1995 [7] Kosterev, D.N, Kolodziej, W.J, Mohler, R.R, Mittelstadt, W. A, “Robust Transient Stability Control Using Thyristor-Controlled Series Compensation“, Proc. of 4th IEEE Conf. on Control Applications, 1996 [8] Hague, M. H , “Improvement of First Swing Stability Limit by Utilizing full Benefit of Shunt FACTS devices”, IEEE Trans. on Power Systems vol. 19, No. 4, November 2004 [9] Åström, J. K, Wittenmark, B, “Adaptive Control”, Addison-Wesley, 1995, pages 41-55 [10] Kundur, P, “Power system stability and control”, McGraw-Hill, 1994, pages 813-816 and pages 827-835

IX. BIOGRAPHIES Nicklas Johansson (S’05) was born in Luleå, Sweden in 1973. He received the M.Sc degree in Engineering Physics from Uppsala University, Sweden in 1998. He worked at ABB Corporate Research, Västerås, Sweden 1998-2002 as a development engineer within the group of Power Electronics. He later worked as a hardware electronics consultant at Styrex AB, Uppsala, Sweden before joining the Dept of Electrical Engineering at the Royal Institute of Technology in Stockholm, Sweden. as a PhD student in 2005. His research is focused on control of FACTS devices. Lennart Ängquist was born in Växjö, Sweden, in 1946. He graduated (M.Sc.) from Lund Institute of Technology in 1968 and graduated (PhD) from the Royal Institute of Technology, Stockholm, in 2002. He has been employed by ABB (formerly ASEA) in various technical departments. He was working with industrial and traction motor drives 1974-1987. Thereafter he has been working with FACTS applications in electrical power systems. He now holds the position of Technical Specialist in the FACTS division of ABB and he is Adjunct Professor at the Royal Institute of Technology in Stockholm, Sweden. Hans-Peter Nee (S'91-M'96-SM'04) was born in 1963 in Västerås, Sweden. He received the M.Sc., Licentiate, and Ph.D degrees in electrical engineering from the Royal Institute of Technology, Stockholm, Sweden, in 1987, 1992, and 1996, respectively, where he in 1999 was appointed Professor of Power Electronics. His interests are power electronic converters, semiconductor components and control aspects of utility applications, like FACTS and HVDC, and variable-speed drives. Prof. Nee has served in the board of the IEEE Sweden Section for many years and was the chairman of the board during 2002 and 2003.