Modeling of UPFC operation under unbalanced ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002

395

Modeling of UPFC Operation Under Unbalanced Conditions With Dynamic Phasors ˇ Stefanov and Aleksandar M. Stankovic´ Predrag C.

Abstract—The paper describes an analytical large-signal model for unbalanced operation of the unified power flow controller (UPFC). This nonlinear, time-invariant model is expressed in terms of dynamic symmetric components, and it is validated on a benchmark power system example taken from the literature. The model is evaluated via simulations in unbalanced operation and during unbalanced (one phase to ground) faults. In both cases, it achieves a very good accuracy, in addition to a reduction in simulation time when compared with detailed time-domain models. Index Terms—Dynamic phasors, dynamical models, flexible ac transmission systems (FACTS), unbalanced conditions, unified power flow controller (UPFC).

I. INTRODUCTION AND BACKGROUND

V

OLTAGE-SOURCED power electronic converters, often referred to as flexible AC transmission systems (FACTS), promise to play an important role in emerging deregulated power systems. By building on technologies developed for high-power electronic converters and drives, these components offer a number of advantages in control of power systems, including speed and accuracy of the controlled response. For a better understanding and control the interactions between FACTS components and the utility system, there is an increasing need for convenient models that will allow large-signal stability analysis, fast and accurate transient simulations, and facilitate control design. However, the analysis of the dynamics of voltage-sourced converters is challenging. These hybrid systems amalgamate continuous-time dynamics (associated with the voltages and currents on capacitors and inductors) and discrete events (associated with the switching of the thyristors). The standard quasi-static approximation models FACTS components as a variable fundamental-frequency reactance and internal FACTS system dynamics are omitted [1]. This approach is widely used because of its simplicity, but relies on the assumption that the transmission system is operating in sinusoidal steady state, with the only dynamics being that of the generators and possibly loads. The quasi-static approximation lacks accuracy when voltage stability, transient stability, or other dynamic phenomena are of interest; several authors have already shown that, for example, thyristor-controlled Manuscript received April 20, 2000; revised November 28, 2001. ˇ Stefanov was with the Department of Electrical and Computer EngiP. C. neering, Northeastern University, Boston, MA 02115 USA. He is now with the Department of Electrical Engineering, University of Belgrade, Yugoslavia. A. M. Stankovic´ is with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA. Publisher Item Identifier S 0885-8950(02)03808-7.

series capacitor (TCSC) dynamics cannot always be neglected [2], [3]. The main alternative to quasi-static descriptions are detailed time-domain models intended for simulation. Time-domain models offer improved accuracy, but their nonlinear time-varying (nonautonomous) nature makes the unsuitable for analysis. Our main aim is to explore the possibly useful middle ground between quasi-static and detailed time-domain models, and to derive time-invariant (autonomous) nonlinear dynamic phasor models that approximate the detailed time-domain models to a degree needed in system analysis and design. The complexity of dynamic phasor models can be selected by the analyst, and in steady state, such models reduce to quasi-static descriptions. Specifically, the paper derives a continuous-time large-signal model of the unified power flow controller (UPFC) under unbalanced operation. The proposed methodology derives a dynamical extension of the standard symmetrical components, and it is applied to the case of modeling and analysis of asymmetrical faults in the vicinity of the UPFC. Our large-signal nonlinear models describe time evolution of various frequency components of the waveforms of interest by decomposing them into dynamical positive, negative, and zero sequence components. Widely cited IEEE reports on FACTS technology include [4]–[6]; a standard reference on UPFC is [7], expanded in more detail in [8] and [9]. A common controller structure in the synchronous ( – ) frame for the shunt part of the UPFC is described in [10]; control of the series branch is described in [8] and [9]. These are reviewed in [11] together with a dynamical model of the UPFC which includes only the dynamics of the dc link capacitor voltage (expressed in terms of the stored energy). A more detailed model for the UPFC (with an idealized switch model) is given in [12]; an argument that explains why models with idealized switching are adequate for control-oriented studies of multilevel inverters is presented in [13]. In this paper, we will also consider switching to be ideal; the capabilities of dynamic phasors to model converters that substantially deviate from this assumption are presented in [14]. For more details about operation of multilevel converters and about transformer connections that minimize harmonics, see [15]. We will be interested in behavior of UPFC during and after short circuit faults; a physics-based description of such events is presented in [16]. Time-domain models for simulation of balanced UPFC are presented in [17], [18]. A time-domain model for simulation of unbalanced STATCOM is given in [19]. This paper follows [20] in applying dynamic phasors to analysis of UPFC, but considers a more realistic network model. A novel feature of this paper is in addressing unbalanced operation, and in derivation of an analytical model for that purpose.

0885-8950/02$17.00 © 2002 IEEE

396

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002

For model validation we consider a single-machine infinite-bus benchmark power system from [21]; a similar system is used in [7]. This model is selected for its simplicity, so that modeling details can be highlighted. However, the presented methodology is equally applicable to the multimachine case. Again, for simplicity, we consider a standard (nonoptimized) controller for the UPFC. The rest of paper is organized as follows. In Section II, we describe the concept of dynamical symmetric components, and in Section III, we present time-domain and dynamic phasor models for the UPFC. In Section IV, we describe the benchmark power system used in simulations, in Section V we present simulation results for both time-domain and dynamic phasor models, while brief conclusions are given in Section VI.

notation, we introduce ; then domain waveform can be written as

. Then a time-

(4) and we denote the square transformation matrix with . It can is unitary, as , where debe checked that notes complex conjugate transpose (Hermitian). As commonly are encountered in transforms, scaling factors other than possible in the definition of matrix , but they require adjustments in the inverse transform. The coefficients in (4) are

II. DYNAMIC PHASORS A. Single-Phase Systems The generalized averaging that we perform to obtain our models is based on the property [22] that a possibly complex can be represented on the interval time-domain waveform using a Fourier series of the form

(5)

(1)

negative , Equation (5) defines dynamical positive symmetric components at frequency and zero-sequence as

and are the complex Fourier coeffiwhere cients, which we shall also refer to as phasors. These Fourier coefficients are functions of time since the interval under consideration slides as a function of time. We are interested in cases when only a few coefficients provide a good approximations of the original waveform, and those coefficients vary slowly with time. The th coefficient (or -phasor) at time is determined by the following averaging operation: (2) Our analysis provides a dynamic model for the dominant Fourier series coefficients as the window of length slides over the waveforms of interest. More specifically, we obtain a state-space model in which the coefficients in (2) are the state variables. A key fact for our development is that the derivative of the th Fourier coefficient is given by the following expression: (3) This formula is easily verified using (1) and (2), and integration by parts. The describing function formalism is useful in evaluating the th harmonic of the right hand side of the time-domain . Another straightforward, but very important model result is that the phasor set of a product of two time-domain variables is obtained from a discrete-time convolution of corresponding phasor sets of each component. B. Polyphase Systems The definitions given in (1) and (2) will now be generalized for the analysis of three phase systems. Following the standard

(6) is defined in (2). Our where the averaging operation definition of dynamical symmetrical components differs from the notion of instantaneous symmetrical components introduced by Lyon [27] in one very important aspect—(5) includes integration over a period of the fundamental waveform, and this is absent in [27]. This difference has important consequences—while the (time-varying) transformation used in instantaneous symmetrical components proved useful in certain problems, it does not change the time-varying nature of the model in phase ( - - ) coordinates during transients or in unbalanced operation. On the other hand, the presence of the integral term in (5) will allow us to develop time-invariant models. In the case of quantities expressed in a rotating reference frame (like the rotor frame used in Park transformation), the would follow in (5). The use transformation matrix of rotor frame offers distinct advantages in analysis and control, as key variables appear as constant or slowly varying quantities, significantly simplifying convergence, and stability evaluation. The use of positive, negative, and zero sequence components is also compatible with models employed in protection studies. Among the salient features of the proposed definitions are the compatibility with conventional symmetric components in a periodic steady state, and a similarity to the single-phase case; observe that (5) is a vector generalization of (2). Dynamic pha-

STEFANOV AND STANKOVIC´: MODELING OF UPFC OPERATION UNDER UNBALANCED CONDITIONS

Fig. 1.

397

Basic system configuration.

sors can be used for modeling of unbalanced polyphase systems that include power converters (e.g., rectifiers and inverters, such as active filters [23]), electric machines [24], power systems [25], and arcing fault models in protection studies [26]. In such analyses, we can vary the number of phasors at different frequencies to address a particular problem. Dynamic phasor models have a number of useful features: 1) these large-signal models are time-invariant, allowing a tremendous simplification of analysis; 2) inputs and consequently states tend to vary slowly compared to the driving frequencies, resulting in faster simulations; 3) dynamic phasors achieve “simultaneous demodulation” as all variables are constant (“dc”) in a steady state; 4) dynamic phasors are very effective in revealing dynamical couplings between various quantities; 5) both refinements and simplifications are possible for various accuracy requirements; 6) dynamic phasors models of FACTS components are modular (i.e., involve only the FACTS components and replace just these), and completely compatible representations based on static phasors that are used for components that are modeled in less detail, such as distant transmission lines and generators. III. MODEL OF THE UPFC A. Time-Domain Model We consider a UPFC which is a part of the system shown in Fig. 1 (modified from [21, ex. 13.4]). We start with the model of the UPFC (shunt branch with subscript and series with subscript ) in the rotor ( – ) reference frame [10]

where in each of the axes ( and ) index

denotes the modulation

(8) and the real and reactive power are given by (9) The dynamics of the dc link is given by

(10) With our goal of maintaining model simplicity, we excluded the equations for the zero-sequence quantities from our model of the UPFC, as we consider three-legged converters. While in our particular benchmark example connections of transformers in addition prevent the zero sequence currents from flowing through the line with the UPFC, the general case would be straightforward, as one equation would have to be added for the shunt and series branch each. These additional equations would be completely decoupled from either of the – axes, and the zero sequence quantities do not affect the dc link dynamics in the case of three-legged converters. We consider a model of the synchronous machine with seven electrical states and two mechanical states (i.e., two damper windings in the axis and one in the axis); the details about this standard model are omitted, and the reader is referred to [21]. B. Dynamical Phasor Model

(7)

The dynamical phasor model is derived from the time-domain model using (3) and (6). We assume that the generator speed has only the dc component, the ac currents with only the fun) in positive and negative sequence (what gets damental ( mapped into dc and second harmonic after the Park transformation), and the dc link voltage and the electrical torque with

398

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002

Fig. 2. UPFC shunt controller.

Fig. 4. Electrical torque following the onset of unbalance at t = 0:02 s: time-domain switched simulation (dashed line) and phasor model (solid line).

Fig. 3.

UPFC series (load flow) controller.

the dc and second harmonic (the same holds for real and reactive power). It will turn out that these assumptions result in accurate dynamical models; it is certainly possible to include more harmonics for a better accuracy, but at a price of increased model complexity. This increase in model order (by including, for example, 6th and 12th harmonics in the rotor – reference frame) would be justified in a study of effects of UPFC harmonics. Similarly, more harmonics in the dc link voltage could be useful in UPFC design. Given our emphasis on modeling of the UPFC, we prefer simple models for other system components, e.g., we assume that the mechanical torque and the field voltage are held constant. These assumptions are acceptable for relatively short transients that we analyze here, and could be removed in a straightforward way in other cases. For example, in our case, the addition of a very fast thyristor exciter with transient gain reduction (controller (iii) in [21, p. 814]) does not lead to any significant changes in the simulated waveforms. With our assumptions the UPFC model becomes

Fig. 5. DC link capacitor voltage following the onset of unbalance at t = 0:02 s: time-domain switched simulation (dashed line) and phasor model (solid line).

where

(12) and from (9)

(13) and ) of the dc link voltage Each harmonic (i.e., (14) (written in detail for illustration purposes) is given by

(11)

STEFANOV AND STANKOVIC´: MODELING OF UPFC OPERATION UNDER UNBALANCED CONDITIONS

Fig. 6.

399

Electrical torque following the onset of unbalance at t = 0:02 s: time-domain nonswitched simulation (dashed line) and phasor model (solid line).

(14) denotes the real part of a complex number. These where equations are nonlinear in general, involving multiplications of states, and of states and control inputs. The inclusion of more harmonic components (e.g., second harmonic in the generator speed) is straightforward in this framework [24]. Note that the phasor dynamic model increases the number of states when compared to the time-domain model, as equations are complex for non-dc components, and thus each corre-

sponds to two real equations. In particular, we have four real and four complex equations for UPFC ac currents (second harmonic in the Park frame, generated by the fundamental of the inverse sequence), one real and one complex equation for the dc link voltage. Overall, there are 12 states for the currents (four real, four complex that each have real and imaginary parts, or magnitude and phase) and three states for the dc link voltage (one real, one complex). Thus, we are dealing with a 15th-order model for UPFC; the order of the model can be changed downwards (if some variables turn out to be negligible), or upwards (e.g., if additional harmonics need to be included). While 15 equations per UPFC may seem to be a large increase in model complexity, we want to emphasize: 1) model accuracy (which we illustrate later) and 2) the fact that the phasor model is time-invariant (autonomous), and thus much more amenable to analysis, and possibly faster to simulate, as we explore later. In a steady state, the dynamic phasor model (11)–(14) can yield complete equivalent circuits, by setting all time derivatives to zero. The dynamic model itself, together with possible refinements to include additional harmonics, has a potential to be useful in transient stability, short circuit and protection studies; we illustrate that point in the next two sections. IV. BENCHMARK EXAMPLE Our benchmark example is modified from [21, ex. 13.4] by adding a UPFC in the lower branch (see Fig. 1). The reactance of the shunt branch is 0.1 p.u., the capacitor size is 0.5/377 p.u.,

400

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002

(a)

(a) Fig. 7. DC link voltage components following the onset of unbalance at t = 0:02 s: DC component (top panel), and the real part (solid line) and the imaginary part (dashed line) of the second harmonic (bottom panel).

the reactance of the series branch is selected to maintain the two lines equal and the converter losses are neglected. Note that zero sequence currents flow only through the generator step-up transformer (because of assumed transformer connections). Ini-

tial operating point corresponds to a unit voltage at generator p.u. The terminals, and the generator loading of control structure assumed for the UPFC regulates the real and reactive power flow in the series branch, and the reactive power

STEFANOV AND STANKOVIC´: MODELING OF UPFC OPERATION UNDER UNBALANCED CONDITIONS

401

Fig. 8. Electrical torque during a one phase to ground fault: time-domain switched simulation (dashed line) and phasor model (solid line).

and dc voltage in the shunt branch; all controllers are standard PI regulators, as shown in Figs. 2 and 3. We consider two unbalanced modes of operation: 1) voltage asymmetry with 5% negative sequence voltage and 2) one phase to ground fault at the beginning of the line parallel to the one with the UPFC, where after the fault the affected line is disconnected. The control of the series UPFC branch is disabled during the fault [8], [9]. Our large-signal transient simulations offer a way to directly evaluate the validity of nonlinear dynamic phasor models.

V. MODEL VALIDATION A. Simulation Results We first present the simulation results in the case of operation with unbalanced voltages (the unbalance starts at time s). The solid line in all figures is the prediction of the dynamic phasor model, while the dashed line corresponds to the detailed switched (“48-pulse”) time-domain model (see, for example, [13], [15]). The higher number of pulses improves the operation of UPFC, and today it is achieved by multilevel converters. In the future, the same effect may be accomplished by pulsewidth modulation (PWM), as is done today at lower power levels. In Fig. 4 we display the electrical torque, while in Fig. 5 we show the dc link capacitor voltage; in both cases an excellent agreement is evident. There is little overall difference between switched and nonswitched simulation of the time-domain model, as evidenced by Fig. 6, which compares the nonswitched

simulation of the electrical torque with the phasor model (compare with Fig. 4). In our particular implementation, the phasor model is typically at least an order of magnitude faster than the simulation of the switched model, and two to three times faster than the time-domain simulation of (7)–(10) without switching (no effort was made to speed-up any of these Simulink setups). A reason for this computational speed-up in the case of the dynamic phasor model is the relatively slow variation of key harmonics. In Fig. 7, we display the components of the dc link voltage—the dc component in the top panel, and the real (solid line) and imaginary (dashed line) component of the second harmonics (bottom panel). Next, we consider the case of the one phase to ground fault described earlier; in Fig. 8 we show the electrical torque, in Fig. 9 we display the dc link voltage. Note that again the overall agreement is satisfactory; following this very abrupt transient, the phasor models are still able to provide good tracking of the switched time-domain waveforms. B. Participation Factor Analysis Our large-signal dynamic phasor model can be linearized for the purpose of control analysis and design. We are interested in the participation of states corresponding to the UPFC in various modes of the system (see, for example, [21]). For our selection of UPFC parameters, it turns out that states corresponding to the series branch (dc and second harmonic in the Park frame) participate highly in two pole pairs (modes) with the real part of

402

Fig. 9.

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002

DC voltage during a one phase to ground fault: time-domain switched simulation (dashed line) and phasor model (solid line).

35 and 40, respectively; note that these modes are affected by line inductance. States corresponding to the dc link voltage are a good deal faster (participate in a pole pair with the real part of 321 and in faster states), while the states of the shunt part are even faster (participate highly in modes with real parts of 2000 or less). If the dc link capacitor is increased ten times, the corresponding modes become as slow as the modes dominated by the series branch. We thus conclude that the modeling of the dynamics of the series branch is likely to be a key part of system-wide stability studies, and that the dynamics of the dc link may become important as well if the dc link capacitor is relatively large.

VI. CONCLUSIONS This paper derives an analytical dynamical model for unbalanced UPFC. The same methodology is, of course, applicable to simpler voltage-sourced converters like STATCOM and SSSC. The main theoretical benefits stem from the time-invariant nature of this approximate large-signal model, as it substantially simplifies stability and performance analyses. The dynamic phasor models are quite accurate, and result in fast simulations. The paper presented only one in a family of possible models, as a different choice of retained harmonics leads to a different model. This hierarchical nature of the dynamic phasor approach is valuable when models of a FACTS system are needed with varying levels of detail.

REFERENCES [1] IEEE Special Stability Controls Working Group, “Static VAR compensator models for power flow and dynamic performance simulation,” IEEE Trans. Power Syst., vol. 9, pp. 229–240, Feb. 1994. [2] S. G. Jalali, R. H. Lasseter, and I. Dobson, “Dynamic response of a thyristor-controlled switched capacitor,” IEEE Trans. Power Delivery, vol. 9, pp. 1609–1615, July 1994. [3] S. G. Jalali, R. A. Hedin, M. Pereira, and K. Sadek, “A stability model for the advanced series compensator (ASC),” IEEE Trans. Power Delivery, vol. 11, pp. 1128–1137, Apr. 1996. [4] IEEE, “Modeling and analysis of system transients using digital programs,”, Piscataway, NJ, IEEE Press TP-133-0, 1998. [5] , “Facts overview,”, Piscataway, NJ, IEEE Press 95-TP-108, 1995. [6] , “Facts applications,”, Piscataway, NJ, IEEE Press 96-TP-116, 1996. [7] L. Gyugyi, “Unified power-flow control concept for flexible AC transmission systems,” Proc. Inst. Elect. Eng., pt. C, vol. 139, pp. 323–331, July 1992. [8] N. G. Hingorani and L. Gyugyi, Understanding FACTS—Concepts and Technology of Flexible AC Transmission Systems. Piscataway, NJ: IEEE, 2000. [9] Y. H. Song and A. T. Johns, Eds., Flexible AC Transmission Systems (FACTS). London, U.K.: Inst. Elect. Eng., 1999. [10] H. Shauder and H. Mehta, “Vector analysis and control of advanced static VAR compensators,” Proc. Inst. Elect. Eng., pt. C, vol. 140, pp. 299–305, July 1993. [11] Z. Huang, Y. Ni, C. M. Shen, F. F. Wu, S. Chen, and B. Zhang, “Application of unified power flow controller in interconnected power systems—Modeling, interface, control strategy, and case study,” in IEEE PES Summer Meet.Paper, July 1999, PE399PRS. [12] A. Nabavi-Niaki and M. R. Iravani, “Steady-state and dynamic models of unified power flow controller (UPFC) for power system studies,” IEEE Trans. Power Syst., vol. 11, pp. 1937–1943, Nov. 1996. [13] R. Caldon, P. Mattavelli, and B. M. Han, “Dynamic analysis and control of UPFC using transient simulation,” in Proc. Int. Conf. Power System Transients—IPST’99, July, pp. 527–532.

STEFANOV AND STANKOVIC´: MODELING OF UPFC OPERATION UNDER UNBALANCED CONDITIONS

[14] V. A. Caliskan, G. C. Verghese, and A. M. Stankovic´, “Multifrequency averaging of DC/DC converters,” IEEE Trans. Power Electron., vol. 14, pp. 124–133, Jan. 1999. [15] K. K. Sen and E. J. Stacey, “UPFC—Unified power flow controller: Theory, modeling, and applications,” IEEE Trans. Power Delivery, vol. 13, pp. 1453–1460, Oct. 1998. [16] C. D. Shauder, D. M. Hamai, L. Gyugyi, T. R. Reitman, A. Edris, M. R. Lund, and D. R. Torgerson, “Operation of unified power flow controller (UPFC) under practical constraints,” IEEE Trans. Power Delivery, vol. 13, pp. 630–639, Apr. 1998. [17] P. Cao, L. Zhang, and M. L. Crow, “Modeling and control of a unified power flow controller,” in Proc. North Amer. Power Symp., Oct. 1999, pp. 119–123. [18] A. R. Bakhshai, G. Joos, and H. Jin, “EMTP simulation of multipulse unified power flow controllers,” in Proc. IEEE CCECE, 1996, pp. 847–850. [19] C. Hochgraf and R. H. Lasseter, “STATCOM controls for operation with unbalanced voltages,” IEEE Trans. Power Delivery, vol. 13, pp. 538–544, Apr. 1998. [20] A. M. Stankovic´, P. Mattavelli, V. Caliskan, and G. C. Verghese, “Modeling and analysis of FACTS devices with dynamic phasors,” in Proc. PES Winter Meet., Feb. 2000. [21] P. Kundur, Power System Stability and Control. New York: McGrawHill, 1994. [22] S. R. Sanders, J. M. Noworolski, X. Z. Liu, and G. C. Verghese, “Generalized averaging method for power conversion circuits,” IEEE Trans. Power Electron., vol. 6, pp. 251–259, Apr. 1991. [23] P. Mattavelli and A. M. Stankovic´, “Dynamical phasors in modeling and control of active filters,” in Proc. IEEE Int. Symp. Circuits Syst., vol. 5, May 1999, pp. 278–282. [24] A. M. Stankovic´, S. R. Sanders, and T. Aydin, “Analysis of unbalanced AC machines with dynamic phasors,” in Proc. Naval Symp. Elect. Machines, Oct. 1998, pp. 219–224.

403

[25] A. M. Stankovic´ and T. Aydin, “Analysis of unbalanced power system faults using dynamic phasors,” IEEE Trans. Power Syst., vol. 15, pp. 1062–1068, Aug. 2000. [26] A. M. Stankovic´, “Dynamic phasors in modeling of arcing faults on overhead lines,” in Proc. Int. Conf. Power Syst. Transients, June 1999, pp. 510–514. [27] W. V. Lyon, Transient Analysis of Alternating Current Machinery. New York: Wiley, 1954.

ˇ Stefanov received the Dipl.Ing. and M.S. degrees from the UniverPredrag C. sity of Belgrade, Belgrade, Yugoslavia, in 1988 and 1995, respectively. Since 1990, he has been an Assistant Lecturer with the Electrical Engineering Department, University of Belgrade. He was a Visiting Scientist with the Department of Electrical and Computer Engineering at Northeastern University, Boston, MA, in 1999 and 2000. His research interests are in modeling, analysis, and control of power systems.

Aleksandar M. Stankovic´ received the Dipl.Ing. and M.S. degrees from the University of Belgrade, Belgrade, Yugoslavia, in 1982 and 1986, respectively, and the Ph.D. degree from the Massachusetts Institute of Technology, Cambridge, in 1993, all in electrical engineering. He has been with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, since 1993, where he is presently an Associate Professor. Dr. Stankovic´ served as an Associate Editor for the IEEE TRANSACTIONS ON CONTROL SYSTEM TECHNOLOGY and is presently an Associate Editor for the IEEE TRANSACTIONS ON POWER SYSTEMS.