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Abstract—Analysis of frequency dynamics due to large active

power imbalance is an important but time-consuming task of power system operation. Ignoring influence of reactive power and voltage on active power-frequency dynamics, a new direct current loadflow based frequency response model (DFR) is proposed in this paper. It is developed with “flat voltage” assumption to simplify generating unit and load models. Unlike average system frequency model (ASF) and system frequency response model (SFR), network is preserved in DFR model with direct current network equations. Accuracy and efficiency of DFR model are verified test systems. DFR model finds a balance point between full-time domain simulation and ASF model. It is a promising method for on-line evaluations.

Index Terms—Active power, direct current (DC) network,

frequency response, frequency stability

I. INTRODUCTION REQUENCY is an important index of balance between active power generation and load. Active power-frequency

dynamics analysis is an important task of power system operation. For small-scale power systems, major disturbances such as large unit tripping will cause enormous active power imbalance, and lead to large frequency deviation, even system collapse. Frequency stability is a key concern of these power systems. For interconnected power systems, frequency is supposed to be stable with reciprocal reserve of each subsystem. However, greater inter-area power transfer and higher requirement for efficiency make power system operated under higher stress and strain. The risk of breaching frequency security or stability is increasing. Some large frequency incidents from the 1970s to the 1990s are reported in [1]. A fast frequency drop to 49.518Hz (nominal value of 50Hz) was detected on Nov. 20th, 2005 in East China Power Grid with 3,000MW active power loss due to HVDC blocking [2]. Some reports show that unit tripping due to turbine underfrequency protection and improper setting of underfrequency load shedding (UFLS) schemes play important roles in system collapse [3-5]. With fast development of renewable energy sources, power system frequency dynamics shows more complex characteristics due to uncertainty of such intermittent energy sources as wind power. The availability of new tools for robust frequency control strategy analysis with large-scale

Project Supported by National Natural Science Foundation of China (50807031).

Authors are all with the School of Electrical Engineering, Shandong University, Jinan 250061, P. R. China (e-mail: springlee@mail.sdu.edu.cn, liuyt@sdu.edu.cn, zhanghx@sdu.edu.cn).

wind power penetration is an urgent task[6-7]. Further development of analysis method is needed to meet growing requirement for fast active power-frequency dynamics analysis.

Essentially, active power-frequency dynamics is coupled with reactive power-voltage dynamics and frequency is distributed differently between different places, i.e., space-time features. Full-time domain simulation is the most sophisticated method considering both frequency-voltage dynamics and frequency space-time features[8-9]. Though accurate and reliable, full-time domain simulation is time-consuming due to exploding computation burden when applied to systems of increasing size.

With frequency space-time features neglected, uniform frequency assumption is usually made in simplified models of frequency dynamics. With voltage dynamics considered, simplified method is usually adopted in long-term simulation of frequency stability and voltage stability [8]. If voltage dynamics is neglected aggressively, network information can be neglected and average system frequency (ASF) model [10] and system frequency response (SFR) model [11] can be derived.

This paper presents a novel direct current loadflow based frequency response model (DFR) for fast active power-frequency dynamics analysis, in which frequency space-time feature is preserved and voltage dynamics is neglected. This paper is organized as follows. Section II shows derivation of the DFR model. Some simulations are performed to verify accuracy and fast speed of the DFR model in section III. Conclusions are made in section IV.

II. DC NETWORK BASED FREQUENCY RESPONSE MODEL With sensitivity analysis, reference[12] proves the fact that

a mismatch in active power balance primarily affects system frequency, but leaves bus voltage magnitudes essentially unaffected. It is an important phenomenon that should be recognized in active power-frequency dynamics analysis. Thus, reactive power-voltage dynamics is eliminated in ASF and SFR models for simplification. This is acceptable for well-designed power systems of which reactive power reserve and excitation systems are so strong that dynamic voltage response has a good performance when an active power disturbance occurs. However, the elimination of network in ASF or SFR model makes active power dynamics of different branches and machines unavailable.

In order to look further into active power dynamics while

Fast Analysis of Active Power-Frequency Dynamics Considering Network Influence

Changgang Li, Yutian Liu, Senior Member, IEEE, Hengxu Zhang, Member, IEEE

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978-1-4673-2729-9/12/$31.00 ©2012 IEEE

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reducing computation burden, network is preserved with DC network equations in the proposed DFR model. This section shows how the DFR model is developed.

A. Model of Full-Time Domain Simulation and ASF A typical model of full-time domain simulation is described

in Fig. 1 [9]. Pm is mechanical power of turbine-governor, Pe is electrical power output of generator, ω is angular velocity of rotor, Vt is terminal voltage of generator, Efd is field voltage of excitation system, Vref is reference voltage of excitation system, Vs is output signal of PSS (Power System Stabilizer), H is inertia constant, D is damping coefficient.

Fig. 1. Typical model of full-time domain simulation

In full-time domain simulation, generating units, network, loads and other equipments such as FACTS devices and HVDC links are modeled in detail. Dynamics of active power and frequency is coupled with that of reactive power and voltage.

To highlight active power-frequency dynamics, uniform frequency is assumed in ASF model. Reactive power-voltage dynamics and network are eliminated. Fig. 2 shows the structure of ASF model. PmΣ and PeΣ are system total mechanical power and electrical power, i.e., system total load. Δω is system average frequency.

Fig. 2. Diagram of average system frequency model

In the proposed DFR model, flat voltage assumption is made like ASF model, but network is preserved like full-time domain simulation. Simplification of DFR model is discussed in detail in the flowing sections.

B. Simplification of Generating Unit Model With flat voltage assumption, terminal voltage of generator

is considered to be constant. Thus, both excitation system and PSS can be eliminated. Fast dynamics of generator stator windings and rotor windings are not simulated. Dynamics of turbine-governors and inertia equations is preserved for its significant influence on active power-frequency dynamics. Simplified generating unit model in DFR model is shown in Fig. 3. Pe is dependent on external constraint of network and δ (rotor angle) is set equal to voltage angle of bus where the generating unit locates. Model of boiler should also be preserved if long-term simulation is required.

Fig. 3. Simplified generating unit model in DFR model

C. Simplification of Network Model In both ASF and SFR models, network information is

eliminated due to uniform frequency assumption. On the contrary, DFR model reflects imbalanced power redistribution between different units and space-time features of frequency dynamics with preservation of network.

Since only active power is considered, the assumption of “constant terminal voltage” is extended to “flat” voltage profile, i.e., voltage magnitudes of each node are assumed to be 1.0 p.u. uniformly. Direct current power flow is introduced to model network when performing active power flow calculation of initial operating condition[13]

(1) where P and θ are active power injection and voltage angle of all buses except slack bus, B is network susceptance matrix.

When performing dynamics analysis, the network is modeled with the following direct current network equations

(2)

where PG and δG are vectors of electrical power injection and rotor angle of all generators including the one connecting to the slack bus, PL and θL are vectors of active power injection and voltage angle of loads, BGG, BLL, BGL and BLG are network susceptance matrix.

δG and PL are known quantity in each time step, and θL and PG can be directly calculated with

(3)

Since no iteration is needed for solving direct current network equations, computation burden of DFR model in network solution is much smaller than full-time domain simulation.

Traditionally, direct current network equations are usually used in direct current power flow calculation for static security analysis [13-14]. DFR model extends application field of direct current network equations for network emulation of dynamics analysis. Characteristic of direct current network equations in DFR model is the same as direct current power flow. Reference [15] verified the usefulness of direct current power flow and showed that it can accurately reflect active power distribution especially for high-voltage network.

D. Simplification of Load Model The flat voltage assumption leads to load model

simplification. Taking the widely used polynomial model for example, model IEEL of PSS/E[16] is shown as

3

(4)

where PL and QL are active and reactive components of load when bus voltage is U, PL0 and QL0 are values of the respective variables at initial operating condition, n1 to n3 and m1 to m3 are exponents of each load component, a1 to a3 and b1 to b3 are proportion coefficients of each component satisfying a1+a2+a3=1.0 and b1+b2+b3=1.0, Kpf and Kqf are coefficients of frequency dependency, and Δf is bus frequency deviation.

Since U is set constant, and reactive power is eliminated, the polynomial model IEEL can be simplified as a static active power load considering frequency dependency

(5) where P0 is active power of load at initial operating condition with bus voltage of U0, and is given by

(6)

Other equipments can also be simplified with reasonable assumptions. For example, HVDC link can be represented with a constant positive (for sending-end) or negative (for receiving-end) active load without frequency dependency.

E. Model of DFR With the simplifications of generating units, network, loads

and other equipments, the DFR model proposed in this paper can be illustrated in Fig. 4.

Fig. 4. Schematic diagram of DFR model

Similar to full-time domain simulation, DFR model can be expressed in terms of differential-algebraic equations (DAEs)

(7)

(8) The differential equations (7) are used to describe dynamics

of turbine-governors and inertia equations. The algebraic equations (8) are to describe network and loads.

DFR model can be solved with ordinary methods of DAEs, such as modified Euler method. Since algebraic equations can be solved directly without iteration, DFR model reduces tremendous computation burden as shown in section III.

F. Treatment of System Loss Loss is usually neglected in direct current power flow. It

will lead to error in power generation of generator at the slack bus, especially for large-scale power system of which system loss should not be omitted. To avoid this error, system loss must be taken into account carefully. This paper treats system loss in a simple way by allocating it to each load. A new virtual load without frequency dependency is added to each load, and its value is in proportion with original load

(9)

where PLOSS is system total loss under initial operating condition, Ploss i is loss (virtual load) redistributed to load i, PL i and PL j are original power of load i and j , respectively.

G. Features of DFR Model DFR model is a new method between full-time domain

simulation and ASF model. It aims to conduct active power-frequency dynamics analysis with fast speed while preserving as much information as possible. Computation burden of DFR model is much smaller than full-time domain simulation due to model simplifications. Unlike ASF and SFR models, network is preserved in DFR model with direct current network equations. Thus, individual frequency dynamics of each generator instead of uniform system frequency can be revealed by DFR model. Active power dynamics of network and each generator can be also obtained. This is one of important advantages of DFR model over other simplified methods. However, it should be noticed that small voltage deviation is the core of model assumption and attention must be paid if voltage deviates greatly from initial operating condition.

III. SIMULATIONS Similar to ASF and SFR models, DFR model can be used

for basic disturbances of active power imbalance, such as unit tripping and load increase or decrease. With the network preservation, DFR model can be also used for disturbances of transmission line outage while other simplified models fail. Above disturbances are considered to meet the requirement of[10], i.e. these disturbances may lead to active power imbalance or redistribution and cause system frequency shift, but no large voltage deviation. Disturbances that may result in significant voltage deviation are out of the scope of DFR model, e.g. short-circuit of transmission lines.

In this section, characteristics of DFR model are discussed with some simulations.

A. Test Systems and Simulation Description Three power systems are chosen for simulations in this

paper. They are IEEE 3-machine 9-bus system, New England 10-machine 39-bus system, and Shandong Grid, a provincial grid of China with 973 buses. Information of the 9-bus system and the 39-bus system can be found in[9] and[17], respectively. They are both operated at 60Hz.

Simulations are conducted with DFR model, full-time domain simulation and ASF model, respectively. PSS/E is chosen as full-time domain simulation tool. Programs of DFR model and ASF model are both composed in C++ with the same modified Euler method as PSS/E[16]. No simulation is performed with SFR model for its difficulty in model aggregation and poor performance under large active power imbalance.

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B. Unit Frequency Dynamics With similar model simplifications, the system uniform

frequency of ASF model can be considered as average system frequency of DFR model. Fig. 5 shows frequency dynamics of the 9-bus system with load increase of 10MW at load 8. It can be found from Fig. 5 that oscillation occurs among each unit in DFR model with network preservation, and the minimum frequency of each unit in DFR model is smaller than ASF model. It is also easy to conclude that the residual frequency of DFR model is the same value as ASF model (i.e. 59.954Hz in this test).

1 2 3 4 5

59.85

59.9

59.95

60

time (s)

freq

uenc

y (H

z)

DFRASF

Fig. 5. Frequency dynamics of 9-bus system with load increase of 10MW

With preserved network, DFR model can reflect frequency dynamics of each unit rather than system uniform frequency of ASF model or SFR model. Fig. 6 shows frequency dynamics of generators 35 in the 39-bus system with unit tripping of generator 34 (loss of generation: 508MW).

0 10 20 3059.5

59.6

59.7

59.8

59.9

60

time (s)

freq

uenc

y (H

z)

DFRPSS/E

Fig. 6. Frequency dynamics of generator 35 with tripping unit 34 of 39-bus system

It can be seen from Fig. 6 that DFR model can reflect frequency dynamics with fine accuracy. At the first few seconds after disturbance occurs, frequency dynamics of DFR model is close to that of full-time domain simulation. The minimum frequency of DFR model is 59.518, and is 0.035Hz smaller than full-time domain simulation. The residual frequency of DFR model is 59.851Hz, and is 0.011Hz smaller than full-time domain simulation.

30 32 34 36 38−0.06

−0.04

−0.02

0

unit number

nadi

r er

ror

(Hz)

30 32 34 36 380

0.5

1

1.5x 10

−3

unit number

RM

S (H

z)

Fig. 7. Frequency nadir error and RMS of frequency error between DFR model and full-time domain simulation

Fig. 7 shows the frequency nadir error and root mean square (RMS) of frequency error between DFR model and full-time domain simulation with tripping unit 34 of the 39-bus system.

It can be seen from Fig. 7 that frequency nadir of DFR model is smaller than full-time domain simulation. The reason is that DFR model can not take into account voltage fluctuation of real power system. Extra load reduction due to voltage drop when tripping unit 34 makes actual load of full-time domain simulation smaller than DFR model. Thus, frequency deviation of DFR model is larger than full-time domain simulation. Result of Fig. 7 shows that the frequency nadir error of DFR model is no more than 0.05Hz, and RMS of DFR model is smaller than 1.3×10-3 Hz. The frequency nadir error between system uniform frequency of ASF model and full-time domain simulation is -0.0376Hz, and RMS is 5.339×10-4Hz. DFR model has the similar accuracy as ASF model in frequency dynamics.

C. Frequency Space-Time Features With network preservation, DFR model is capable of

reflecting frequency space-time features. Taking unit tripping of generator 34 of the 39-bus system for example, Fig. 8 shows the rate of change of frequency (ROCOF) of each unit when disturbance occurs and time delay when frequency deviation of each unit exceeds 0.05Hz (tΔf>0.05Hz). Black bars correspond to frequency dynamics of DFR model while white bars are frequency dynamics of full-time domain simulation.

30 32 34 36 38−4

−2

0

unit number

RO

CO

F (H

z/s)

30 32 34 36 380

0.5

1

1.5

unit number

t Δf >

0.0

5 H

z (s)

Fig. 8. Generator frequency space-time features of the 39-bus system

It can be found from Fig. 8 that except for generator 33, i.e., generator near to generator 34, the ROCOF of DFR model is close to that of full-time domain simulation. Since load reduction due to voltage drop is not considered in DFR model, frequency of DFR model changes faster than full-time domain simulation. Fig. 8 also reveals that frequency dynamics of DFR model is close to that of full-time domain simulation on frequency deviation detection.

D. Generator Active Power Dynamics Unlike ASF or SFR model, with network preservation,

DFR model is able to reflect active power dynamics of each generator and branch. Fig. 9 illustrates active power of each generator when a sudden load loss of 90MW occurs at load 6 in the 9-bus system.

It can be found from Fig. 9 that active power generation of each generator also shows fine consistency between DFR model and full-time domain simulation. Both instantaneous active power redistribution when disturbance occurs and active power when system reaches steady state coincide with those of full-time domain simulation.

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0 5 10 15 20 25 30−10

30

70

110

150

190

time (s)

pow

er (

MW

)

DFR

PSS/Egenerator 2

generator 3

generator 1

Fig. 9. Active power of generating units with load disturbance

E. Branch Active Power Dynamics With preserved network, active power dynamics of

transmission lines and transformers can be obtained with DFR model. Taking the 39-bus system for example, line 14-4 is operated with initial active power of about 270MW and is suddenly tripped for some reason at time 1.0s. Active power dynamics of line 11-6 and line 25-26 is illustrated in Fig. 10.

0 5 10 15 200

200

400

600

time (s)

pow

er (

MW

)

DFR

PSS/E

line 11−6

line 25−26

Fig. 10. Active power dynamics of two branches in the 39-bus system

TABLE I shows some critical values of active power dynamics of line 11-6 and line 25-26. P0 is initial active power before disturbance, Pdist is instantaneous active power at the time when disturbance occurs and indicates active power redistribution among network, PSS is active power when system reaches steady state, Perror is active power error between DFR model and full-time domain simulation and is defined as

(10)

where PPSS/E is active power of full-time domain simulation, PDFR is active power of DFR model.

TABLE I ACTIVE POWER DYNAMICS OF AC LINES IN THE 39-BUS SYSTEM

Model P0 (MW) Pdist (MW) PSS (MW)

11-6 25-26 11-6 25-26 11-6 25-26

PSS/E 344.482 76.611 473.197 70.712 513.039 58.597

DFR 347.219 68.241 476.862 62.847 520.282 50.644

Perror (%) 0.795 10.925 0.774 11.122 1.412 13.571

Fig. 10 and TABLE I show that DFR model is accurate enough to reflect active power dynamics of line 11-6. But for line 25-26, the accuracy of active power dynamics is poor. The reason is that line 25-26 is weakly loaded. Therefore, the absolute value of Perror is insignificant for line 25-26, which also is the conclusion of [15].

F. Rotor Angle Dynamics

Generator rotor angle δ is closely related to frequency dynamics. Rotor angle information is a by-product of DFR model with fine accuracy of frequency dynamics. Fig. 11 illustrates maximum rotor angle difference of all generators (Δδmax) in the 39-bus system with line 16-17 tripped at 1.0s. It can be found from Fig. 11 that rotor angle difference obtained by DFR model coincides with that of full-time domain simulation. However, it should be reminded that rotor angle provided by DFR can not be used for angle stability.

0 5 10 15 2018

20

22

24

26

28

30

time (s)

Δδ

max

( o )

DFRPSS/E

Fig. 11. Maximum rotor angle difference of the 39-bus system

G. Computation Speed To analyze the speed of DFR model qualitatively, time

consumption of two disturbances is recorded. They are unit tripping of generator 34 of the 39-bus system and single-polar HVDC blocking of Shandong Grid. They are both analyzed with DFR model, full-time domain simulation and ASF model, respectively. All simulations are performed under the same condition: uniform simulation time span of 30s and uniform time step of 0.01s. TABLE II gives dimension of differential equations and consumed CPU time of three methods on the same PC with CPU of 3.0GHz.

TABLE II COMPUTATION BURDEN COMPARISON

ModelNumber of

differential equations CPU time (s)

39-bus 973-bus 39-bus 973-bus

DFR 45 735 0.047 0.765

PSS/E 144 3538 0.938 17.642

ASF 28 442 0.015 0.120

Since constant terminal voltage is assumed in DFR, exciters and PSS should be reserved to provide fine voltage response in PSS/E. It makes differential equations of PSS/E much more than DFR and ASF.

It can be found from TABLE II that DFR model is about 20 times faster than full-time domain simulation in the two tests, and can achieve significant time advantage over full-time domain simulation. DFR model is slower than ASF model mainly because of network preservation and more inertia equations.

H. Summary With preserved network, DFR model is capable of

reflecting frequency dynamics of each unit rather than average

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system frequency of ASF model. Simulations show that the DFR model possesses fine accuracy since critical factors affecting active power-frequency dynamics are preserved, e.g. nonlinearity of turbine-governors. Due to similar model simplifications, DFR model has the same accuracy in frequency dynamics as ASF model. With reasonable model simplifications, differential equations and algebraic equations are significantly reduced and DFR model is about 20 times faster than full-time domain simulation.

IV. CONCLUSIONS A new DC network based frequency response model for

active power-frequency dynamics analysis is proposed in this paper. The key difference between DFR model and other simplified methods is network preservation. With preserved direct current network, uniform frequency assumption is no longer a prerequisite for simplified active power-frequency dynamics analysis. Important information such as active power dynamics of transmission lines and frequency dynamics of each generator can be obtained with DFR model. Since the nonlinearity of turbine-governors is considered, the accuracy of DFR model can be guaranteed under different types of disturbances. The efficiency of DFR model is much higher than full-time domain simulation especially for large-scale power systems. DFR model provides an alternative for fast active power-frequency dynamics analysis. Frequency dynamics and active power dynamics obtained by DFR model can be used for further researches such as UFLS setting and contingency screening of dynamic security analysis.

V. REFERENCES [1] CIGRE Task Force 38-02-14, "Large Frequency Disturbances: Analysis

and Modeling Needs," in Proc. 1999 IEEE Power Engineering Society Winter Meeting, New York, USA, pp. 554-558.

[2] Xiang Gao, Fuying Gao and Zenghui Yang, "Frequency Accident Analysis in East China Grid Due to DC Line Fault," Automation of Electrical Power Systems, vol.30, no.12, pp. 102-107, 2006(in Chinese).

[3] "Final Report of the Investigation Committee on the 28 September 2003 Blackout in Italy", UCTE, 2004, http://www.rae.gr/old/cases/C13/italy/UCTE_rept.pdf.

[4] G. Andersson, P. Donalek and R. Farmer, et al., "Causes of the 2003 Major Grid Blackouts in North America and Europe, and Recommended Means to Improve System Dynamic Performance," IEEE Transactions on Power Systems, vol.20, no.4, pp. 1922-1928, 2005.

[5] Abdullah I. Al-Odienat, "Power System Blackouts Analysis and Simulation of August 9,2004 Blackout in Jordan Power System," Information Technology Journal, vol.5, no.6, pp. 1078-1082, 2006.

[6] I. Erlich, K. Rensch and F. Shewarega, "Impact of Large Wind Power Generation on Frequency Stability," in Proc. 2006 IEEE Power Engineering Society General Meeting, Montreal, Canada, pp. 1-8.

[7] Nayeem Rahmat Ullah, Torbjorn Thiringer and Daniel Karlsson, "Temporary Primary Frequency Control Support by Variable Speed Wind Turbines - Potential and Applications," IEEE Transactions on Power Systems, vol.23, no.2, pp. 601-612, 2008.

[8] Prabha Kundur, Power System Stability and Control, New York: McGraw-Hill Education, 1994.

[9] Paul M. Anderson and A. A. Fouad, Power System Control and Stability, New York: IEEE Press, 1994, p. 464.

[10] Man L. Chan, R. D. Dunlop and Fred Schweppe, "Dynamic Equivalents for Average System Frequency Behavior Following Major Disturbances," IEEE Transactions on Power Apparatus and Systems, vol.PAS-100, no.5, pp. 2635-2642, 1972.

[11] P. M. Anderson and M. Mirheydar, "A Low-Order System Frequency Response Model," IEEE Transactions on Power Systems, vol.5, no.3, pp. 720-729, 1990.

[12] Olle I. Elgerd and Charles E. Fosha, "Optimum Megawatt-Frequency Control of Multiarea Electric Energy Systems," IEEE Transactions on Power Apparatus and Systems, vol.PAS-89, no.4, pp. 556-563, 1970.

[13] Brain Stott, Jorge Jardim and Ongun Alsac, "DC Power Flow Revisited," IEEE Transactions on Power Systems, vol.24, no.3, pp. 1290-1300, 2009.

[14] Allen J. Wood and Bruce F. Wollenberg, Power Generation, Operation and Control, New York: John Wiley & Sons, 1996.

[15] Konrad Purchala, Leonardo Meeus and Daniel Van Dommelen, et al., "Usefulness of DC Power Flow for Active Power Flow Analysis," in Proc. 2005 IEEE PES General Meeting, San Francisco, USA, pp. 454-459.

[16] PSS/E User Manual, And Power Technology International Siemens Power Transmission And Distribution Inc., 2007

[17] T. Athay, R. Podmore and S. Virmani, "A Practical Method for Direct Analysis of Transient Stability," IEEE Transactions On Power Apparatus and Systems, vol.PAS-98, no.2, pp. 573-584, 1979.

VI. BIOGRAPHIES

Changgang Li received his B.E. in electrical engineering from Shandong University, Jinan, China, in 2006 and is currently pursuing a Ph.D. degree in the School of Electrical Engineering, Shandong University. His research interests focus on power system frequency dynamics and control.

Yutian Liu (SM’96) received his B.E. and M.S. from Shandong University of Technology, Jinan, China, in 1984 and 1990, respectively and his Ph.D. from Xi’an Jiaotong University, Xi’an, China, in 1994. He is now a professor of the School of Electrical Engineering, Shandong University. His research interests include power system analysis and control.

Hengxu Zhang (M’06) received his B.E. from Shandong University of Technology, in 1998, and his M.S. and Ph.D. from Shandong University, in 2000 and 2003, respectively. He is now an associate professor in the School of Electrical Engineering, Shandong University. His research interests lie in power system stability and control.