Grants Publications (Abstracts) Students

Recent Research:

Microgrids

Due to significant line resistances in a microgrid, active power variations produced by  doubly fed induction generator (DFIG) based generation translate to corresponding power quality problems. We have proposed simple localized control schemes exercised through the rotor side converters for voltage regulation.  Detailed dynamic simulations accounting for wind shear and tower shadow on a IEEE-13 bus distribution system  conducted in EMTDC/PSCAD show that tight regulation ( < 1 %)  can be achieved with the proposed method compared to   ~5% without control.  We have also examined the effectiveness of  energy-storage methods on frequency regulation in such systems. Our results show that  10 % (with respect to the machine rating) storage is effective at restricting frequency deviations within 1 %.

R. Aghatehrani and Rajesh G. Kavasseri, Reactive Power Management of a DFIG Wind System in Microgrids Based on  Voltage Sensitivity Analysis,  IEEE Trans. on Sustainable Energy, 2(4), Oct 2011, pp: 451-458.

Computational methods for large to very-large scale power systems

Our goal is to improve the efficiency and scalability of algorithms used in the analysis, operation and control of electric power systems. In the future, static and dynamic analysis on large-scale (thousands of buses) to very-large scale (tens of thousands of buses) power systems may need to be conducted in (near) real-time. Our current focus is on two important problems: (a) reconfiguration in distribution networks and (b) identifying extreme contingencies in bulk power systems.

Network reconfiguration is the primary mechanism to ensure  service reliability, restoration and maintenance of optimal operating conditions in  distribution systems. Computationally, this is challenging because of two main reasons:(i) the combinatorial nature of the solution space: closing tie and opening sectionalizing switches (i.e. reconfiguration) while preserving radiality yields a very large number of network topologies that need to be analyzed while seeking the optimal configuration and (ii) evaluation of each configuration requires solving the power flow problem. Our goal was to develop a scalable reconfiguration algorithm to system sizes ranging to thousands of buses, given the future growth in complexity of modern power distribution systems.  To address the combinatorial aspect (i), our reconfiguration algorithm proposes  concurrent first-order branch exchanges through a minimum cost maximum flow formulation. Motivated by the success of random-walks based network solutions in the VLSI community (640,000 + nodes), we proposed a random walks based power-flow solver for radial distribution systems to address aspect (ii). Its distinct characteristic of allowing  localized computation lends itself perfectly to situations where specific portions of the system need to be updated, such as when the distribution network is reconfigured through branch exchanges. Our results ondistribution systems with sizes of up to 10476 buses demonstrate that the proposed techniques can achieve computational runtimes shorter with up to 7.78 X with similar or better loss reduction compared to existing methods while offering computational complexity linear in the number of buses.  A public domain tool pro-NERDS  is available  here.

C. Ababei and Rajesh G. Kavasseri,  Efficient Network Reconfiguration using minimum cost maximum flow based branch exchanges and random walks based loss estimations,   IEEE Trans. on Power Systems, 26(1), pp: 30-37, Feb 2011.

Extreme Contingency Screening : Determining contingencies that can potentially culminate in a blackout is a challenging  computational task in large-scale power systems due to the combinatorial nature of the problem.  Prediction tools to identify such cases generally restrict the search to scenarios with severe  consequences that may arise from relatively few contingencies. One such approach is based on graph  partitioning where the ratio of power imbalance to cut-size serves as a heuristic measure to identify  critical line outages. However, algorithms based on nonlinear optimization or spectral partitioning  may become computationally expensive especially for large-scale power systems. Current approaches have a worst case computational complexity of $O(MN^3)$ ($M$ is the number of lines and $N$ is the number of buses in the system). Motivated by this, we proposed an algorithm based on unbalanced-constrained partitioning and developed a public domain tool  pro-PART that is: scalable, efficient and simple to implement. For example, the average CPU runtime is less than 0.1 s and 1.5 s for systems with 2831 buses (large-scale) and 43,501 buses ( very large-scale) respectively. We are currently working on extensions of this approach to identify a sequence of contingencies that may culminate in a blackout.

Cristinel Ababei and Rajesh Kavasseri,  Efficient Extreme Event Screening for Power Systems Using Constrained and Unbalanced Partitioning,  Proc. IEEE PES General Meeting, Minneapolis, MN, July 2010.

Voltage Stability: Grobner bases techniques:

The solution to the power flow equations (PFE) is fundamental and indispensable in power systems analysis. In contrast to numerical approaches to  voltage stability analysis, we were motivated to examine the use of symbolic techniques rooted in algebraic-geometry which can provide analytical information. Expressed in cartesian coordinates, the PFEs can be viewed as a system of polynomials which can be reduced using Gr\"{o}bner bases via  Buchberger's algorithm and solved successively (similar to Gaussian elimination). This formulation allows the determination of an explicit polynomial relation between the bus voltage components and the real/reactive loadings at that bus.  Using these relations: (i) the sensitivity of the bus voltage (to the real/reactive loadings) can be analytically expressed as rational functions and (ii) the {\em PV}, {\em QV} curves up to the point of collapse can be determined without resorting to repeated power flow calculations.  Incidentally,  {\em all} the solutions to the PFEs can be computed with this approach.  While the explicit determination of voltage sensitivities is a distinct advantage, the explosive  computational complexity limits this application to relatively small systems. This project was supported by NSF.

Rajesh Kavasseri and P. Nag, An Algebraic Geometric Approach to Analyze Static Voltage Collapse in a Simple Power System Model,   Proc. NPSC 2008, IIT Bombay, Mumbai, India.

Research Grants

1. John Deere Power Electronics Laboratory: [Jan 10 - Jan 12, $50,000] - John Deere 2. Control of Wind Generation for Inter-Area Oscillation Damping [NSF :$240,001 Aug 09 - June 12]
3. Static Voltage Stability Analysis using Grobner Basis Techniques [NSF : $75,357, Nov 08 - Nov 09] Abstracts of recent grants: Control of Wind Generation for Inter-Area Oscillation Damping [NSF :$240,001 Aug 09 - June 12]

The objective of this research is to improve the damping of inter-area oscillations in power systems by integrating damping controllers in grid-connected doubly-fed induction-generator-based wind farms. The approach is to employ two rotor control loops that allow independent modulation of active and reactive powers while providing damping benefits. This project addresses the problem of stability enhancements in power systems, given the increasing presence of and unique challenges in wind farms. The focus lies in developing robust damping controllers through a novel concept of real/reactive power modulation in wind farms to help mitigate instability concerns in the overall interconnected power system. The project will also help convey the benign effects of stability enhancements if grid interconnected systems are equipped with such controllers. The project will help reduce some of the barriers to grid integration of wind farms. If successful, the research will facilitate penetration of large scale wind power into the existing grid. Increased integration of wind resources will benefit society by reducing fossil fuel dependence on electricity generation and thus help build a sustainable energy infrastructure. This project will help resolve some of the skepticism surrounding the stability of grid interconnected power systems. Overall, the activities will help promote and develop wind resources in the midwest region and the nation at large.

Static Voltage Stability Analysis using Grobner Basis Techniques

The phenomenon of voltage (in)stability has been identified as a significant threat to power system security and reliability. Previous research efforts to study voltage stability have been based on numerical techniques. While such techniques can be efficiently implemented on large scale power systems, they yield little analytical information. On the other hand, symbolic algebraic-geometric based methods, while capable of yielding explicit analytical information pertaining to bus voltage and load sensitivities, are limited to very small systems because of their large computational complexity. This effort addresses the scalability issue by adopting a mixed symbolic/numerical approach exploiting the strengths of both conventional power-flow based and symbolic algebraic/geometric techniques to extend static voltage stability analysis on larger power systems. The objective is to obtain local symbolic sensitivities of bus voltage and loads. These can be used in the design of VAR support devices at such buses. The investigation will further focus on the identification of system conditions under which the resulting parameterized power flow equations can always be reduced to triangular form using Gröbner basis (GB) reduction.

Abstracts of selected publications (based on research areas)

Doubly Fed Induction Generators (DFIG) integrated operation of power systems

Modeling of DFIG-based Wind Farms for SSR Analysis, IEEE Trans. on Power Delivery 25(4), pp: 2073-2082, Oct 2010.
Lingling Fan, Rajesh G. Kavasseri, Z. Miao and Chanxia Zhu

This paper conducts an analysis of subsynchronous resonance (SSR) phenomena in doubly-fed induction generator (DFIG)-based wind farms interconnected with series compensated networks. A dynamic model is developed to analyze the induction generator effect (IGE) and torsional interaction (TI) in such systems. A test system derived from the IEEE first benchmark model is considered for the analysis. The effect of two factors namely: 1) series compensation level and 2) wind speed on the IGE and TI are studied. In addition, impact of the inner current converter controller parameters and turbine parameters on SSR is also addressed. Small signal (eigenvalue) analysis is conducted to assess the damping of network and torsional modes followed by dynamic (time domain) simulations. The major contribution of this paper is the analytical investigation on SSR phenomena presented in DFIG-based wind farms interconnected with series compensated networks. The paper clearly demonstrates that IGE instead of TI is the major reason for SSR in such systems.

Harmonic Analysis of a DFIG for Wind Energy Conversion System, IEEE Trans. on Energy Conversion, 25(1), March 2010, pp: 181-190.
Lingling Fan, S. Yuvarajan and Rajesh G. Kavasseri

This paper develops a framework for analysis of harmonics in a doubly fed induction generator (DFIG) caused by nonsinusoidal conditions in rotor and unbalance in stator. Nonsinusoidal rotor voltages are decomposed into harmonic components and their corresponding sequences are identified. Induced harmonics in stator are analyzed and computed, from which the torques produced by these interactions between stator and rotor harmonic components can be found. During unbalanced stator conditions, symmetric component theory is applied to the stator voltage to get positive-, negative-, and zero-sequence components of stator and rotor currents. The steady-state negative-sequence equivalent circuit for a DFIG is derived based on the reference frame theory. Harmonic currents in the rotor are computed based on the sequence circuits. In both scenarios, the harmonic components of the electromagnetic torque are calculated from the interactions of the harmonic components of the stator and rotor currents. Three case studies are considered, namely: 1) nonsinusoidal rotor injection; 2) an isolated unbalanced stator load scenario; and 3) unbalanced grid-connected operation. The analysis is verified with results from numerical simulations in Matlab/Simulink. For illustration, the second case is verified using experiments. The simulation results and experimental results agree well with the results from analysis.

Microgrids

Reactive Power Management of a DFIG Wind System in Microgrids Based on Voltage Sensitivity Analysis,  IEEE Transactions on Sustainable Energy, 2(4), Oct 2011, pp: 451-458.
Rasool Aghatehrani and R. Kavasseri

This paper addresses the problem of voltage regulation in microgrids that include doubly fed induction generator (DFIG)-based wind generation. Due to significant line resistances in microgrids, active power variations produced by wind turbines can lead to significant fluctuations in voltage magnitudes. This paper proposes a voltage sensitivity analysis-based scheme to achieve voltage regulation at a target bus in such microgrids. The target voltage can be of an important central bus, or a bus with sensitive voltage loads. The method is local and can be implemented in the absence of a widespread communication system or remote measurements. The performance of the method is illustrated on the IEEE-13 bus distribution network. Dynamic models are considered for the DFIG, converters, and internal controllers along with their operational limits. Stochastic fluctuations in wind speed are modeled with NREL Turbsim while accounting for tower shadow and wind shear. Dynamic simulations (in PSCAD/EMTDC) are presented to assess the voltage regulation characteristics under different load conditions and network contingencies.

Sliding Mode Control Approach for Voltage Regulation in Microgrids with DFIG Based Wind Generation , Proc. PES GM 2011, July 24-29, Detroit, MI.
Rasool Aghatehrani and R. Kavasseri

This paper presents a direct torque and reactive power control method which addresses the problem of voltage regulation in microgrids including doubly fed induction generator (DFIG) based wind generation. Due to significant line resistances in a microgrid, active power variations produced by wind turbines can lead to significant fluctuations in voltage magnitudes and results in power quality problems. This paper uses a nonlinear sliding mode control scheme to directly control torque and reactive power of a DFIG system. The control system adjusts the reactive power of DFIG to achieve voltage quality improvement in the important central bus of a microgrid. There is no decoupled proportional-integral (PI) control based method, therefore the control system is not highly dependent to the accuracy of the system parameters. Also, the method is local and can be implemented in the absence of a widespread communication system or remote measurement. The performance of the method is illustrated on the IEEE 13 bus distribution network. Dynamic models are considered for the DFIG, converters and internal controllers along with their operational limits. Stochastic fluctuations in wind speed are modeled with NREL TurbSim while accounting for the tower shadow and wind shear. Dynamic simulations are presented to assess the voltage fluctuation compensation and control system robustness.

Power Smoothing of the DFIG Wind Turbine Using a Small Energy Storage Device, Proc. PES GM 2010, July 25-29, Minneapolis, MN.
Rasool Aghatehrani, R. Kavasseri and R. Thapa

The active power produced by wind generators is subject to fluctuations due to the stochastic nature of wind. Depending upon the size of the wind farm and the network to which it is connected, active power variations may result in frequency deviations. This can trigger frequency protection devices and lead to undesirable unit trippings. This paper proposes the addition of a small supercapacitor at the DC link in the power converted of a doubly fed induction generator (DFIG). Based on this, a new method is proposed which simultaneously balances the MPPT as well as output power smoothing objectives. Frequency variations in the range of 0.1-1 Hz are investigated considering variations in wind speed, tower shadow and wind shear effects. Numerical simulations are carried out in PSCAD/EMTDC to illustrate the effectiveness of the proposed method in limiting frequency deviations.

Phasor measurement unit (PMU) applications to power systems

Joint Placement of Phasor and Power Flow Measurements for Observability of Power Systems, IEEE Transactions on Power Systems, 26(4), Nov 2011, pp: 1929-1936.
Rajesh G. Kavasseri and S. K. Srinivasan.

We consider the problem of joint optimal placement of phasor measurement units (PMU) and conventional measurements to ensure full observability in power systems. The formulation is initially posed as a nonlinear integer programming problem and then transformed in to an equivalent integer linear programming (ILP) problem by introducing auxiliary variables and constraints. The resulting ILP problem is solved for the optimal solution on IEEE 14-, 57-, and 118-bus systems considering zero-injection buses. To extend the formulation to large-scale systems, two heuristics are proposed where the nonlinear problem is decomposed into two separate problems of lesser complexity. The heuristics are evaluated on standard IEEE test cases and a large 2383-bus Polish system. The heuristics yield solutions close to optimal (difference of 1 PMU) solutions on standard IEEE systems, while substantially reducing problem complexity and run time. The placement results obtained with the proposed formulation require fewer PMUs for observability compared to systems with fixed locations of conventional measurements. The results thus potentially provide a more economical solution to system observability compared to those obtained solely with PMU placement.

Joint Placement of Phasor and Conventional Power Flow Measurements for Fault Observability of Power Systems", IET Transactions on Generation, Transmission and Distribution, 5(10), Oct 2011, pp: 1019-1024.
Rajesh G. Kavasseri and S. K. Srinivasan.

The authors consider the problem of joint optimal placement of phasor measurement units (PMUs) and conventional power flow measurements to ensure observability under faulted conditions in power systems. The formulation is initially posed as a non-linear integer programming problem and then transformed into an equivalent integer linear programming (ILP) problem through boolean implications. The resulting ILP problem is solved for the optimal solution on IEEE 14, 30, 57 and 118 bus systems and a large 2383 bus Polish system. The placement results obtained with the proposed formulation require fewer PMUs for fault observability compared with systems with fixed locations of conventional measurements. The results thus potentially provide a more economical solution to observability under faults compared with those obtained solely with PMU placement.

Identification of System Wide Disturbances Using Synchronized Phasor Data and Ellipsoid Method, Proc. IEEE Power Engineering Society General Meeting 2008, Pittsburgh, PA
L. Fan, Rajesh Kavasseri, Zhixin Miao, Dale Osborn, Terry Bilke

With Phasor Measurement Units (PMU) installed in power systems, synchronized measurements are now available in real time. These global measurements can be utilized to develop real time visualization and system monitoring tools. The characteristic ellipsoid (or minimum volume enclosing ellipsoid (MVEE)) method is one such recently proposed tool for identification of system disturbances.This paper examines: (i) the effectiveness of different input signals and (ii) the attributes (volume, orientation and position) of the ellipsoid that are most sensitive in detecting a system wide disturbance. Specifically, we consider two Eastern interconnection events namely: (a) a frequency deviation event arising from a substantial loss of generation and (b) an angle deviation transient. Real time system wide PMU data corresponding to (i) bus frequencies (ii) voltage magnitudes and (iii) phase angles are considered as inputs to the MVEE algorithm and the sensitivities of the ellipsoid attributes are studied for these inputs for the two disturbances. From the study, the most appropriate (input signal, attribute) pair is identified to detect a given system disturbance. This preliminary study can be potentially useful in designing a dashboard to enhance real-time wide area situational awareness of the power grid.

Power Systems Reconfiguration

Efficient Network Reconfiguration using minimum cost maximum flow based branch exchanges and random walks based loss estimations, IEEE Trans. on Power Systems, 26(1), pp: 30-37, Feb 2011.
Cristinel Ababei and Rajesh Kavasseri.

Abstract: The efficiency of network reconfiguration depends on both the efficiency of the loss estimation technique and the efficiency of the reconfiguration approach itself. We propose two novel algorithmic techniques for speeding-up the computational runtime of both problems. First, we propose an efficient heuristic algorithm to solve the distribution network reconfiguration problem for loss reduction. We formulate the problem of finding incremental branch exchanges as a minimum cost maximum flow problem. This approach finds the best set of concurrent branch exchanges yielding larger loss reduction with fewer iterations, hence significantly reducing the computational runtime. Second, we propose an efficient random walks based technique for the loss estimation in radial distribution systems. The novelty of this approach lies in its property of localizing the computation. Therefore, bus voltage magnitude updates can be calculated in much shorter computational runtimes in scenarios where the distribution system undergoes isolated topological changes, such as in the case of network reconfiguration. Experiments on distribution systems with sizes of up to 10476 buses demonstrate that the proposed techniques can achieve computational runtimes shorter with up to 7.78× and with similar or better loss reduction compared to the Baran’s reconfiguration technique.

Speeding-up Network Reconfiguration by Minimum Cost Maximum Flow Based Branch Exchanges, Proc. IEEE PES Transmission and Distribution Conference and Exposition, New Orleans, LA, Apr. 2010
Cristinel Ababei and Rajesh Kavasseri.

We propose a novel and efficient heuristic algorithm for solving the distribution network reconfiguration problem for loss reduction. We formulate the problem of finding incremental branch exchanges as a minimum cost maximum flow (MCMF) problem. This novel approach finds the best set of concurrent branch exchanges during each iteration of the algorithm and leads to larger loss reductions and a reduced number of iterations, hence significantly reducing the computational runtime. Experiments using distribution systems with sizes of up to 10476 buses demonstrate that the proposed technique leads to an average speed-up of 2.3× with similar or better solution quality compared to the Baran’s reconfiguration technique.

Grobner bases

An Algebraic Geometric Approach to Analyze Static Voltage Collapse in a Simple Power System Model,  Proc. National Power Systems Conference (NPSC) Dec 2008, IIT Bombay, Mumbai, India.
Rajesh Kavasseri and P. Nag

This paper presents an algebraic geometric method to analyze static voltage collapse in a simple power system model. The method is based on computing a lexicographic ({\em lex}) ordered Gr\"{o}bner basis for the ideal generated by the parameterized loadflow equations (LFEs). Computing the solutions to the LFEs is then equivalent to computing the algebraic variety corresponding to  this ideal. Incidentally, this method allows the determination of {\em all} the solutions to the set of LFEs. The formulation also allows the determination of an explicit polynomial relation between the bus voltage components and the real/reactive loadings
at that bus. Using this relation, we show that (i) the sensitivity of the bus voltage (to the real/reactive loadings) can be analytically expressed as rational functions and (ii) the {\em PV}, {\em QV} curves up to the point of collapse can be determine without resorting to repeated load-flow calculations. The proposed approach is exemplified on a simple three bus power system along with a discussion on its limitations.

A Computational Algebraic Geometry Based Global Optimization Technique to Address Economic Dispatch, Proc. IEEE Power Engineering Society, General Meeting Tampa, FL (2007).
Rajesh Kavasseri and P. Nag

In algebraic geometry, the concept of Gr¨obner basis allows a systematic study of the solution of a system of polynomial equations. This concept can be applied to find the global (and all local optima) optimum of a nonlinear, not necessarily convex function, the only restriction being that the objective function be polynomial. The method is based on computing a lexicographic (lex) ordered Gr¨obner basis for the ideal generated by the first order necessary conditions defined by the Lagrangian. Computing the optimal solution is then equivalent to computing the variety corresponding to this ideal. By virtue of the (lex) ordering, the system is transformed in to set of polynomials which can be solved successively to obtain the solutions. Here, we illustrate the application of the method on a non-convex function and identify the global optimum from the set of fifteen stationary points (6 local minima, 2 local maxima and 7 saddles). Then we apply the method to solve the classical economic dispatch problem including a combined cycle heat plant (CCHP) whose piecewise linear cost function is approximated by a smooth tenth order polynomial. Interestingly, the the method yields two possible solutions from which the least cost solution can be picked. While the work reported here is only preliminary, we find the results encouraging and hope that the method will find applicability in identifying the global optimum of non-convex power systems optimization problems.

Time series analysis

Day Ahead Wind Speed Forecasting using f-ARIMA models, Renewable Energy 34(5), May 2009, pp: 1388-1393
Rajesh G. Kavasseri and K. Seetharaman

With the integration of wind energy in to electricity grids, it is becoming increasingly important to obtain accurate wind speed/power forecasts. Accurate wind speed forecasts are necessary to schedule dispatchable generation and tariffs in the day-ahead electricity market. This paper examines the use of {\em fractional}-ARIMA, or $f$-ARIMA models to model, and forecast wind speeds. The models were applied to wind speed records obtained from four potential wind generation sites in North Dakota. Results indicate that significant improvements in forecasting accuracy are obtained with the proposed models compared to the persistence forecast.

Evidence of Crossover Phenomena in Wind Speed Data  IEEE Transactions on Circuits and Systems : Part I : Fundamental Theory and Applications. Vol.51 (11), pp : 2255-2262, November 2004
Rajesh G. Kavasseri and R. Nagarajan

In this report, a systematic analysis of hourly wind speed data obtained from three potential wind gen- eration sites (in North Dakota) is analyzed. The power spectra of the data exhibited a power-law decay characteristic of 1/f processes with possible long-range correlations. Conventional analysis using Hurst exponent estimators proved to be inconclusive. Subsequent analysis using detrended fluctuation analysis (DFA) revealed a crossover in the scaling exponent. At short time scales, a scaling exponent of ~1.4 indicated that the data resembled Brownian noise, whereas for larger time scales the data exhibited long range correlations (  0.7). The scaling exponents obtained were similar across the three locations. Our findings suggest the possibility of multiple scaling exponents characteristic of multifractal signals.

Nonlinear dynamics

Analysis of subharmonic oscillations in a ferroresonant circuit, International Journal of Electrical Power & Energy Systems Volume 28, Issue 3, March 2006, pp: 207-214
Rajesh G. Kavasseri

Ferroresonance is a nonlinear oscillatory phenomenon that occurs in capacitively coupled transformers or reactors under certain conditions. In this paper, an averaging method is utilized to compute the domain in 2D parameter space where subharmonic (period-3) ferroresonant oscillations could persist. The accuracy of the analytical results is verified using numerical simulations and the power spectral density. It is shown that the proposed method yields a quick means to determine (i) the proximity to initiation of subharmonic resonance and (ii) the effect of core loss on the domains of subharmonic oscillations.

Delay Induced Oscillations in a Fundamental Power System Model", "Nonlinear Phenomena in Complex Systems",. Vol.8, No.1 pp : 62-67, 2005
Rajesh G. Kavasseri

In this paper, we study the dynamics and stability of a fundamental power system model when a time delay is imposed on the excitation of the generator. It is observed that sustained oscillations can arise in an otherwise stable power system through a delay induced Andronov-Hopf bifurcation. Numerical simulations are conducted to explore the dynamics of the time delayed system after the bifurcation which indicate period doublings culminating in a strange attractor.

Bifurcation Analysis of a three node power system with detailed models, International Journal of Electrical Power and Energy Systems,21 (5), 2000, pp : 375-393
Rajesh G. Kavasseri (as K. G. Rajesh) and K. R. Padiyar

This article presents a comprehensive study of bifurcations in a realistic power system model. The two-axis model for the generator with the field winding on the d-axis and a damper winding on the q-axis (1.1 model), along with the excitation system is considered to represent the dynamics of the generator. The load is described by a dynamic load model. The dynamics of the resulting system is studied using (i) input power to the generator, (ii) both active and reactive power demand at the load bus, (iii) reference voltage to the AVR as bifurcation parameters. It is found that model refinement results in significant qualitative changes in the system behaviour. Quasiperiodic behaviour is shown to result from a torus bifurcation. The system also exhibits chaotic behaviour resulting from cascades of period-doubling bifurcations. Detailed numerical simulations are presented to illustrate the types of dynamic behaviour and attractors encountered.

Analysis of Bifurcations in a Power System Model with Excitation Limits,  International Journal of Bifurcations and Chaos, Vol.11 (9), 2001, pp : 2509 - 2517
Rajesh G. Kavasseri and K. R. Padiyar

This paper studies bifurcations in a three node power system when excitation limits are considered. This is done by approximating the limiter by a smooth function to facilitate bifurcation analysis. Spectacular qualitative changes in the system behavior induced by the limiter are illustrated by two case studies. Period doubling bifurcations and multiple attractors are shown to result due to the limiter. Detailed numerical simulations are presented to verify the results and illustrate the nature of the attractors and solutions involved.

Miscellaneous Forays (Pseudorandom sequences, (in)security,.........)

Secure pseudo-random bit sequence generation using coupled linear congruential generators", Proc. IEEE International Symposium on Circuits and Systems (ISCAS), 18-21 May 2008, Seattle, WA, pp: 2929 - 2932
R. S. Katti and Rajesh G. Kavasseri

Linear congruential generators (LCGs) of the form xi+1 = axi + b(mod m), have been used to generate pseudorandom numbers. However these generators have been known to be insecure. This implies that if a small sequence of numbers generated by an LCG is known then it is possible to predict the remaining numbers in the sequence that will be generated. We propose to generate a secure pseudorandom bit sequence by coupling two LCGs as follows. A 1 is output if the first LCG produces an output that is greater than the output of the second LCG and a 0 is output otherwise. The security of this sequence is shown by demonstrating the diculty of obtaining the initial conditions of the two LCGs given the pseudorandom bit sequence output. If the modulus m is a power of 2 then efficient circuits can be designed for the proposed generators.

Pseudorandom Bit Generation using Coupled Congruential Generators, IEEE Trans. on Circuits and Systems II, 25(1), March 2010, pp: 203-207
R. S. Katti, Rajesh G. Kavasseri, and V. Sai

In this paper we propose the generation of a pseudorandom bit sequence (PRBS) using a comparative linear congruential generator (CLCG) as follows. A bit “1” is output if the first LCG produces an output that is greater than the output of the second LCG and a bit “0” is output otherwise. Breaking this scheme would require one to obtain the seeds of the two independent generators, given the bits of the output bit sequence. We prove that the problem of uniquely determining the seeds for the CLCG requires (i) a knowledge of at least log2 m2 (m being the LCG modulus) bits of the output sequence and (ii) the solution of at least log2 m2 inequalities where each inequality (dictated by the output bit observed) is applied over positive integers. Computationally, we show that this task is exponential in n (where n = log2 m is the number of bits in m) with complexity O(22n). The quality of the PRBS so obtained is assessed by performing a suite of statistical tests (NIST 800-22) recommended by NIST. We observe that a variant of our generator that uses two CLCGs (called dual CLCG), pass all the NIST pseudorandomness tests
with a high degree of consistency.

Nonce Generation for the Digital Signature Standard, International Journal of Network Security, 11(1), July 2010, pp: 23-32
R. S. Katti and Rajesh G. Kavasseri

The Digital Signature Algorithm is the underlying algorithm to form a signature in the Digital Signature Standard. The Digital Signature Algorithm uses a new random number (or nonce) each time a signature is generated for a message. In this paper, we present a linear congruential generator (LCG) based approach to generate nonces for the digital signature standard. Linear congruential generators have been shown to be insecure for nonce generation. If two message-signature pairs are known along with the parameters of the LCG used to generate the nonce then the private key in the signature scheme can be found, with high probability, by solving three congruences over di®erent moduli. We
use a comparison of the output of two LCGs to generate the nonces and show that our approach is secure. We also show that coupled multiple recursive generators which are similar to LCGs are also safe for nonce generation. Congruences can no longer be set up to solve for the private key. The advantage of LCG based schemes for pseudo-random number generation is their efficiency.