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.

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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.

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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.

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Nonlinear dynamics



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 diculty 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.

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Graduate students

Current students

1. Arshad Chaudhry (Ph.D.)
2. Druhin Bala (M.S.)
3. Anushree Sharma (M.S.)

Past students

Student	Degree (Graduation)	Thesis	Position
Rasool Aghatehrani	Ph.D. (2011)	Control measures for ancillary services in microgrids with renewable energy resources	Systems Engineer, SunEdison, Belmont, CA
Ravi Thapa	M.S. (2011)	Damping inter-area oscillations in power systems with DFIGs	Engineer, Cummins, Minneapolis
Gregory Owen	M.S. (2009)	On the impact of CFLs on electrical distribution networks	Engineer (PS protection), Sebesta Blomberg, Minneapolis
Krithika Seetharaman	M.S. (2005)	Wind speed forecasting by f-ARIMA method	Engineer, Sunnyvale, CA
Prakash Ranganathan	M.S. (2004)	A method for flicker severity evaluation using the Hadmard transform	Assistant Professor (Electrical Engr.), Univ of North Dakota, Grand Forks, ND.