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A Tracing-based Realistic State Space Selection Method for Composite Power System Reliability Assessment in the Restructured Scenario
A. K. Verma, Senior Member, IEEE, and V. Vijay Venu, Student Member, IEEE.
Abstract-- Electric power industry deregulation has brought about the unbundling of generation, transmission and distribution services and as such, new techniques for reliability assessment are being developed to account for the consequent structural changes in the restructured environment through direct analytical techniques or stochastic simulation. To this end, reliability equivalent techniques have been proposed in recent literature and are continuously being improvised upon, especially for the multi-bilateral contracts market structure. Power flow tracing, a potential tool that has so far only been effectively employed in transmission pricing in the open access environment, is deemed to be equally effective in capturing the effect of structural and economic alterations for the purpose of reliability evaluation in the liberalized regime. This paper elaborates on the idea that when used in tandem with reliability equivalent methods, tracing is bound to improve the accuracy of the indices in vogue. The contribution of individual generators and loads to line flows is obtained using a graph theoretic approach, relying on the proportional sharing principle. This information is then proposed to be used in the transmission line Failure Modes and Effects Analysis (FMEA) phase of the established procedure of reliability network equivalents. Comparisons are drawn to highlight the computational as well as accuracy benefits accrued in doing so. Index Terms-- Bilateral contracts, composite power system reliability, deregulation, power flow tracing, reliability equivalents.
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I. INTRODUCTION
HE ramifications of the trend of deregulation in power systems have been quite pronounced all over the world. The consequent structural changes, which further the operational transmutations in the ensuing liberalization, have put several pressing issues pertaining to power system expansion planning and reliability related studies in perspective. With the increase in uncertainties more than ever in the new regime, the focus is on probabilistic tools which
A. K. Verma is a professor with the Reliability Engineering Group, Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai – 400076, India. (e-mail: akv@ee.iitb.ac.in). V. Vijay Venu is a doctoral candidate with the Reliability Engineering Group, Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai – 400076, India. (e-mail: vvv@ee.iitb.ac.in).
capture the effect of stochasticity inherent in the operation of power systems. Newer reliability modeling paradigms suitable for the changing scenario are on the anvil. Centralized operations that aid in easier decision-making at all levels are no more relevant in the deregulated environment. Cost-based mechanisms of vertically integrated utilities have transitioned to price-based mechanisms in horizontally operated power systems. Effective transmission management now vests in the hands of the Independent System Operators (ISOs) irrespective of the market design – PoolCo model, Bilateral/multilateral contractual model or a Hybrid model. With the advent of power flow tracing schemes, a reasonable basis for transmission pricing and loss allocation in the open access environment has been evolved, also including means to address congestion management issues. This paper champions the idea that tracing can prove to be an indispensable tool in the era of liberalization even in the sphere of power system reliability studies. Price spikes and volatility in the spot market drive riskaverse customers to indulge in bilateral contracts. Customersay in relation to reliability requirements can be easily incorporated in the operational aspects of the contractual market. Reliability modeling through equivalent components of the composite power system network [1-2] makes this situation feasible. Implementation of non-uniform reliability based on demand-side management oriented participation, a no-go in traditional power systems, is now a concrete possibility. Customers get to choose power generation vendors on the basis of their quantified credentials by way of estimated load point adequacy indices – Loss of Load Probability (LOLP) and Expected Energy Not Served (EENS) [1-10]. The reliability contribution of all the market players can be calculated and presented to customers, who can then exercise their options judiciously. The inability of a Genco to honor a contractual agreement either partially or in totality due to unforeseen circumstances (e.g. random failures), may or may not entail the ISO to make provisions for backup supply. Hence, Gencos usually involve in prior reserve agreements with other competing parties to strengthen their reliability claims. Incorporation of reserve
?2008 IEEE.
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agreements slightly modifies the modeling strategy of equivalents [4, 6]. The well-being framework, which implants deterministic considerations into the probabilistic analysis for a more meaningful and comprehensive interpretation of the power system adequacy indices, can further be made use of in arriving at appropriate criteria to determine the extent of spinning reserve requirements the Gencos would have to make arrangements for [5]. Complex real time operational features in the reliability modeling can be accounted for by utilizing Monte Carlo simulation techniques alongside the network equivalents [10]. Universal Generating Functions (UGFs) of the reliability equivalents can also be developed to aid in optimal reserve management [9]. Though considerable effort has been expended on the issues of reliability modeling for a Bilateral market structure, thorough models for PoolCo and Hybrid market structures are yet to be developed from their existing nascency. All the preceding mentioned applications of equivalents can benefit from the implications made in this paper, with respect to the adoption of tracing as a tool to alter some of the reliability modeling aspects in a Bilateral market structure. Power flow tracing methods basically rely on the proportional sharing principle [11-13]. Bialek [11] adopts a simultaneous equations approach involving a matrix inversion mode, which however proves to be computationally burdensome. Topological generation distribution factors are calculated, which indicate the portion of generation in debt to a generator that flows in a line. The upstream-looking algorithm analyses nodal inflows while its dual, downstreamlooking algorithm, analyses the nodal outflows. The upstreamlooking algorithm applied to the gross flows determines how the power output from each of the generators would be distributed between the loads. The downstream-looking algorithm applied to the net flows determines how the demand of each of the loads would be distributed between individual generators. Kirschen et al. [12] introduced the concept of ‘common’, a set of contiguous buses supplied by the same generator, with one or more external branches connecting the common constituting ‘links’. The results include the contribution of each generator to each common, thereby pointing to how much each generator contributes to each load and the proportion of use of each branch that can be apportioned to each generator. Graph theoretic approach based tracing methodology as propounded by Wu et al. [13], involving a step by step node elimination technique is made use of in this paper. This method is applicable only in networks where circular flows do not exist, which otherwise create the problem of convergence. In the event that circulating power exists, an OPF approach [14] is used to eliminate it, a sequential quadratic programming being used for the OPF solution.
II. METHODOLOGY A. Reliability Equivalent Methods A generation serving entity (Genco), in general, has the ownership of several individual generating units. It is a service provider for real/reactive power generation and/or reserve needs. It is represented as an equivalent multi-state generation provider (EMGP) [1]. The reliability model of an EMGP is an Available Capacity Probability Table (ACPT), which indicates all possible contingency states in which the Genco can reside alongside the respective occurrence probabilities. To obtain this, contingency analysis, based on the unit addition algorithm [16], is made use of for relatively smaller Gencos. Where the number of units is higher, a Conditional Probability Capacity Outage Probability Table (CPCOPT) method [15] can be employed to ease the computational effort. For the case of an EMGP ‘x’, in a state i, where there are ‘y’ units in service and ‘z’ units out of service:
Pxi =∏ A j *∏ U k
j=1 k=1 y z
(1)
Frequency of occurrence of a state can be obtained as: Fxi = Pxi * λxi where
λ xi =
(2)
∑ ∑?
y
λj+
z
k
(3)
j=1
k=1
Aj and λj are the unavailability and the failure rate of the unit indexed by j, respectively; Uk and ? k are the unavailability and the repair rate of the unit indexed by k, respectively and λxi is the net departure rate from state i. Energy is delivered from an EMGP to the customers, who are represented as Equivalent Bulk Load Points (EBLPs) through the transmission network, which is represented as an Equivalent Multi-state Transmission Provider (EMTP) [1,2]. The reliability model of an EMTP is a Deliverable generating Capacity Probability Table (DCPT) [3,6], whose defining entries (on the lines of (1), (2) and (3)) are obtained using the FMEA, also known as the contingency enumeration approach. For every selected contingency state of the transmission network, the routine check for any constraint violations on the basis of the load flow solution obtained for the resulting network configuration is carried out. Corrective actions are employed to alleviate the voltage and the line-overload violations (steady state security criteria) if any, firstly through generation rescheduling, phase shifters, transformer tap setting adjustments or reactive power injection. Controlled load curtailment is resorted to only in the case of inevitability. The characterizing parameters of the DCPT are accumulated till all the ‘required’ contingency simulations are performed. Once the equivalent models as explained above are quantified, the load point indices - LOLP and EENS [3,6] can be obtained as:
LOLPk =
j∈LC
∑P
j
(4)
3
EENSk =8760
j∈LC
∑ PL
j
kj
(MWh/Yr)
(5)
where Pj is the state probability of outage event j; Lkj is the load curtailed at bus k due to contingency j, and LC is the set of contingencies leading to load curtailment. A summary of the general procedure for reliability assessment using network equivalents [3] is as follows: 1. Identify the EMGPs and EMTPs. 2. Obtain the modeling parameters of each EMGP, i.e. ACPT. 3. Obtain the modeling parameters of each EMTP, i.e. DCPT. 4. Convolve a. ACPT of an EMGP with the load of EBLP in question. b. DCPT of an EMTP with the load of EBLP in question. 5. Calculate a. Load point indices caused by EMGP b. Load point indices caused by EMTP 6. The total LOLP and EENS of each EBLP can be estimated by adding the individual LOLP and EENS caused by the EMGP and the EMTP, respectively. Inclusion of reserve agreements between Gencos can be easily incorporated in the EMGP modeling, resulting in EMGPWR (Equivalent Multi-state Generation Provider With Reserve agreements). ACPTWR [6] is then obtained, additionally relying on the Equivalent Assisting Unit Approach [15]. In the aforementioned procedure, identification of the EMGPs is straightforward. In a contract between any unique EMGP and any unique EBLP, the EMTP is not unique. The prevalent practice is to include the whole of the transmission network in the modeling of EMTP. This results in the allocation of the same EMTP to every which pair of buyers and sellers of energy, a certain glaring drawback in the modeling. Once the feasibility study of bilateral transactions [17] is done to decide upon the finalization of contracts, a realistic option would be to take advantage of the might of power flow tracing methodology. B. Power Flow Tracing Wu et al. [13] in a ground breaking research presented a scheme with which power transfer allocation could be done in deregulated power systems, by making use of the proportional sharing principle, which assumes nodal inflows as being shared proportionally in nodal outflows. Graph theoretic approaches have been used to calculate the contributions of individual generators and loads to line flows, and the real power transfer between individual generators and loads that are significant to transmission open access. Based on ac load flow solution, this novel method can obtain the downstream and the upstream power flow tracing paths swiftly and calculate the contribution factors of generations and loads to the line flows efficiently. This method is suitable for both active and reactive power tracings in power systems. The application of the Algorithm [13] can be summarized qualitatively as briefly outlined in the following steps: 1). Determining Downstream Tracing Sequence and
Upstream Tracing Sequence: Downstream tracing sequence is the sequence of bus numbers starting from a pure source node to a pure sink node of the network. This is done by initially identifying the pure source node in the given network graph, then eliminating this node, with the consequent sub graph checked for the new pure source, making it the next bus in the sequence. This is repeated until all the buses in the network are accounted for. The upstream tracing sequence is similar to the procedure as mentioned above except that the starting point is a pure sink and a sequence is built by successively eliminating the resulting pure sinks of the corresponding sub graphs until all the buses are accounted for. 2). Determining Extraction Factor Matrix (A): The passing power at a bus is defined as the total power injected into the bus either by a generator at that bus or by a transmission line carrying power to the node. Out of this passing power, some fraction in turn is the outgoing flow over other transmission lines, while the remaining fraction is the outgoing power consumed at that node. Extraction Factor Matrix (A) is the collection of all such fractions. The row size is equal to the number of lines plus the number of loads, while the column size is equal to the number of buses. Each entry tells what fraction of the passing power at that bus is taken by which load or which line. 3). Determining Contribution Factor matrix (B): This matrix defines the contribution of power generation to the passing power of each bus. The number of rows of B is same as the number of buses, and the number of columns is equal to the number of generators. The matrices A and B can be readily calculated once the load flow results are available in the form of a directed graph. 4). Determining Generation Contribution Factors to Line Flows and Loads: The contribution factors of individual generators to the line flows and the loads are determined based on the matrices A and B as obtained in the steps 2 and 3. The product of these matrices is the Contribution Factor Matrix. These factors show in what proportion each load is being supplied by each generator, and in what proportion each line is carrying the power generated by each generator. 5). Determining Load Extraction Factors to Line Flows and Generators: The preceding four steps of the algorithm have to be repeated using the upstream sequence of buses to determine the extraction factors of individual loads to line flows and generators. C. Tracing and Equivalents in Tandem Assuming a two state model for a transmission line, the total number of possible states for a network with ‘n’ lines is 2n. Evaluating all possible contingencies becomes quite tedious in a practical power system. Precisely for this reason, in the evaluation of traditional power system adequacy indices, a basis is chosen to limit the assessment to credible contingencies, whose impact is pivotal. It can be safely assumed then that the impact of higher order contingencies is negligible. What constitutes the threshold of this ‘higher’ order has been the focus of several researchers.
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To limit the number of contingencies, fixed criteria such as the selection of single or double level contingencies and/or variable criteria such as frequency/probability cut-off limit and/or ranking cut-off limit are presently used [18]. Selection of an appropriate cut-off level is dictated by various factors such as the size of the system, the failure and repair rates of lines, the severity associated with an outage event, the purpose of the adequacy studies and the computation time required to evaluate each outage event [18]. Ranking of contingencies by an appropriate Performance Index (PI) is also a viable option. This selectively chooses a subset of outage states from the set of all credible contingency states. Since the transmission paths involved in the transfer of power from an EMGP to an EBLP can be authoritatively determined by employing a tracing tool, only those active lines of the transmission network pegged by the tool for a given bilateral transaction can be included in the modeling of the EMTP. This considerably reduces the state space involved, allowing for the evaluation of FMEA for all possible states (in case of lesser lines) or the further application of various contingency cut-off criteria as mentioned earlier to the filtered set (in case of large number of lines still to be considered). This not only reduces the computational burden, but also yields results that are optimistic, i.e. closer to reality. The contingency analysis now carried out for obtaining the DCPT corresponding to the EMTP in consideration will have a listing including only the requisite combinations of the transmission lines, making the subsequent calculations closer to the actual values of the indices. This is so because knowing how the generation in the contractual system is distributed among its participant loads and what share of the generation is carried through which lines would circumvent the approximations involved, which add to over redundancy in its implications. The EMTPs will vary from contract to contract, depending on the quantity of power involved and the existent multilateral deals among various parties. III.
RESULTS
proposed method are illustrated.
2*40 MW 1*20 MW 1*10 MW EMGP1 G1 1*40 MW 4*20 MW 2*5 MW G2
EMGP2
Bus1
L3
Bus2
BLP2 (20 MW) EMTP2
L1
L2 EBLP2
L4
BLP3 (85 MW)
Bus3 L5 L6
Bus4
BLP4 (40 MW)
EMTP3
Bus5 L7 EMTP4
EBLP3
Bus6 BLP5 (20 MW) BLP6 (20 MW) EMTP5 Equivalent EBLP4
EMTP6
EBLP5
EBLP6
Fig. 1. RBTS employed for deregulation studies. The identical parallel lines are lumped as L1 and L2.
Tables I through V constitute the power flow tracing solution. Load flow solution for the base case contingency enumeration (i.e. all components intact) of the equivalent RBTS is shown in Table I. Bus 1 is chosen as the slack bus.
TABLE I LINE FLOWS FOR THE BASE CASE OF RBTS Bus I 1 2 1 3 3 4 5 J 3 4 2 4 5 5 6 Line No. L1 L2 L3 L4 L5 L6 L7 R (p.u) 0.0171 0.057 0.0912 0.0228 0.0228 0.0228 0.0228 X (p.u) 0.09 0.3 0.48 0.12 0.12 0.12 0.12 B (p.u) 0.0424 0.1408 0.0564 0.0142 0.0142 0.0142 0.0142 Pij (MW) 98.27 71.63 -27.626 -5.71 17.314 22.982 20.097 Pji (MW) -97 -69 28.4 5.72 -17 -23 -20
An equivalent Roy Billinton Test System (RBTS) for deregulated studies is as shown in Fig. 1. The line and generation data are the same as that of RBTS. For the sake of convenience in the load flow/tracing tool employment, identical transmission lines between a pair of nodes are lumped and the standard RBTS line data is adjusted accordingly. The generating system is divided into two independent generating companies EMGP 1 and EMGP 2. Distribution systems/customers are represented by five EBLPs. The transmission system for each EBLP is represented by the corresponding EMTP. The total installed generating capacity is 240 MW. The system peak load is 185 MW. Under the existing methods, each of the EMTPs has the whole of the transmission network components. Employing the method suggested in this paper renders them different. For the sample case of a bilateral contract between EMGP at bus 2 and EBLP at bus 3, the significant advantages of the
Contribution of generation in loads through the downstream tracing algorithm for the base case of RBTS is detailed in Table II.
TABLE II DOWNSTREAM TRACING FOR THE BASECASE OF RBTS Load at Generation Bus 2 (MW) G1 G2 1.67E-16 20 Bus3 (MW) 57.695 27.305 Bus4 (MW) 9.16E-16 40 Bus5 (MW) 5.8375 14.163 Bus6 (MW) 5.8375 14.163 Load at Load at Load at Load at
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Table III shows the contribution of generation in loads through the upstream tracing algorithm for the base case of RBTS.
TABLE III UPSTREAM TRACING FOR THE BASECASE OF RBTS Load at Generation Bus 2 (MW) G1 G2 2.01E-15 20 Bus3 (MW) 58.69 28.524 Bus4 (MW) 2.01E-15 41.704 Bus5 (MW) 5.9628 14.85 Bus6 (MW) 5.9918 14.922 Load at Load at Load at Load at
is such that the share of generator 1 in it is 70.6 MW and that of generator 2 is 27.6 MW. Generator 1 provides 57.6 MW to the load of 85 MW at bus 3; generator 2 providing 27.3 MW. Line 3 has the generator 2 share of 28.4 MW flowing towards bus 1. In effect, the EMTP will consist of lines 1 and 3, as against the conventional procedure of including all the seven lines. Failure Modes Effect Analysis can be carried out using only these two lines in the contingency list. Thus, there is a significant reduction in the transmission system state space. The associated DCPT, which is to be convolved with the ACPT of the Genco in consideration, can be obtained without compromising on the accuracy, while simultaneously reducing the computational burden. IV. CONCLUSIONS Tracing can conclusively provide a fundamental basis for evolving a realistic transmission system state space selection criterion in power system reliability studies in the deregulated environment. However, deeper investigation is warranted for obtaining the quantitative indices of composite restructured power systems through the combination of network equivalents and tracing, where several load curtailment management issues during the contingency simulations are required to be addressed. The policies to be adopted for generation re-dispatch also need to be effectively attended to. Reserve management issues invariably figure in these decisions. The existing equivalent methods, in arriving at the values of indices such as LOLP and EENS of the load points, conveniently sidestep these issues by using a lot of approximations. The approach as suggested in this paper, a first of its kind, is expected to be another watershed in the emergence of bankable reliability procedures for the competitive markets all around the world. In the deregulated scenario, customer choices can be effectively incorporated into the reliability apportioning unlike in a vertically integrated environment where ‘uniform’ reliability is implemented irrespective of the customer choices. Reliability network equivalents in tandem with power flow tracing can be used to represent each market player and the obtained indices can be presented to the customer, who can then choose a generation provider depending upon his economic and reliability considerations. The price and reliability difference, inclusive and exclusive of reserve agreements, can be determined by using the reliability equivalent techniques, which information can then be used by the ISO to price reserve. There is bound to be significant reduction in the utilization of computational resources and considerable improvement in the accuracy of reliability indices, when information obtained from power flow tracing is embedded in the modeling aspects of EMTP. The reliability indices so obtained would be indicative of the realistic scenario.
Table IV gives details of the flow decomposition of generation in various lines using the downstream tracing algorithm for the base case of RBTS.
TABLE IV FLOW DECOMPOSITION FOR THE BASECASE OF RBTS (DOWNSTREAM TRACING) Line L1 L2 L3 L4 L5 L6 L7 G1 (MW) 70.644 5.97E-16 2.36E-16 1.31E-16 1.18E+01 5.26E-16 5.8658 G2 (MW) 27.626 71.63 2.84E+01 5.72 5.5619 2.30E+01 14.231
Table V gives details of the flow decomposition of generation in various lines using the upstream tracing algorithm for the base case of RBTS.
TABLE V FLOW DECOMPOSITION FOR THE BASECASE OF RBTS (UPSTREAM TRACING) Load at
Line
Load at Bus3 (MW) 80.256 4.7521 2.30E+01 4.74 8.62E-16 1.14E-15 1.00E-15
Load at Bus4 (MW) 1.76E-15 40 7.85E-16 1.04E-16 8.62E-16 1.14E-15 1.00E-15
Load at Bus5 (MW) 8.1539 11.946 2.33 0.48196 8.6002 1.14E+01 1.00E-15
Load at Bus6 (MW) 8.1935 12.004 2.34 0.4843 8.642 11.455 20
Bus 2 (MW) L1 L2 L3 L4 L5 L6 L7 1.76E-15 2.25E-15 7.85E-16 1.04E-16 8.62E-16 1.14E-15 1.00E-15
For the case of a bilateral contract between EMGP at bus 2 and EBLP at bus 3, the flow pattern as can be noted down from the above tables is as follows: The 98 MW flow in line 1
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V. REFERENCES
[1] P. Wang and R. Billinton, “Implementation of nonuniform reliability in a deregulated power market,” Proc. Canadian conference on electrical and computer engineering, Toronto, vol. 2, pp. 857-861, May 2001. [2] P. Wang, R. Billinton and L. Goel, “Unreliability cost assessment of an electric power system using a reliability network equivalent technique,” IEEE Trans. Power Syst., vol. 13, no. 3, pp. 549-556, Aug. 2002. [3] P. Wang and R. Billinton, “Reliability assessment of a restructured power system using reliability network equivalent techniques,” IEE Proc. – Gener. Transm. Distrib., vol. 150, no. 5, pp. 555-560, Sept. 2003. [4] P. Wang and L. Goel, “Reliability-based reserve management in a bilateral power market,” Electric Power Systems Research, vol. 67, no. 3, pp. 185189, Dec. 2003. [5] L. Goel, Z. Song and P. Wang, “Well-being analysis of spinning reserve in a bilateral power market,” Electric Power Systems Research, vol. 69, no. 1, pp. 37-42, April 2004. [6] P. Wang and R. Billinton, “Reliability assessment of a restructured power system considering the reserve agreements,” IEEE Trans. Power Syst., vol. 19, no. 2, pp. 972-978, May 2004. [7] L. Goel, P. A. Viswanath and P. Wang, “Montecarlo simulation-based reliability evaluation in a multi-bilateral contracts market,” IEE Proc. – Gener. Transm. Distrib., vol. 151, no. 6, pp. 728-734, Nov. 2004. [8] Y. Ding and P. Wang, “Reliability and price risk assessment of a restructured power system with hybrid market structure,” IEEE Trans. Power Syst., vol. 21, no. 1, pp. 108-116, Feb. 2006. [9] Y. Ding, P. Wang and A. Lisnianski, “Optimal reserve management for restructured power generating systems,” Reliability Engineering and System Safety, vol. 91, no. 7, pp 792-799, July 2006. [10] Y. Ding, P. Wang, L. Goel, R. Billinton and R. Karki, “Reliability assessment of restructured power systems using reliability network equivalent and pseudo-sequential simulation techniques,” Electric Power System Research, vol. 77, no. 12, pp. 1654-1664, Oct. 2007 [11] J. W. Bialek, “Tracing the flow of electricity,” IEE Proc. – Gener. Transm. Distrib., vol. 143, no. 4, pp. 313-320, July 1996. [12] D. Kirschen, R. Allan and G. Strbac, “Contribution of individual generators to loads and flows,” IEEE Trans. Power Syst., vol. 12, no. 1, pp. 52-60, Feb. 1997. [13] F. F. Wu, Y. Ni and P. Wei, “Power transfer allocation for open access using graph theory-fundamentals and applications in systems without loopflow,” IEEE Trans. Power Syst., vol. 15, no. 3, pp. 923-929, Aug. 2000. [14] P. Wei, Y. Ni and F. F. Wu, “Load flow tracing in power systems with circulating power,” Int. J. of Electrical Power and Energy Systems, vol. 24, no. 10, pp. 807-813, Dec. 2002. [15] A. Abdulwhab and R. Billinton, “Generating system wellbeing index evaluation,” Int. J. of Electrical Power and Energy Systems, vol. 26, no. 3, pp. 221-229, March 2004. [16] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, New York: Plenum, 1984. [17] G. Hamoud, “Feasibility assessment of simultaneous bilateral transactions in a deregulated environment,” IEEE Trans. Power Syst., vol. 15, no. 1, pp. 22-26, Feb. 2000. [18] R. Billinton, M. E. Khan and S. K. Agarwal, “Contingency cut-off criteria in transmission system adequacy assessment,” IEE Proc., vol. 136, pt. C, no. 4, pp. 215-221, July 1989.
ICQRIT 2006 and a patron of ICRESH 2005.He has authored a book on ‘Fuzzy Reliability Engineering:Concepts and Applications’ He is a Senior Member of IEEE and Life Fellow of IETE. His areas of research in Reliability Engineering are interdisciplinary applications in power systems, software engineering, computing and maintenance. V. Vijay Venu was born in Andhra Pradesh, India in 1980. He obtained his B.Tech. (EEE) in 2000 from JNTU College of Engineering, Hyderabad and M.Tech. (Reliability Engineering) in 2006 from Indian Institute of Technology Bombay, Mumbai. He is currently a Ph.d. candidate in the Interdisciplinary Programme in Reliability Engineering, Department of Electrical Engineering at IIT Bombay. His research interests are in the areas of power system reliability, planning, deregulation, maintenance engineering and probabilistic methods applied to systems reliability.
VI. BIOGRAPHIES
Ajit Kumar Verma, B. Tech (Hons) (EE, IIT Kharagpur), Ph.d.(Engg.) (IIT Kharagpur) has been with IIT Bombay as a faculty since 1988. He is currently a Professor in Reliability Engineering, Department of Electrical Engineering at IIT Bombay. He has over 130 research papers to his credit and has supervised eighteen Ph.d. theses and seventy Masters theses at IIT Bombay. He has been a Guest Editor of Special Issues on Quality Management of Electronics, Communications & IT of IETE Technical Review, International Journal of Performability Engineering, IJRQSE and IJAC and is on the editorial board of various journals. He has been a Conference Chairman of various International Conferences, ICQRC-2001, ICMD-2002 & ICQRIT-2003,