An Evolutionary Algorithm For Evaluation Of Emission ... - CiteSeerX

An Evolutionary Algorithm For Evaluation Of Emission Compliance Options in view of the Clean Air Act Amendments Dipti Srinivasan

Andrea G. B. Tettamanzi1

Department of Electrical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore 0511

Dipartimento di Scienze dell’Informazione Universita` degli Studi di Milano Via Comelico 39/41, I-20135 Milano, Italy

Abstract - An integrated framework for modeling and evaluating the economic impacts of environmental dispatching and fuel switching is presented in this paper. It explores the potential for operational changes in utility commitment and dispatching to achieve least cost operation while complying to rigorous environmental standards. The work reported here employs a heuristics-guided evolutionary algorithm to solve this multiobjective constrained optimization problem, and provides the decision maker a whole range of alternatives along the Pareto-optimal frontier. Heuristics are used to ensure the feasibility of each solution, and to reduce the computation time. The capabilities of this approach are illustrated via tests on a 19-unit system. Various emission compliance strategies are considered to reveal the economic trade-offs that come into play. INTRODUCTION The main objective of unit commitment and dispatch decisions has traditionally been the minimization of system operating costs subject to constraints related to reliability of operation, and the physical and economic characteristics of the generating units [1]. The passage of the Clean Air Act Amendments of 1990 has forced the utilities to modify their operating strategies to meet rigorous environmental standards set by this legislation. There is a substantial volume of literature discussing various emission compliance strategies in view of the Clean Air Act [2]. These strategies include installation of emission control equipment, replacement of old thermal generators with cleaner and more efficient ones, modifications to existing generating and fuel burning equipment, load management, emission dispatching, fuel switching and/or blending, and emission trading. Of these, the first three options involve considerable capital outlay, and are generally considered to be long-term options. The cost of installing advanced emission-control equipment may cost the utilities many times more than the increase in production cost to perform emission dispatch [3]. The last four of the above mentioned options can be implemented in relatively short time frames. Emission

dispatching is an attractive short-term alternative in which the primary objective is to minimize the overall emissions by loading the cleaner generating units as much as possible while forcing those with higher emission rates to generate less. An excellent description of the commonly used environmental dispatch algorithms can be found in [4]. Many authors suggest using the permissible emission limit as a constraint in the formulation of economic dispatch problem [4, 5]. [6] presented a method for estimating the costs and emissions due to changes in the fixed or variable costs, emissions, or capacity of generating units. Acid Deposition Control, Title IV of the Clean Air Act Amendments of 1990 sets limits on the annual emission of SO2 from existing fossil fuel plants. One viable alternative to reduce the SO2 emissions from thermal plants is fuelswitching [7]. Utilities burning high sulfur fuel can switch to a low sulfur fuel in order to meet the stringent SO2 requirements. The legislation allows emission trading, thus permitting the utilities to select the most cost-effective manner in which to realize SO2 reductions. Various methods for calculating the cost of a transaction involving emission trading have been analyzed in [8]. The economic benefits of fuel-switching can be evaluated against the market value of SO2 allowances to achieve the optimum operating point. The model described in this paper aims to provide a flexible framework in which to evaluate various operational planning options for emission compliance. In particular, it performs a cost-benefit analysis of short-term options such as, fuel switching and emission dispatching to allow the utility planners determine the best way to realize these options. It can be used to (1) determine the optimum unit commitment and loading levels of each affected unit so as to meet the emission targets, (2) perform multiobjective dispatch considering cost and emissions as competing objectives, (3) appraise the alternative schemes to facilitate the utility planner in determining whether to buy/sell emission allowances, do emission dispatching, or fuelswitching. In practice, the determination of trade-offs between economic and environmental factors is a very difficult task. The main factor complicating the process is that benefits cannot be easily expressed in monetary terms for a direct determination of trade-offs in relevant physical quantities. The optimization techniques currently in practice do not provide a convenient way to solve this type of multiobjective problems. Various assumptions are usually made to make the problem solvable using realistic computational resources. The hybrid approach presented in this paper overcomes this 1

The work described in this article was carried out during the author’s appointment as a Visiting Industrial Fellow in the Computer Science division of the University of California at Berkeley, USA, from 1994-1995.

problem by combining the advantages offered by knowledgebased approaches with the strengths of evolutionary computation [9] techniques. Heuristics are used to ensure that all the constraints, both linear and nonlinear, are fulfilled for each member of the genetic population, while the evolutionary algorithm works towards simultaneously optimizing the objective functions to obtain high quality solutions. Together, these two overcome the limitations of the traditional optimization approaches to solve the generation scheduling problem, compounded in complexity by the emission compliance requirements. The principle and algorithm of the proposed method are given in the paper. Test results on a system consisting of 19 thermal generating units are presented. II. UNIT COMMITMENT AND DISPATCH PROBLEM Dynamic programming (DP) has so far been the most widely used approach to solve the coupled unit commitment and generation dispatch problems [1]. The main advantage of the DP method is its ability to handle various system constraints. The main limitation of this method is its inefficient handling of time-dependent constraints, and exponential increase in computational time as the problem size increases. Use of heuristics is required to limit the search space when large systems are considered. This, however, leads to suboptimal solutions. Recently, Lagrangian relaxation methods have become popular for solving the unit commitment and dispatch problems for large systems. Although, these methods are more flexible for handling various constraints, the solutions are very sensitive to variations of the Lagrange multiplier value. In addition, the optimality of the final solution cannot be ensured as the algorithm is inherently suboptimal. With increasing size and complexity of the systems considered, many researchers have proposed the use of knowledge-based methods. Apart from easy implementation on the computer, the formulation of the problem is simple and appealing. But in spite of the fact that heuristic rules are effective in making decisions based on local information, the overall solutions produced are far from being globally optimal. The unit commitment and dispatch problem is traditionally solved to minimize the overall system cost subject to various operational constraints. The rising awareness regarding the environmental pollution has forced the utility planners to consider emission as an equally important objective. A real-time dispatch solution to minimize the emissions was first proposed in [10]. The solution methodology was similar to that used for economic dispatch. The objective function was formulated to calculate the emissions, expressed as a combination of a straight line and an exponential term. Most of the approaches developed so far [4] express the maximum allowable emission rates as constraints in the formulation of unit commitment and dispatch problem. Other approaches solve the multiobjective problem by converting it into a single-objective problem and assigning relative weights to each objective [4, 11]. Some recent works have considered emission-constrained dispatch problem including the legislation and conditions stipulated in the Clean Air Act Amendments [12-14]. The approach proposed in this paper treats economy and emissions as competing objectives, instead of simplifying the

multiobjective unit commitment and dispatch problem to a single-objective problem. It uses a novel solution strategy in order to overcome the above mentioned drawbacks of conventional techniques. Emphasis has been placed on making it generic and robust to handle a spectrum of objectives and constraints, and produce solutions with realistic computational requirements. The problem is formulated as described below. A. Problem formulation - Minimizing cost The fuel cost of a power system consisting of n generators each with individual production cost Ci expressed mainly as a function of its real power output Pi can be modeled by the quadratic polynomial [1]. Ci = ai + biPi + ciPi2 (1) Here ai, bi and ci are the cost coefficients of generator i. The objective function (O1) to be minimized for optimization of overall system cost is expressed as the sum of the running cost (1), the total start-up cost (SUi), shut-down cost (SDi), and hot-stand-by cost (HSi). The last three variables are non-zero only for those units started/shut down/kept stand-by in that particular hour. n O1 = ΣCi(Pi) + SUi + SDi + HSi $/h (2) i=1 B. Minimizing emissions - Treatment of pollutants Since SO2 emission is generally taken to be proportional to the unit’s fuel consumption [4], the emission function to represent SO2 emissions used in this paper has the same form as that for the fuel cost function. NOx emissions, being highly nonlinear in P, are more difficult to model. This paper adopts the commonly used[4] second order polynomial function to represent the NOx emissions function. Similar expressions are also used for CO 2 and particulate emissions. The jth pollutant from the ith unit can thus be calculated as: Eij = αij + βij Pi + γij Pi2 (3) Here, αi, βi and γi are the emission coefficients of unit i for each pollutant j. The total emission from each unit (Ei) can be calculated as the sum of individual pollutants. m Ei = Σ Eij (4) j=1 where m is the total number of pollutants considered in the dispatch. Use of weighting factors for each type of pollutant, depending on its degree of harm, has been suggested as one possible way to calculate total emissions[11]. The results shown in this paper are based on eqn (4), assigning equal weight to each pollutant. Eqn. (4), however, can be easily modified to attach different weights to the pollutants. The objective function O2 to be optimized to minimize the total emissions can be expressed as[4]: n O2 = Σ Ei (Pi) lbs/h (5) i=1 The optimization of objective functions O1 and O2 is subject to a number of constraints arising from restrictions on the operation of generating units, as well as, from system requirements. Constraints included in this formulation are:

a) b) c) d) e) f) g) h)

Power balance requirement Spinning reserve requirement Unit maximum and minimum output limits Unit minimum up and down times Power rate limits Unit initial conditions Unit status restrictions Plant crew constraints III. EVOLUTIONARY ALGORITHM

The term Evolutionary Algorithm (EA) encompasses a family of stochastic optimization techniques based on the key concept of evolution. Evolutionary computation-based models are weak implicit-enumeration like methods suitable for search and optimization. Unlike other enumeration techniques, they incorporate a learning element into the search which enables them to narrow down quickly on the solution from randomly chosen points in the search space. Being population based models, these are able to produce a family of very good solutions with respect to the optimal. This class of computing algorithms emphasizes adaptation and operates in a manner analogous to biological evolution. An EA makes a population of appropriate representations, also called genotypes, of candidate solutions to the problem at hand (phenotypes) evolve by iteratively applying a set of stochastic operators, known as mutation, recombination, reproduction and selection. Mutation randomly perturbs a candidate solution; recombination decomposes two distinct solutions and then randomly mixes their parts to form a novel solution; reproduction replicates the most successful solutions found in a population, whereas selection purges poor solutions from a population. Starting from an initial generation of candidate solutions, this process produces advanced generations with candidates that are successively better suited to their environment. The basic assumption motivating the use of EAs for operation optimization problems is that optimal solutions can be found by exploitation of favorable features in suboptimal solutions. The objective function is external to the main program and can be easily modified. Evolutionary approaches are powerful search and optimization techniques particularly suited for problems where the search space of possible solutions is too large to be solved with traditional techniques, and where the problem structure and its parameters vary over time. The effectiveness of Genetic Algorithms (GAs) for solving the unit commitment and dispatch problems has been demonstrated in some recent works [15-17]. GA-based approaches have been shown to be superior than dynamic programming [15] and Lagrangian techniques [16], and suitable for solving large-scale problems [17]. IV. THE INTEGRATED FRAMEWORK Generation scheduling is a complex optimization task, requiring attention to a myriad of constraints, and poses a special challenge to EAs. As such, the solutions generated by mutation or recombination may not always be feasible. In addition, an exhaustive search of the space of all possible schedules for each hour of the scheduling period is almost impossible within reasonable computing time. This paper uses a practical approach to overcome these problems by using heuristic search. This allows the space of possible

action sequences to be searched intelligently in order to find near optimal, multi-step schedules for the entire planning horizon of 24 hours. To accomplish this, the solution strategy starts with an evolutionary algorithm which utilizes a mating scheme based entirely on the objective function which measures the quality of the solutions. Due to the presence of various constraints as described above, the new genotypes generated by mutation or recombination may not correspond to feasible solutions. This paper approaches this issue by using an indirect representation for solutions and by defining a decoding procedure that always generates a feasible solution. The algorithm, implemented as a steady state EA, is illustrated in Fig. 1 and described as follows. The parameters of the EA are initialized by seeding the population with randomly generated individuals, which are weight matrices of dimension [number_of_units x number_of_hours]. The elements of the weight matrix are floating point numbers between zero and one, associated with each unit for each hour of the day. The other inputs to the algorithm include generating unit data, heat rate curves, initial conditions, and the daily load curve. A slightly modified heuristic algorithm previously proposed by one of the authors [18] is used to build a feasible unit commitment pattern given a weight matrix. Selection of the best unit for turn on/off, as well as the output of each unit, is based on these weights. Starting from the first hour in the scheduling period, for each hour, an initial solution is obtained by multiplying the components of the weight matrix at that hour for each unit by its maximum output limit. Dynamic constraints, such as, ramp-rate and minimum up/down time, and plant crew constraints are enforced at this stage. If the initial solution violates any of the constraints, the schedule is modified. Thus, the feasibility of the population is enforced by using heuristics which pays attention to the fulfillment of all the constraints listed in Section II. A check is then performed to see if the power balance constraint is satisfied by this schedule. In case of a deficiency/surplus, the best unit or the combination thereof, is searched for turn on/off based upon the numbers in the weight matrix. Once the power balance constraint is met, a final check against all the unit operating constraints is made. If a constraint is violated for any unit, its output is fixed at the limit and the outputs of all other units are readjusted. Following the load curve, a commitment and dispatch schedule for each hour is obtained using the steps described above. Based on the schedule for each hour, the objective functions are also evaluated. The result of this decoding is a matrix of dimension [number_of_objectives] containing the values for each objective, over the entire scheduling period. Eqns (2) and (5) are used for this calculation. If required, the model can be easily extended to include other objectives and constraints related to the reliability and security. Two individuals are randomly selected from the population and a stochastic competition, based on the value of one of the objectives chosen randomly, is performed to find the winner. The process to find the non-dominated individuals is repeated until the size of the mating pool is the same as the population size (pop-size). Recombination is implemented through uniform crossover so that each offspring is selected from either parent with equal probability.

Initialization, input data Generate initial population of vectors Decode vectors, use heuristics to generate feasible schedules Evaluate objective functions Perform competition, form mating pool Perform selection, crossover and mutation Place the offspring in new population pop. < pop-size? Yes No Replace old population with new population gen. < max-gen? Yes No Decode solution vector Fig. 1: Flowchart of the hybrid algorithm

Mutation is implemented such that each component of the weight matrix has independent and identical probability of being corrupted. The selection procedure is based on a version of binary tournament selection. This avoids the need for an explicit fitness function, which would be difficult to form given the necessity of composing conflicting objectives. The off-springs evolved though the process of crossover, mutation and selection are weight matrices of dimension [number_of_units x number_of_hours]. The above process is repeated until the number of these off-springs equals a predefined population size. The old population is replaced with this new population of candidates and the above process is repeated until the number of generations reaches a pre-defined value (maxgen). As the evolution progresses, the algorithm generates the optimum set of weights which lead to non-dominated solutions. The final solutions are decoded using heuristics, as described above. The local search performed by the algorithm thus obtains a highly fit offspring which is also a feasible solution. In this manner, the global search of evolutionary algorithm is combined with the local heuristic search to obtain a hybrid algorithm which efficiently searches the feasible solution space. V. IMPLEMENTATION AND RESULTS The application of the above stated approach to an illustrative utility consisting of coal, natural gas and oil generating units is shown in this section. The potential of emission dispatching and fuel switching to decrease the emissions is analyzed.

The algorithm was implemented on an HP 712/60 workstation. The EA was allowed to run for 400,000 steps, with population size of 200 individuals, crossover rate of 60% and mutation rate of 1%. The database was created of generating unit characteristics, actual performance curves, fuels, and load data for the test system. Experiments were conducted on test systems containing 10, 19 and 40 units. The computing times were found to grow only linearly as the problem size increased. The results shown here are for the 19 unit system, which comprised of six coal-fired units of maximum capacities 250 MW and 120 MW, six oil-fired units of maximum capacity 120 MW, and seven gas units of maximum capacity 60 MW. The algorithm was tested for different load curves and initial conditions. The emission data for the units is given in Table I. The table includes emission rates for low sulfur coal of grades A and B, and low sulfur oil of grades A, B, and C, with the sulfur content shown in parenthesis. The particulate emission for the coal units was between 0.14-0.65 ton/MWh. Fuel type Coal - A (2.3%S) Coal - B (0.8%S) Oil - A (1.3%S) Oil - B (0.75%S) Oil - C (0.3%S) Natural gas

Table I Emission data NOx SO2 lb/MWh lb/MWh 1.7 - 3.48 6.5 - 11.3 0.62 - 1.3 2.7 - 5.6 0.81 - 2.15 4.63 - 6.8 0.53 - 1.17 2.1 - 3.5 0.41 - 0.93 0.8 - 1.2 1.03 - 1.16 0.0

CO2 ton/MWh 0.63 - 0.76 0.45 - 0.57 0.51 - 0.70 0.51 - 0.70 0.51 - 0.70 0.30 - 0.45

A. Commitment and dispatch of units to minimize emissions Single objective optimization

The summary of results obtained for unit commitment and dispatch over a scheduling period of 24 hours is shown in Table II. The load varies between 925 MW and 1950 MW during the day. The fuels used are of grade A. The evolutionary algorithm was run to minimize only one objective at a time. The minimum cost solution using this algorithm is very close to that found using dynamic programming ($428973.02) under same initial conditions.

Objective

Table II Single objective optimization Cost ($)

Minimize NOx

507762.6250

Minimize SO2

516511.5625

Minimize total emissions (NOx , SO2 , CO2, particulates) Minimize total cost (Economic dispatch)

548772.5315 428973.1250

Emission 60080.5 lbs 213489.1 lbs 22150.2684 tons 24694.3791 tons

B. Commitment and dispatch of units to minimize cost as well as emissions - multiobjective optimization

The algorithm was run to simultaneously optimize both the objectives. The final population contained a family of feasible solutions, lying on the Pareto-optimal cost-emission frontier. However, it also carried some inferior solutions on the right of this frontier which need to be ignored. The population (200 individual solutions) for each case is plotted in Figs. 2-5. The results are for fuels (both oil and coal) of grade A. Here, the cost and emission are shown for the entire scheduling period of 24 hours. The left-most and

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Fuel switching can involve either switching from one type of fuel to another (for example, coal to oil), or switching to fuels with low sulfur content. The former option involves considerable capital outlay while the latter is an attractive option in the short term. Table III shows the summary of results for this option. The experiments were based on data obtained for fuels with three different grades of sulfur (Table I). Case 1 is the result of minimum emission dispatch when coal and oil of grade A are used (same as case 1 in Table II). Case 2 is the result with both coal and oil of grade B, while Case 3 is with grade B of coal and grade C of oil. The results for simultaneous optimization of cost and emissions are shown in Figs. 6-8. SO2 Emission (x 1000 lbs)

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C. Commitment and dispatch with fuel switching - use of fuels with low sulfur content

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Fig. 3: Cost-emission frontier (SO2 v/s cost)

Fig. 6: Cost-emission frontier (Coal and oil of Grade B)

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SO2 Emission (x 1000 lbs)

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Fig. 2: Cost-emission frontier (NOx v/s cost)

the emissions as a constraint, an appropriate operating strategy can be chosen for commitment and dispatch of units to meet the desired emission levels. In these figures, the minimum values of emissions achievable are higher than those reported for single objective optimization (Table II) because the algorithm aims to simultaneously optimize both cost and emission.

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Fig. 4: Cost-emission frontier (NOx + SO2 v/s cost)

Fig. 7: Cost-emission frontier (Coal of Grade B, Oil of Grade C)

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right-most points in these figures represent minimum-cost and minimum-emission solutions respectively, while all other points on the surface of the curves represent nondominated solutions with a certain trade-off between the objectives. This gives the utility planner a whole range of alternative solutions showing cost-emission trade-offs. Instead of using a maximum allowable limit for the daily or annual value for

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Fig. 5: Cost-emission frontier (Total emission v/s cost)

Fig. 8: Cost-emission frontier ((Coal of Grade B, Oil of Grade C)

Case 1 2 3 4

Table III Results for fuel switching option Approach Cost $ Minimum SO2 dispatch 516511.5625 Coal - grade A, Oil - grade A Minimum SO2 dispatch 529654.9375 Coal - grade B, Oil - grade B Minimum SO2 dispatch 542262.6250 Coal - grade B, Oil - grade C Minimum (SO2 + NOx) dispatch 540690.7500 Coal - grade B, Oil - grade C

Emission lbs 213489.1 105090.7 89569.5 99372.0

VI. DISCUSSION Given a set of initial conditions and a load curve, the evolutionary algorithm can be run to produce these costemission trade-off curves, each point on which is a feasible unit commitment and dispatch schedule for the day. This allows the utility planner the flexibility of choosing any point depending on the desired level of emission or cost. Alternatively, Figures 2-5 can be used to assess the incremental cost of emission reduction option for a particular type of pollutant against its marginal price for emission allowance trading. Figures 3, 6 and 7 show trade-off curves for different grades of coal and oil. Evidently, the most effective way to reduce SO2 emission to significantly low levels is the use of low sulfur fuels which are also more expensive. The additional benefit of fuel-switching is that total (NOx + SO2) emission also reduces since these low sulfur fuels are generally cleaner, and consequently, NOx emission is correspondingly smaller. The decision maker can assess the market value of SO2 allowances against the additional cost for switching to a low-sulfur fuel. However, the current implementation of the algorithm does not allow for dynamic switching of fuels. The additional cost incurred due to fuel switching should also be weighted against the cost of installing emission-control equipment. From computational viewpoint, the distinguishing aspects of this approach are the following: 1. Multiple near-optimal solutions to the problem involving multiple constraints and conflicting objectives can be obtained in a reasonable time with the use of heuristics. 2. It works only with feasible solutions generated based on heuristics, thus avoiding the computational burden entailed by simple GA methods which first generate all feasible solutions and then purge the infeasible ones. 3. The solution time increases almost linearly with the number of units, thus making the approach suitable for large-scale problems. 4. The solution time remains the same for both single and multi-objective problems, since at any point, the population members are evaluated based on any one objective only. CONCLUSIONS The hybrid model presented in this paper provides a practical and flexible framework for evaluating the emission compliance strategies. The optimization algorithm generates trade-off curves between cost and emission based on these strategies, such as, emission dispatching and fuel switching for existing fossil fired power plants. The algorithm can be used to (a) execute single objective optimization to minimize one of the specified objectives, (b) perform multiobjective optimization to simultaneously optimize the competing objectives and provide the decision maker a whole range of alternatives to choose from, or (c) carry out multiobjective

optimization with fuel-switching option to evaluate various alternatives and analyze the trade-offs that come into play. Some options for utilities to systematically evaluate and select technically and economically attractive compliance plans have been discussed. The results shown here are for a scheduling horizon of 24-hours. Work is underway to extend the model to evaluate the trade-offs in real time, as well as, on an annual basis. ACKNOWLEDGMENTS The authors would like to thank Prof. Lotfi Zadeh (University of California at Berkeley) for his encouragement and constructive criticism on this paper. This work was supported in part by the BISC program and SGS-Thomson Microelectronics through Co.Ri.M.Me.. REFERENCES [1] A. J. Wood, B. F. Wollenberg, Power Generation, Operation and Control, John Wiley & Sons, New York, 1984. [2] A. A. El-Keib, H. Ma, J. L. Hart, “Economic dispatch in view of the Clean Air Act of 1990”, IEEE Trans. Power Systems, Vol. 9, No. 2, May 1994, pp. 972-978. [3] K. D. Le, et. al, “Current issues in operational planning”, IEEE Trans. Power Systems, Vol. 7, No. 3, August 1992, pp. 1197-1210. [4] J. H. Talaq, F. El-Hawary, M. E. El-Hawary, “A summary of environmental/ economic dispatch algorithms”, IEEE Trans. Power Systems, Vol. 9, No. 3, August 1994, pp. 1508-1516. [5] J. W. Lamont, E. V. Obessis, “Emission dispatch models and algorithms for the 1990’s”, IEEE Trans. Power Systems, Vol. 10, No. 2, May 1995, pp. 941947. [6] W. Huang, B. F. Hobbs, “Estimation of marginal system costs and emissions of changes in generating unit characteristics”, IEEE Trans. Power Systems, Vol. 7, No. 3, August 1992, pp. 1251-1258. [7] J. S. Heslin and B. F. Hobbs, “A multiobjective production costing model for analyzing emissions dispatching and fuel switching”, IEEE Trans. Power Systems, Vol. 4, No. 3, August 1989, pp. 836-842. [8] R. Ramanathan, “Short-term energy and emission trading analysis”, IEEE Trans. Power Systems, Vol. 10, No. 2, May 1995, pp. 1118-1124. [9] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1992. [10] M. R. Gent, J. W. Lamont, “Minimum-emission dispatch”, IEEE Trans. PAS, Vol. PAS-90, November/December 1971, pp. 2650-2660. [11] T. Denise King, M. E. El-Hawary, F. El-Hawary, “Optimal environmental dispatching of electric power systems via an improved hopfield neural network model”, paper no: 95 WM 166-9 PWRS, IEEE/PES Winter Meeting, January 1995, New York, NY, USA. [12] B. F. Hobbs, “Emissions dispatch under the underutilization provisions of the 1990 Clean Air Act Amendments: Models and Analysis”, IEEE Trans. Power Systems, Vol. 8, No. 1, February 1993, pp. 177-183. [13] S. Hass, et. al., “Planning system operations to meet NOx constraints”, IEEE Computer Applications in Power, Vol. 5, No. 3, July 1992. [14] N. S. Rau, S. T. Adelman, “Operating strategies under emission constraints”, paper no: 95 WM 176-8 PWRS, IEEE/PES Winter Meeting, January 1995, New York, NY, USA. [15] A. G. Bakirtzis, V. Petridis, S. A. Kazarlis, “A genetic algorithm solution to the economic dispatch problem”, IEE Proceedings - C, Generation, Transmission, Distribution, Vol. 141, No. 4, July 1994, pp. 377-382. [16] G. B. Sheble, K. Brittig, “Refined genetic algorithm - Economic dispatch example”, IEEE Trans. Power Systems, Vol. 10, No. 1, February 1995, pp. 117-124. [17] P. H. Chen, H. C. Chang, “Large-scale economic dispatch by genetic algorithm”, paper no: 95 WM 167-7 PWRS, IEEE/PES Winter Meeting, January 1995, New York, NY, USA. [18] D. Srinivasan, C. S. Chang, A. C. Liew, “Multi-objective generation scheduling using fuzzy optimal search technique”, IEE Proceedings C Generation, Transmission and Distribution, Vol. 141, No. 3, May 1994, pp. 233-242.

BIOGRAPHIES Dipti Srinivasan (M) obtained her M.Eng. and Ph.D. degrees in EE from the National University of Singapore (NUS) in 1991 and 1994 respectively. She worked at the University of California at Berkeley’s CS Division as a postdoctoral researcher from 1994 to 1995. In June 1995, she joined the faculty of the EE department at the NUS, where she is a lecturer. Her research interests are in the application of soft computing techniques in power system operation, economics and control. Andrea G. B. Tettamanzi (Non-member) received his MS in Computer Science in 1991 and is in the process of getting a Ph.D. in Computational Mathematics and Operations Research from the University of Milan, Italy. His research interests are in the field of evolutionary computing, fuzzy logic and soft computing in general.