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Long-Term Optimal Operation of Hydrothermal Power Systems

  • G. S. Christensen
  • S. A. Soliman
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 38)

Abstract

The problem treated in the previous chapters was concerned with a pure hydro power system, where we maximized either the total benefits from the system (benefits from the hydro generation plus benefits from the amount of water left in storage at the end of the planning period) or the total firm hydro energy capability for the system. We discussed almost all techniques used to solve these problems. Most of the utility companies have a combination of hydro and thermal power plants to supply the required load on the system, where the hydro power plants are used to supply the base load, since they cost nothing to run (almost all the running costs are very small compared to those of thermal plants), while the thermal plants are used to supply the peak load, since these loads occur for a small period of time with peak demand.

Keywords

Power System Fuel Cost Hydroelectric Plant Load Demand Optimization Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 7.1.
    Bosch, P. P. J., “Optimal Static Dispatch with Linear, Quadratic and Nonlinear Functions of the Fuel costs,” IEEE Transactions on Power Apparatus and Systems PAS-104(12), 3402–3408 (1985).CrossRefGoogle Scholar
  2. 7.2.
    Shoults, R. R., Venktatesh, S. V., Helmick, S. D., Ward, G. L., and Lollar, M. J., “A Dynamic Programming Based Method for Developing Dispatch Curves When Incremental Heat Rate Curves are Non-Monotinically Increasing,” IEEE Transactions on Power Systems PWRS-l(l), 10–16 (1986).CrossRefGoogle Scholar
  3. 7.3.
    Kusic, G. L., Computer-Aided Power Systems Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1986.Google Scholar
  4. 7.4.
    Happ, H. H., “Optimal Power Dispatch—A Comprehensive Survey,” IEEE Transactions on Power Apparatus and Systems PAS-96(3), 841–854 (1977).CrossRefGoogle Scholar
  5. 7.5.
    van den Bosch, P. P. J., and Honderd, G., “A Solution of the Unit Commitment Problem via Decomposition and Dynamic Programming,” Preprints IEEE PES Summer Conference, paper 84 SM 609–4, Seattle, July 1984.Google Scholar
  6. 7.6.
    van den Bosch, P. P. J., “Optimal Dynamic Dispatch Owing to Spinning-Reserve and Power-Rate Limits,” Preprints IEEE PES Winter Conference, New York, January 1985.Google Scholar
  7. 7.7.
    Ottenhof, F. A. “Economische Optimalisatie van een Hierarchisch Electriciteits-Productie Systeem” M.Sc. thesis, Delft University of Technology, Laboratory for Control Engineering, 1978.Google Scholar
  8. 7.8.
    Murty, K. G., Linear and Combinatorial Programming, John Wiley and Sons, New York, 1976.MATHGoogle Scholar
  9. 7.9.
    van den Bosch, P. P. J., “Short-Term Optimization of Thermal Power Systems,” Ph.D. thesis, Delft University of Technology, 1983.Google Scholar
  10. 7.10.
    van den Bosch, P. P. J., and Lootma, F. A., “Large-Scale Electricity-Production Scheduling via Nonlinear Optimization,” Report 84–07 of the Department of Mathematics and Information, Delft University of Technology 1984, Submitted for possible publication in Mathematical Programming.Google Scholar
  11. 7.11.
    Vivianni, G. L., “Practical Optimization,” IEEE PES Summer Meeting, Paper 84 SM 613–6, Seattle, 1984.Google Scholar
  12. 7.12.
    Venkatesh, S. V., “A New Approach for Performing the Economic Dispatch Calculation Based upon the Principle of Dynamic Programming,” Master’s Thesis, The University of Texas at Arlington, August 1984.Google Scholar
  13. 7.13.
    Wood, A. J., and Wollenberg, B. F., Power Generation, Operation, and Control, Wiley, New York, 1984.Google Scholar
  14. 7.14.
    Hiller, F. S., and Lieberman, F. J., Introduction to Operations Research, Holden-Day Inc., San Francisco, 1967.Google Scholar
  15. 7.15a.
    Draper, N. R., and Smith, H., Applied Regression Analysis, Wiley, New York, 1981, pp. 85–89.MATHGoogle Scholar
  16. 7.15b.
    Draper, N. R., and Smith, H., Applied Regression Analysis, Wiley, New York, 1981, pp. 122.MATHGoogle Scholar
  17. 7.16.
    Bellman, R., and Roth, “Curve Fitting by Segmented Straight Lines,” American Statistical Association Journal 64(327), 1079–1084 (1967).MathSciNetCrossRefGoogle Scholar
  18. 7.17.
    Saha, T. N., and Khaparde, S. A., “An Application of a Direct Method to the Optimal Scheduling of Hydrothermal Systems,” IEEE Transactions on Power Apparatus and Systems PAS-97(3), 977–983 (1978).CrossRefGoogle Scholar
  19. 7.18.
    Soares, S., Lyra, C., and Tavares, H., “Optimal Generation Scheduling of Hydrothermal Power Systems,” IEEE Transactions on Power Apparatus and Systems PAS-99(3), 1107–1115 (1980).CrossRefGoogle Scholar
  20. 7.19.
    Narita, S., Oh, Y., Hano, I., and Tamura, Y., “Optimum System Operation by Discrete Maximum Principle,” Proceedings of the PICA Conference, 1967, pp. 189–207.Google Scholar
  21. 7.20.
    Bernholtz, B., and Graham, L. J., “Hydrothermal Economic Scheduling,” AIEE, Transactions Pt. III Power Apparatus and Systems 79, 921–932 (1960).CrossRefGoogle Scholar
  22. 7.21.
    Oh, Y. N., “An Application of the Discrete Maximum Principle to the Most Economical Power-System Operation,” Electrical Engineering Japan 4, 17–28 (1967).Google Scholar
  23. 7.22.
    Agarwal, S. K., “Optimal Stochastic Scheduling of Hydrothermal Systems,” Proceedings of the IEEE, 120(6), 674–678 (1973).Google Scholar
  24. 7.23.
    Agarwal, S. K., and Nagrath, I. J., “Optimal Scheduling of Hydothermal Systems,” Proceedings of the IEEE 119(2), 169–173 (1971).Google Scholar
  25. 7.24.
    Gupta, P. C, “Statistical and Stochastic Techniques for Peak Power Demand Forecasting,” Ph.D. thesis, Purdue University, Lafayette, Indiana, 1970.Google Scholar
  26. 7.25.
    Benjamin, J. R., and Cornell, C. A., Probability Statistics and Decision for Civil Engineers, McGraw-Hill, New York, 1970.Google Scholar
  27. 7.26.
    Powell, M. J. D., “A Method for Nonlinear Constraints in Minimization Problem,” presented at the conference on optimization, Keele University, Keele, England, 1968.Google Scholar
  28. 7.27.
    Kushner, H. J., Stochastic Stability and Control, Academic Press, New York, 1967.MATHGoogle Scholar
  29. 7.28.
    Aoki, M., Optimization of Stochastic Systems, Academic Press, New York, 1967.MATHGoogle Scholar
  30. 7.29.
    Narita, S., Oh, Y., Hano, L., and Tamura, Y., “Optimum System Operation by Discrete Maximum Principle,” Proceedings of PIC A conference, Pittsburg, Pennsylvania, 1967, pp. 189–207.Google Scholar
  31. 7.30.
    Papoulis, A., Probability, Random Variables, and Stochastic Process, McGraw-Hill, New York, 1965.Google Scholar
  32. 7.31.
    Feldman, A. A., Optimum Control System, Academic Press, New York, 1965.Google Scholar
  33. 7.32.
    Skorkhod, A. V., Studies in the Theory of Random Processes, Addison-Wesley, Reading, Massachusetts, 1965.Google Scholar
  34. 7.33.
    Fletcher, R., and Reeves, C. M., “Function Minimization by Conjugate Gradients,” Computer Journal 7, 149–154 (1964).MathSciNetMATHCrossRefGoogle Scholar
  35. 7.34.
    Hadley, G., Nonlinear and Dynamic Programming, Addison-Wesley, Reading, Massachusetts, 1964.MATHGoogle Scholar
  36. 7.35.
    Kirchmayer, L. K., Economic Operation of Power Systems, Wiley, New York, 1958.Google Scholar
  37. 7.36.
    Quintana, V. H., and Chikhani, A. Y., “A Stochastic Model for Mid-Term Operation Planning of Hydro-Thermal Systems with Random Reservoir Inflows,” IEEE Transactions on Power Apparatus and Systems PAS-100(3), 1119–1127 (1981).CrossRefGoogle Scholar
  38. 7.37.
    Croley, II T. E., “Sequential Stochastic Optimization for Reservoir System,” Journal of the Hydraulic Division, HYL, 10263, 201–219 (1974).Google Scholar
  39. 7.38.
    Baleriaux, J., Jamoule, E., and Deguertechin, R. L., Simulation de l’Exploitation d’un Pare de Machines Thermiques de Production d’Electricite Couple a des Stations de Pompage, Revue T., Edition SB RE, Vol. V, No. 7, 1967.Google Scholar
  40. 7.39.
    Booth, R. R., “Power System Simulation Model Based on Probability Analysis,” IEEE Transactions on Power Apparatus and Systems PAS-91, 62–69 (1972).CrossRefGoogle Scholar
  41. 7.40.
    Booth, R. R., “Optimal Generation Planning Considering Uncertainty,” IEEE Transactions on Power Apparatus and Systems PAS-91, 70–71 (1972).CrossRefGoogle Scholar
  42. 7.41.
    Joy, D. S., and Jenkins, R. T., “A Probabilistic Model for Estimating the Operating Cost of an Electrical Power Generating System,” Oak Ridge National Laboratory, Report No. ORNL-TM-3549, Oak Ridge, Tennessee, 1971.Google Scholar
  43. 7.42.
    Wu, F., and Gross, C., “Probabilistic Simulation of Power System Operation for Production Cost and Reliability Evalutation,” Special Session on Power Systems, IEEE International Symposium on Circuit and Systems, Phoenix, Arizona, 1977.Google Scholar
  44. 7.43.
    Viramontes, F. A., and Hamilton, H. B., “Optimal Long Range Hydro Scheduling in the Integrated Power System,” IEEE PES Winter Meeting, New York, Paper No. F-77–112-6, 1977.Google Scholar
  45. 7.44.
    Ringlee, R. J., and Wood, A. J., “Frequency and Duration Methods for Power Reliability Calculations: II—Demand Model for Capacity Reserve Model,” IEEE Transactions on Power Apparatus and Systems PAS-84, 61–78 (1965).Google Scholar
  46. 7.45.
    Luenberger, D. G., Introduction to Linear and Nonlinear Programming, Addison-Wesley, Reading, Massachusetts, 1973.MATHGoogle Scholar
  47. 7.46.
    Gagnon, C. R., Hicks, R. H., Jacoby, S. L. S., and Kowalik, J. S., “A Nonlinear Programming Approach to a Very Large Hydroelectric System Optimization,” Mathematical Programming 6, 28–41 (1974).MathSciNetMATHCrossRefGoogle Scholar
  48. 7.47.
    Arvantidis, N. V., and Rosing, J., “Composite Representation of a Multireservoir Hydroelectric Power System,” IEEE Transactions on Power Apparatus and Systems PAS-89(2), 319–326 (1970).CrossRefGoogle Scholar
  49. 7.48.
    Hanscom, M., and Lafond, L., “Modeling and Resolution of the Deterministic Midterm Energy Production Problem for the Hydro-Quebec System,” IREQ Report No. 1453, Project 01570–57351-503, Varennes, P.Q., Canada, 1976.Google Scholar
  50. 7.49.
    Nemhauser, G. L., Introduction to Dynamic Programming, John Wiley, New York, pp. 149–179, 1966.Google Scholar
  51. 7.50.
    Little, J. D., “The Use of Storage Water in a Hydroelectric System,” Journal of the Operations Research Society of America III, 187–197 (1955).CrossRefGoogle Scholar
  52. 7.51.
    Sullivan, R. L., Power System Planning, McGraw-Hill, New York, 1976.Google Scholar
  53. 7.52.
    Hilson, D. W., Sullivan, R. L., and Wilson, J. A., “Theory and Application of the Power System Probabilistics Simulation Method,” IEEE Summer Power Meeting, Paper No. A78 530–8, Los Angeles, July 1978.Google Scholar
  54. 7.53.
    Duran, H., et al, “Optimal of Multireservoir Systems Using an Aggregation-Decomposition Approach,” IEEE Transaction on Power Apparatus and Systems PAS-104(8), 2086–2092 (1985).CrossRefGoogle Scholar
  55. 7.54.
    Rees, F. J., and Larson, R. E., “Computer-Aided Dispatching and Operations Planning for an Electric Utility with Multiple Types of Generation,” IEEE Transactions on Power Apparatus and Systems PAS-10(2), (1971).Google Scholar
  56. 7.55.
    Arvantidis, N., and Rosing, J., “Optimal Operation of Multireservoir Systems using a Composite Representation,” IEEE Transactions on Power Apparatus and Systems PAS-89, (1970).Google Scholar
  57. 7.56.
    Pronovost, R., and Boulva, J., “Long-Range Operation Planning of a Hydro-Thermal System, Modeling and Optimization,” Canadian Electrical Association, Toronto, Ontario, March, 1978.Google Scholar
  58. 7.57.
    Turgeon, A., “Optimal Operation of Multireservoir Power Systems with Stochastic Inflows,” Water Resources Research 16(2), 275–283 (1980).CrossRefGoogle Scholar
  59. 7.58.
    Lederer, P., Torrion, Ph., and Bouttes, J. P., “Overall Control of an Electricity Supply and Demand System: A Global Feedback for the French System,” 11th IFIP Conference on System Modeling and Optimization, Copenhagen, July 1983.Google Scholar
  60. 7.59.
    Davis, R., and Pronovost, R., “Two Stochastic Dyanmic Programming Procedures for Long-Term Reservoir Management,” IEEE Summer Power Meeting, San Francisco, July 1972.Google Scholar
  61. 7.69.
    Duran, H., Querubin, R., Cuervo, G., and Rengifo, A., “A Model for Planning Hydrothermal Power Systems,”. 9th Power Industry Computer Applications Conference, June 1975.Google Scholar
  62. 7.61.
    Delebecque, F., and Quadrat, J. P., “Contribution of Stochastic Control Singular Perturbation Averaging and Team Theories to an Example of Large-Scale System Management of Hydropower Production,” IEEE Transaction on Automatic Control AC-23(2), (1978).Google Scholar
  63. 7.62.
    Soliman, S. A., and Christensen, G. S., “Discrete Stochastic Optimal Long-Term Scheduling of Hydro-Thermal Power Systems,” Applied Simulation and Modeling. IASTED Proceedings Conference, ASM’86, Vancouver, B.C., Canada. June 4–6, 1986, pp.103–106.Google Scholar
  64. 7.63.
    Kiefer, W. M., and Koncel, E. F., “Scheduling Generations on Systems with Fossil and Nuclear Units,” Transactions of the American Nuclear Society 13, 768 (1970).Google Scholar
  65. 7.64.
    Hoskins, R. E., and Rees, F. J., “Power Systems Optimization Approach to Nuclear Fuel Management,” Transactions of the American Nuclear Society 13, 768 (1970).Google Scholar
  66. 7.65.
    Grossman, L. M., and Reinking, A. G., “Fuel Management and Load Optimization of Nuclear Units in Electric Systems,” Transactions of the American Nuclear Society 20, 391 (1975).Google Scholar
  67. 7.66.
    Chou, W. B., “Characteristics and Maneuverability of Candu Nuclear Power Stations Operated for Base-Load and Load Following Generation,” IEEE Transactions on Power Apparatus and Systems PAS-94(3), 792–801 (1975).CrossRefGoogle Scholar
  68. 7.67.
    El-Wakil, M. M., Nuclear Power Engineering, McGraw-Hill, New York, 1962.Google Scholar
  69. 7.68.
    Yasukawa, S., “An Analysis of Continuous Rector Refueling,” Nuclear Science and Engineering 24, 253–260 (1966).Google Scholar
  70. 7.69.
    Millar, C. H., “Fuel Management in Candu Reactors,” Transactions of the American Nuclear Society 20, 350 (1975).Google Scholar
  71. 7.70.
    El-Hawary, M. E., and Christensen, G. S., Optimal Economic Operation of Electric Power Systems, Academic, New York, 1979.Google Scholar
  72. 7.71.
    Porter, W. A., Modern Foundations of Systems Engineering, Macmillan, New York, 1966.Google Scholar
  73. 7.72.
    Hamilton, E. P., and Lamont, I. W., “An Improved Short Term Hydrothermal Coordination Model,” Paper No. A77 518–4, Institute of Electrical and Electronics Engineers Summer Power Meeting, Mexico City, 1977.Google Scholar
  74. 7.73.
    Isbin, H. S., Introductory Nuclear Reactor Theory, Reinhold, New York, 1963.Google Scholar
  75. 7.74.
    Shamaly, A., et al., “A Transformation for Necessary Optimality Conditions for Systems with Polynomial Nonlinearities,” IEEE Transactions on Automatic Control AC-24, 983–985 (1979).MathSciNetCrossRefGoogle Scholar
  76. 7.75.
    Mahmoud, M. S., “Multilevel Systems Control and Applications: A Survey,” IEEE Transactions on Systems, Man and Cybernetics 7(3), 125–143 (1977).MathSciNetMATHCrossRefGoogle Scholar
  77. 7.76.
    Nieva, R., Christensen, G. S., and El-Hawary, M. E., “Functional Optimization of Nuclear-Hydro-Thermal Systems,” Proceedings, CEC, Toronto, 1978.Google Scholar
  78. 7.77.
    Nieva, R., Christensen, G. S., and El-Hawary, M. E., “Optimum Load Scheduling of Nuclear-Hydro-Thermal Power Systems,” Optimization Theory and Applications 35(2), 261–275 (1981).MathSciNetMATHCrossRefGoogle Scholar
  79. 7.78.
    Tsouri, N., and Rootenberg, J., “Optimal Control of A Large core Reactor in Presence of Xenon,” IEEE Transactions on Nuclear Science NS-22, 702–710 (1975).CrossRefGoogle Scholar
  80. 7.79.
    Lin, C., and Grossman, L. M., “Optimal Control of a Boiling Water Reactor in Load-Following Via Multilevel Methods,” Nuclear Science and Engineering 92, 531–544 (1986).Google Scholar
  81. 7.80.
    Christensen, G. S., El-Hawary, M. E., and Soliman, S. A., Optimal Control Applications in Electric Power Systems, Plenum Press, New York, 1987.MATHGoogle Scholar
  82. 7.81.
    Chaudhuri, S. P., “Distributed Optimal Control in a Nuclear Reactor,” International Journal of Control 16(5), 927–937 (1972).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • G. S. Christensen
    • 1
  • S. A. Soliman
    • 2
  1. 1.University of AlbertaEdmontonCanada
  2. 2.Ain Shams UniversityCairoEgypt

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