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# Optimal load scheduling of hydroelectric power stations.

thesis
posted on 2023-05-26, 20:07 authored by Mantera, I Gusti Made
The work presented in this thesis concerns the optimisation of the hour-to-hour generation schedule (over a scheduling interval of 24 hours) of the generating stations in an all-hydro electric - system. The day-to-day system storage policy is assumed known from the long-term schedule. System load demand is first treated as deterministic. Later, attempts are made to treat it as stochastic. Throughout the text, system transmission losses are represented by means of the B-coefficient loss formula. Chapter 1 presents brief discussions on various topics which may play - a part in the optimization process. In particular, the concept of frequency control and the distinction between long-term and daily scheduling are outlined. The optimization objective is then formulated and some of the known methods of obtaining the solution are briefly discussed. In chapter 2, the optimization problem is first formulated . as that of minimizing the instantaneous total power drawn from the system subject to satisfying a . predetermined time-varying load demand.This is analogous to the minimization of the instantaneous total cost rate in thermal systems. Station characteristic curves are approximated by straight line segments and head variations are assumed negligible. The optimising - conditions are derived using the Lagrange multiplier technique. A small system consisting of 4 stations is studied, where optimisation is achieved by means of an analogue computer. By introducing weighting factors in the objective function, the storage policy can be satisfied. (Analysis carried out in chapter 3 later reveals that this is the correct measure which must be taken to meet the storage policy). Problems do arise, however, when - there are multi-unit stations present in the system. Due to the non-monotonic nature . of the incremental Output curves' of such stations, a. number of solutions would satisfy the optimising conditions. The optimum solution can only be established after testing each possible solution, a prohibitive task for large systems. Approximating the incremental output curves of such stations may create undesirable errors. Another weakness of the method is that it cannot readily take into account the effects of head variations. The application of Pontryagin's Maximum Principle is attempted in chapter 3. It is shown that, for systems with fixed‚ÄövÑvÆ head stations, the optimising conditions are exactly identical to that derived using the Lagrange multiplier technique with weightings being introduced in the objective function. Unfortunately, those problems associated with the presence of multi‚ÄövÑvÆunit stations are still unsolved. Under ideal system conditions, it is shown that optimum generation schedule would result if all stations; except the frequency control station, were step loaded. Step loading mode is defined as an operating mode where the instantaneous station discharge rate is only allowed to take one of two discrete values with stepwise transitions. The analysis indicates that the switching instants do not play any part, except they must be so chosen that the output of the frequency control station is kept within its limits. When step loading technique is applied to non‚ÄövÑvÆideal systems, the optimisation. becomes that of searching for the optimum switching instants of the step loaded stations. This is discussed in chapter 4. For practical reasons, only two step loading modes are assumed admissible. A system consisting of 18 stations is studied. Experimental results indicate that the optimum step loading modes can be established within - a reasonably short computation time. One striking feature of the step loading technique is that it can handle the optimal scheduling problem where the load demand is treated as being stochastic. The effects of head variations can be estimated fairly accurately. The application of the principle of dynamic programming is discussed in chapter 5. Due to the multi-dimensional nature of the problem, this principle must be combined with the relaxation principle to minimise the computation time and computer storage requirements. A good initial guess for the optimum schedule may be obtained using step loading technique. The step loading modes are then modified by applying the combination of dynamic programming and relaxaxtion principles. Finally, chapter 6 outlines the general conclusions drawn from the work presented in the preceeding chapters. The possibility. of applying Pontryagin's Maximum Principle to obtain the long-term storage policy is also studied. Related future research areas are suggested. To the author's best knowledge, the materials presented in chapters 3, 4 and 5 are original. Chapter 2 is based on the work of Chandler Jr. and Gabrielle, where the mathematical error found in their text has been corrected and the weighting procedure, among other materials has been included.

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Copyright 1972 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s). Thesis (Ph.D.) - University of Tasmania, 1972. Bibliography: l. 105-109

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