Systems with storage allow the production and use of a commodity to be separated in timeto reduce costs or to make better use of available capacity. Hydro-reservoirs play a centralrole in many electricity systems. On the demand side there is a much greater variety ofstorage plant; buffer storages in manufacturing, ice storage systems and compressed airsystems. Battery storage can also be used in remote area power supply systems (RAPS).Determining an effective and efficient operating strategy for storages can be difficult. Theliterature reveals a wide variety of approaches to the hydro-dispatch problem. More recentlymore emphasis has been placed on the operation of distributed demand-side storages, bethey centrally controlled or individually influenced through time-of-use or spot pricingtariffs.The difficulty of modelling and optimising the operation of storage systems arises fromthe separation over time of production and use of the stored commodity. Determining theoptimal operating strategy is a time-staged problem, presenting practical difficulties withproblem size. The operating strategy also depends on expectations of future plant operationand external conditions which cannot always be known with certainty.This thesis presents an exact and efficient solution method for a general class of deterministic,single storage systems. While many real systems are more complex than this, theapproach developed combines elements of both dynamic programming and generalmathematical programming methodology and so offers good prospects for extension tomore complex multiple storage or stochastic systems.An important insight used throughout this thesis is that, for a large class of storage problems,the "production" and "storage" elements of the system can be separated. This leads to thefurther insight that the behaviour of a wide variety of production systems can beencapsulated in a single "production cost function" which describes the way all the systemcosts per unit time vary with the rate of flow into (or out of) the store. For the purpose ofthis thesis, this function is taken to be piece-wise linear and convex, although suchrestrictions can largely be removed if the algorithm is modified.Once the production element of the system can be described in this standardised way, itis possible to write both linear programming and dynamic programming representationsof the time-staged optimisation problem to be solved. By analysing the mathematicalproperties of this formulation and the conditions for its solution, a simple, exact and highlyefficient solution algorithm is developed. One advantage of the algorithm is that it has asimple and intuitive graphical representation.The algorithm combines the best features of the linear and dynamic programmingapproaches while eliminating their worst features for the class of problem addressed. Asa dynamic programming approach, the solution is obtained by solving a sequence of small,single period optimisations, which is much more efficient than solving a time-stage linearprogram. As a linear programming approach, the solution is exact and obtained withoutdiscretising the storage variable. The dual properties of the linear programming solutionalso provide useful supplementary information such as the shadow value of the storagecontents over time. As a practical matter, commercial codes for the storage algorithm canbe developed by extending existing mathematical programming codes.Two examples are presented. The first works through a simple model analytically toillustrate the workings of the algorithm. The second is a larger and more complex modelof a pumped storage hydro-electric system.While the thesis concentrates on single storage, deterministic systems, possible extensionsto deal with multiple storage and stochastic systems are also reviewed.
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