Optimal scheduling of hydro and hydrothermal power systems : an investigation carried out within the Department of Electrical Engineering, University of Tasmania

In a power system with only thermal generation, fuel stocks are usually adequate for any generation schedule permitted by plant ratings. This is not so for hydro generation, whose energy availability is determined by water storages and stremflows and ultimately by the weather. In scheduling a system with hydro-generation, this extra limitation must be recognised, and it dictates the form of the scheduling method if the proportion of hydro-generation is high. The optimal schedule is taken as the one supplying the power demand at minimum total cost or resource use over a specified period with adequate reliability, security and quality of supply, subject to physical, operating and statutory constraints. Optimisation of a hydro or hydrothermal system comprises a family of interacting problems characterised by differing time scales, degrees of detail and accuracy of information. The shorter the time span, the greater the detail and data accuracy. The family includes future planning over a decade or so, annual optimisation over a water year, water management over a period of days or weeks, daily optimisation over a load cycle and instantaneous regulation. This work is concerned with the study of the short term (daily) scheduling of generating plant in power systems with only hydro generation or of integrated (hydro-thermal) power systems with a significant proportion of hydro generation. Short-term optimisation of generation for a hydro or hydrothermal power system is a very large variational problem with many operational and physical constraints, the normal approach to its solution has been to apply optimal control or mathematical programming techniques to transform the problem into one of solving a set of equations characterising the optimum. Even for systems of moderate size, solution times for these equations are often high and intermediate stages of the solution may not provide feasible schedules. This thesis presents an alternative strategy by which successive feasible schedules approaching optimality are obtained rapidly. The hydrothermal scheduling problem is variational because of the need to consider overall rather than just instantaneous water use. In the optimisation the power system is modeled by differential equation equality constraints describing the river dynamics, and algebraic constraints describing the transmission system and thermal plants. Although real and reactive system loads and reservoir inflows are stochastic, in the short-term, they may be treated as deterministic without substantial penalty. The scheduling process presented in this thesis starts by committing hydro units and finding a starting schedule by a global search for the step-loading schedule which minimises generation losses and goes some way towards minimising transmission losses. The discussions of the search are reduced by reordering the system load curve and permitting only such combinations of steps in generator loading as are found to characterise optimal step-loading schedules on the reordered load curve. This starting schedule obeys the water use constraints and will, in many cases constitute a feasible schedule. After unit commitment of hydro plants has been fixed by the step-loading schedule, the solution of the integrated problem is approached through a sequence of smaller problems in which alternately only hydro and only thermal plants are rescheduled with reference to the same goal. The initial step-loading schedule is refined, employing optimal load flow computations to schedule thermal generation, VAr allocation and regulator settings, alternating with a gradient or Newton search which uses the optimal load flow results to improve the hydro schedule. The optimal load flow algorithm which schedules thermal plants and ensures conformity with electrical system constraints yields dual variables which are the sensitivities of the objective function to the cost of power flows across hydro plant busbars. The incremental costs of supplying the demand may therefore be calculated in terms of hydro discharge rates. The hydro plants are then rescheduled by a hill-climbing step with hourly flows as independent variables, constrained by the specified reservoir depletions. Each step establishes new power flows at the hydro busbars, which are held during the next optimal load flow computation. In this way, feasible, properly constrained schedules are obtained at the end of each set of optimal load flow solutions. Each step also provides a comprehensible measure of progress towards the optimum in the form of changes in cost and generation schedules. In preceding this local minimum finding search by a restricted global search for unit commitment, convergence to the globally optimal schedule is enhanced. By arranging the optimisation around one of the existing highly developed optimal load flow algorithms, much of the sensitivity information needed to tell an operator not only the optimal schedule, but also the effect of small changes on it, is available and if a Newton type search is used, the sensitivity of the objective function to total discharge of each hydro plant is also available with no further computation. The method is, by virtue of its modular approach, able to make use of any future developments in the optimal load flow field which is still being intensively researched, with additional or superior features being easily incorporated.