Efficient formulation of electric utility resource planning models
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Ef®cient formulation of electric utility resource planning models DT Gardner Algorithmics Inc., Toronto, Canada We show that the z-substitutes method for the ef®cient formulation of electric utility resource planning models may be used in more general circumstances, expanding considerably its range of practical applications. Numerical tests on a sample model provided a 40% to 75% reduction in problem solution time. Keywords: electric power industry; capacity expansion planning; mathematical programming
Introduction Electric utility resource planning is concerned with the acquisition of the resources necessary to meet electricity demands over a long-term planning horizon in an environmentally-responsible, reliable and cost-effective manner. Anderson1 provided an overview of traditional optimisation models used by system planners for this task while Hobbs2 describes more recent work, along with current planning issues requiring research. A well-known method for reducing the solution time of simple linear programming (LP) and mixed integer linear programming (MILP) electric utility resource planning models is the use of z-substitute variables,1 an idea reportedly due to E.M.L. Beale. Beglari and Laughton3 reported decreases in computation time between 50 and 80%, a signi®cant saving. More recently, the z-substitutes method has been extended to the joint planning of combined heat and power and electric power systems.4 An important restriction on the use of the z-substitutes method is that the circumstances under which optimality of the model solution may be guaranteed are quite limited. In particular, it has yet to be shown that the z-substitutes method may be used when there exist constraints on the energy production of multiple technologies or the emissions of different pollutants. Energy production constraints are useful for modelling differences between forced (unscheduled) and average (forced plus maintenance) outage rates. The important limitation today, however, is the fact that emission constraints, though of little importance when the zsubstitutes method was ®rst proposed, are now extremely common in practice.
Correspondence: Dr DT Gardner, Algorithmics Inc., 185 Spadina Avenue, Toronto, Ontario, Canada M5T 2C6. E-mail: [email protected]
In this paper, we rectify this situation by proving that the z-substitutes method may be used with both energy production and emission constraints, expanding the range of practical applications of the method considerably. For example, based on the results of this paper, the models considered by Gardner and Rogers5 and Hobbs2 (LP and MILP models, respectively) could employ the z-substitutes method in their formulation and therefore be solved considerably faster. Alternatively, the linear stochastic programming model of Louveaux and Smeers,6 which does use the z-substitutes method, could add energy production and=or emission constraints. The next sectio
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