Compared with traditional transmission network expansion planning, the exact life cycle cost is worth further studying. A three-dimensional life cycle cost (LCC) model for entire transmission network which consists of...
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Compared with traditional transmission network expansion planning, the exact life cycle cost is worth further studying. A three-dimensional life cycle cost (LCC) model for entire transmission network which consists of time dimension, component dimension and cost dimension is proposed. The device layer, the system layer and the cost of externalities of cost dimension are described and formulated in detail. The conditional value at risk (CVaR) of social welfare is established through optimal power flow calculation so as to take social responsibility into consideration. The multi-objective multi-stage transmission network expansion planning model is constituted with two objectives which are minimum LCC and minimum CVaR of social welfare. Four uncertain factors including wind power are considered and simulated through Monte Carlo method. An effective normal boundary intersection algorithm integrated with improved niche genetic method is presented to solve the proposed model. The case studies carried out on the 18-bus system and 77-bus system not only generate even distributed pareto set but also recommend the optimal planning scheme. The comparisons between the proposed scheme and existing method verify the feasibility and validity. Copyright (c) 2012 John Wiley & Sons, Ltd.
We consider problems where it is desirable to maximize multiple objective functions, but it is impossible to find a single design vector (vector of optimization variables) which maximizes all objective functions. In t...
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We consider problems where it is desirable to maximize multiple objective functions, but it is impossible to find a single design vector (vector of optimization variables) which maximizes all objective functions. In this case, the solution of the multi-objective optimization problem is defined as the Pareto front. The defining characteristic of the Pareto front is that, given any specific point on the Pareto front, it is impossible to find another point on the Pareto front or another feasible point which yields a greater value of all objective functions. The focus of this work is on the generation of the Pareto front for bi-objective optimization problems with specific applications to waterflooding optimization. The most straightforward way to obtain the Pareto front is by application of the weighted sum method. We provide a procedure for scaling the optimization problem which makes it more straightforward to obtain points which are approximately uniformly distributed on the Pareto front when applying the weighted sum method. We also compare the performance of implementations of the weighted sum and normalboundaryintersection (NBI) procedures where, with both methodologies, a gradient-based algorithm is used for optimization. The vector of objective functions maps the set of feasible design vectors onto a set Z, and it is well known that all points on the Pareto front are on the boundary of Z. The weighted sum method cannot find points which are on the concave part of the boundary of Z, whereas the NBI method can be used to find all points on the boundary of Z, even though all points on this boundary may not correspond to Pareto optimal points. We develop and implement an NBI algorithm based on the augmented Lagrange method where the maximization of the augumented Lagrangian in the inner loop of the augmented Lagrange method is accomplished by a gradient-based optimization algorithm with the necessary gradients computed by the adjoint method. Two waterflooding opt
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