dent demand charges, and special rates such as super off- peak pricing, and real time pricing. Many utilities in the U.S. see innovative rate structures as strategic options to improve their competitive position by offering a choice of such rate options to those customers who are most inclined to meet their energy requirements from alternate energy sources such as natural gas, and cogenera- tion. Some of this interest can also be attributed to an emerging recognition in the industry that its traditional practice of providing all users with a uniform and very high level of service reliability and at prices prespecified well in advance has major shortcomings. For one, this mode of operation is sustainable only by incurring costs that are significantly higher than necessary. By introducing dynamic pricing op- tions which can more closely track actual costs, the utility can essentially "unbundle" electric service and offer its customers a range of rate-reliability choices. This tailoring of service should result in a closer matching of customer needs and cost share responsibilities, and therefore in all customers being better off. Finally, there is also growing recognition that utility plan- ning and operations today are characterized by substantial uncertainty. However, most of today's tariffs are pre-speci- fied well in advance (one or more years), and thus do not provide utilities with an effective means for managing de- mand under shifting conditions. Classical tariffs are inflexible and therefore preclude achieving significant opportunistic gains in short-term efficiency; gains which can be to the mutual benefit of the utility and its ratepayers, and to those consumers who have the capability but are at present not responding under such circumstances because of ineffective price signals. By incorporating one or more real time1 elements into a tariff, it can be made more responsive to utility and customer needs. This paper highlights the need for an potential role of flexible pricing options which offer an efficient means for achieving a utility's load/demand management objectives. The focus of this paper is on dynamic tariffs. The term dynamic pricing is used in this paper to broadly encompass tariff structures that have one or more elements which are calculated and posted close to the time of applicability. This definition embraces several concepts developed in the pricing literature such as real time (spot) pricing, responsive pricing, state preference pricing, "flexible pricing", and certain forms of "incentive rates", and "economic development rates". By incorporating real time features within one or more key parameters of the tariff, such pricing options can be tailored to offer the degree of flexibility that is necessary and cost effective for achieving the given demand management objec- tive(s). This paper is organized as follows. First it develops the rationale and role for dynamic pricing. Fundamental to the development of such innovative tariffs is the concept of a utility's short-run marginal cost structure. Next the paper briefly defines and illustrates this concept. It also describes how this cost structure can be estimated, and indicates potential applications. Another section in the paper identifies examples of load/demand management strategies that are dynamic and hence flexible, and that are either being used or have been suggested. Finally, the paper discusses customer response and acceptance of such options. 88 WM 207-3 February 1989 An Optimization Model for Long-Range Transmission Expansion Planning A. Santos, Jr., P. M. Franca, and A. Said State University of Campinas-UNICAMP Faculty of Electrical Engineering 13081 -Campinas-SP-Brazil Keywords-Power Transmission Planning; Mathematical Pro- gramming; Optimization Methods Introduction Long-range transmission expansion planning is carried out with the assistance of computational tools for network synthesis. These routines have as their objective the determi- nation of possible alternatives which must provide power transmission capacity in agreement with load forecasting and generation planning. The alternatives are then subjected to new studies such as reactive planning, dynamic analysis, etc ... in which other electrical performance criteria are taken into account. The network configuration for a future condition of load and generation can be obtained by a one-step network synthesis method. For this the following data is necessary; load forecasts, generation plans, initial configuration, trans- mission parameters and investment costs. Fig. 1 shows the process. Mathematical Formulation The objective of the network synthesis methods is to determine low cost alternatives for transmission capacity for load supply. In general the synthesis methods can be performed with the following approaches: - heuristic methods; - optimization mathematical models. In this paper the static synthesis is formulated as an optimization model which minimizes the network expansion costs subject to constraints of transmission capacity and load supply. The problem formulation considers both economic objectives and a electric power transmission law. The power flow accuracy is obtained by implicitly considering the DC load flow in the optimization model which is stated as a nonlinear mixed-integer network flow problem. This problem can be solved by an exact mathematical optimization proce- dure but when applied to practical problems, the computa- tional times become prohibitive. In order to avoid this difficulty some mathematical manipulations-integrality re- laxation and projection-are made which transform the original problem into a more simple fixed-charge network flow problem (FCNFP). Solution Technique To solve the FCNFP efficiently an implicit enumeration technique that generates a binary decision tree is proposed. Each node of the tree represents a realization of the vector of binary variables present in the fixed charge formulation. A "branch and bound" enumeration tree is built up step by step and at each vertex of the tree fathoming tests are applied in order to evaluate proposed solutions. The fathoming tests make use of a lower bound which is obtained by solving a piecewise linear relaxed version of the FCNFP. The piecewise linear approximation preserves the network flow program- ming features of the original problem. The relaxed problem is solved by a computational code based on the minimum cost network flow algorithm adapted to handle a piecewise linear cost function in the arcs. 42 ______________________________________________________________IEEE Power Engineering Review, February 1989 42