2 TransmissionExpansionPlanning Approaches 14 PDFs of random inputs can be determined based on prediction and uncertainty analysis . The emphasis of this dissertation is on solving the restrictions of transmitting active power by transmission expansion planning. The main contribution of this research work is: 1) Presenting a probabilistic tool for analyzing the electric market and suggesting expansion plans base on market bottlenecks. 2) Defining probabilistic market based criteria for transmission expansion planning in deregulated power systems. 3) Presenting an approach for transmission expansion planning using above probabilistic tool and criteria. The approach must take into account all stakeholders’ desires, uncertainties, and vagueness of deregulated power systems.
3 Probabilistic Locational Marginal Prices In regulated power systems, probabilistic load flow is used to model the random uncertainties in transmission expansion planning -. Probabilistic load flow computes PDFs of line flows and bus voltages based on PDFs of loads. In regulated power systems transmission expansion planning is carried out based on the technical criteria such as probability of violation line flow limits and bus voltage limits. In deregulated power systems in addition to the technical criteria, market based criteria are needed to achieve the objectives of transmission expansion planning in deregulated power systems. Therefore, it is needed to compute the PDFs of variables which show the performance of electric market. This thesis proposes to use PDFs of nodal prices for assessing electric market performance. In this chapter a probabilistic tool for computing PDFs of nodal prices is introduced -. This chapter is organized as follows. In section 3.1, the concept of locational marginal prices is described and a mathematical model for computing nodal prices is presented. In section 3.2, a probabilistic tool, which is named “probabilistic locational marginal prices”, is presented for electric market analysis. The presented approach is applied to an 8-bus network in section 3.3. 3.1 Locational Marginal Prices Nodal pricing is a pricing system for purchasing and selling electric energy in deregulated power systems. In nodal pricing a price is determined for each transmission node or bus. In this pricing system, all consumers purchase energy at the price of their load bus and all producers sell energy at the price of their generator bus. By definition nodal price or locational marginal price (LMP) is equal to the "cost of supplying next MW of load at a specific location, considering generation marginal cost, cost of transmission congestion, and losses" , . Cost of marginal losses is not implemented currently. Figure 3.1 shows the components of LMP. On the other word, LMP of bus i is the additional cost for providing 1 MW additional power at this bus. The marginal cost of providing electric energy at a specific