# Transmission Expansion Planning in Deregulated Power ... - tuprints

Transmission Expansion Planning in Deregulated Power ... - tuprints

3 Probabilistic Locational Marginal Prices

In regulated power systems, probabilistic load flow is used to model the random uncertainties

in transmission expansion planning [9]-[11]. 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 [67]-[68].

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" [62], [64]. 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

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