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

Transmission Expansion Planning in Deregulated Power ... - tuprints

3 Probabilistic locational Marginal Prices 20

Therefore, according to the definition of LMP, LMP of bus i is equal to the shadow price of

power flow equation of bus i (see the examples of appendices C and D).

3.2 Probabilistic Locational Marginal Prices

In regulated power systems, probabilistic load flow is used for analyzing electric networks

and transmission expansion planning [9]-[11]. In this environment technical criteria, such as

the probability of violating line flow limits and bus voltage limits, are used for transmission

expansion planning. Technical criteria are computed based on the PDFs of line flow powers

and bus voltages.

In deregulated power systems in addition the technical criteria, market based criteria must be

used to achieve the objectives of transmission expansion planning in deregulated power

systems. In order to define and compute market based criteria, we need to compute the PDFs

of variables which show the performance of electric market. These variables should be

affected by dynamics of both power system and electric market. This thesis proposes to

compute PDFs of LMPs for assessing the performance of electric markets [67]-[72]. In this

section a probabilistic tool, which is named “probabilistic optimal power flow” or

“probabilistic locational marginal prices”, is presented for computing PDFs of LMPs.

3.2.1 Why Probability Density Functions of Locational Marginal Prices?

According to equations (3.1)-(3.5), LMPs will be affected if:

• producers change their bids,

• producers change minimum or maximum of their submitted power,

• consumers change their bids for load curtailment,

• consumers change minimum or maximum of their submitted demands,

• there is transmission constraint in the network,

• transmission facilities (generator, transmission line, load,…) have forced outage,

input or output power to the study area change due to new contracts with neighboring

areas,

• transmitting power through the study area change due to new wheeling transactions, or

• there is market power in the network.

Hence, PDFs of LMPs contain much information about the power system and electric market.

Therefore, performance of an electric market can be assessed by analyzing its PDFs of LMPs.

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