Transmission Expansion Planning in Deregulated Power ... - tuprints

3 Probabilistic locational Marg**in**al Prices 20

Therefore, accord**in**g to the def**in**ition 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 Marg**in**al Prices

In regulated power systems, probabilistic load flow is used for analyz**in**g electric networks

and transmission expansion plann**in**g [9]-[11]. In this environment technical criteria, such as

the probability of violat**in**g l**in**e flow limits and bus voltage limits, are used for transmission

expansion plann**in**g. Technical criteria are computed based on the PDFs of l**in**e 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 plann**in**g **in** deregulated power

systems. In order to def**in**e 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 assess**in**g the performance of electric markets [67]-[72]. In this

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

“probabilistic locational marg**in**al prices”, is presented for comput**in**g PDFs of LMPs.

3.2.1 Why Probability Density Functions of Locational Marg**in**al Prices?

Accord**in**g to equations (3.1)-(3.5), LMPs will be affected if:

• producers change their bids,

• producers change m**in**imum or maximum of their submitted power,

• consumers change their bids for load curtailment,

• consumers change m**in**imum or maximum of their submitted demands,

• there is transmission constra**in**t **in** the network,

• transmission facilities (generator, transmission l**in**e, load,…) have forced outage,

• **in**put or output power to the study area change due to new contracts with neighbor**in**g

areas,

• transmitt**in**g power through the study area change due to new wheel**in**g transactions, or

• there is market power **in** the network.

Hence, PDFs of LMPs conta**in** much **in**formation about the power system and electric market.

Therefore, performance of an electric market can be assessed by analyz**in**g its PDFs of LMPs.