Transmission Expansion Planning in Deregulated Power ... - tuprints

3 Probabilistic locational Marg**in**al Prices 17

3.1.2 Mathematical Model for Comput**in**g Locational Marg**in**al Prices

Consider a deregulated power system and suppose producers and consumers have submitted

their bids and other data to ISO for a specific period of times. ISO lists generators based on

their bids **in**creas**in**gly. Let’s call this list priority list. If there is no constra**in**t **in** transmission

network, the generators are dispatched accord**in**g to the priority list till sum of generation is

made equal to sum of loads and losses. The last dispatched generator, which is not dispatched

fully, is named marg**in**al generator. If load of a bus is **in**creased by 1 MW, regardless of the

bus location, this 1 MW load will be supplied by the marg**in**al generator. Therefore, accord**in**g

to the def**in**ition of LMP, LMPs of all buses are equal to the bid of marg**in**al generator.

If there is constra**in**t **in** transmission network, the generators are dispatched accord**in**g to

priority list till reach the first constra**in**t. The last dispatched generator can not be dispatched

more because of the constra**in**t. Hence, the next generators of the priority list, which do not

**in**crease the flow of the congested l**in**e, are dispatched respectively till reach the next

constra**in**t or sum of generation is made equal to sum of loads and losses. If the generators

which have been dispatched after reach**in**g the first constra**in**ts decrease the flow of the

congested l**in**es, undispatch cheaper generations are dispatched. This process is cont**in**ued till

sum of generation is made equal to sum of loads and losses. In the presence of constra**in**ts,

there are several marg**in**al generators. If load of a bus is **in**creased by 1 MW, depends on the

bus location, this 1 MW load is supplied by the marg**in**al generators which do not violate lime

flow limits. Hence, LMP of each bus depends on its location **in** the network. Therefore, **in** the

presence of transmission constra**in**ts LMPs of buses are different. A simple example for LMP

is given **in** appendix C. In practice LMPs are computed us**in**g an optimization problem, which

is described **in** the follow**in**g subsections.

3.1.2.1 Optimal **Power** Flow

Optimal power flow is modeled by an optimization problem. Objective function is the total

cost of operation **in**clud**in**g cost of runn**in**g generators and load curtailment cost. **Power** flow

equations, l**in**e flow limits, generation limits, and load limits are the constra**in**ts of this

optimization problem. The objective function and constra**in**ts are modeled **in** (3.1)-(3.5).

Consider a power system with Nb buses, Ng generators, Nd loads, and Nl l**in**es. Optimal power

flow is modeled as below: