3 Probabilistic locational Marginal Prices 16 LMP node depends on: • marginal cost of generators, • operating point of the system, and • transmission network constraints. Fig. 3.1 – Components of LMP Using nodal pricing, customers buy and sell energy at the actual price of delivering energy to their buses. This pricing system encourages an efficient use of transmission system by assigning prices to users based on the physical way that energy is actually delivered to their buses. 3.1.1 Bidding Procedure In deregulated power systems, ISO dispatches the generators so that to meet the demand of loads at the minimum cost while maintaining security and service quality of power system. ISO compute LMPs by running optimal power flow. Bidding process for a specified period, e.g. next two hours, is as below. • Every producer submits the following values to ISO: o Minimum and maximum power which can deliver to the network o Bid price for selling 1 MW electric power • Every consumer submits the following values to ISO: o Minimum and maximum load demand o Load bid for load curtailment in emergency condition (if LMP of a load exceeds its bid then the load is curtailed till its LMP reduces to its bid) • ISO run the optimal power flow and computes the following values: o MW dispatch of each generator o MW dispatch of each load o LMP of each bus Generation Marginal Cost Transmission Congestion Cost = + + Cost of Marginal Losses The mathematical model for computing LMPs is described in the following subsections.
3 Probabilistic locational Marginal Prices 17 3.1.2 Mathematical Model for Computing Locational Marginal 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 increasingly. Let’s call this list priority list. If there is no constraint in transmission network, the generators are dispatched according 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 marginal generator. If load of a bus is increased by 1 MW, regardless of the bus location, this 1 MW load will be supplied by the marginal generator. Therefore, according to the definition of LMP, LMPs of all buses are equal to the bid of marginal generator. If there is constraint in transmission network, the generators are dispatched according to priority list till reach the first constraint. The last dispatched generator can not be dispatched more because of the constraint. Hence, the next generators of the priority list, which do not increase the flow of the congested line, are dispatched respectively till reach the next constraint or sum of generation is made equal to sum of loads and losses. If the generators which have been dispatched after reaching the first constraints decrease the flow of the congested lines, undispatch cheaper generations are dispatched. This process is continued till sum of generation is made equal to sum of loads and losses. In the presence of constraints, there are several marginal generators. If load of a bus is increased by 1 MW, depends on the bus location, this 1 MW load is supplied by the marginal 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 constraints LMPs of buses are different. A simple example for LMP is given in appendix C. In practice LMPs are computed using an optimization problem, which is described in the following subsections. 220.127.116.11 Optimal Power Flow Optimal power flow is modeled by an optimization problem. Objective function is the total cost of operation including cost of running generators and load curtailment cost. Power flow equations, line flow limits, generation limits, and load limits are the constraints of this optimization problem. The objective function and constraints are modeled in (3.1)-(3.5). Consider a power system with Nb buses, Ng generators, Nd loads, and Nl lines. Optimal power flow is modeled as below: