Optimal Proxy-Limited Lines for Representing Voltage Constraints in a DC Optimal Powerflow

Abstract

With the recent restructuring of the electric industry away from the vertically integrated monopolies, electricity markets have emerged in various parts of the country. Independent System Operators (ISOs) and Regional Transmission Organizations (RTOs) have been set up to oversee these markets. While prices for the consumer have remained regulated, on the wholesale side companies are competing everyday to buy and sell power. These electricity markets require a way to value the energy at different locations. One of the most widely used methods today is called the Locational Marginal Price (LMP) or nodal price and can be used to settle markets. It is defined as the cost of supplying one more megawatt of power while abiding to the constraints of the system. There are two commonly-used models for calculating LMPs in a given system, the "AC" optimal power flow (ACOPF) and the "DC" optimal power flow (DCOPF). Although both methods result in finding LMPs of the system while abiding to constraints, loads, and costs, they differ in significant ways. The ACOPF and DCOPF use dissimilar methods to arrive at a solution, and that solution can be very different in some cases. The ACOPF is considered by many to be the correct result, with nothing in this method being assumed or approximated. However, because of its nonlinear approach, the solution can take much longer to solve if it even reaches a solution at all. Many real-time applications use a form of the DCOPF. It neglects resistance, reactive power, and voltage magnitudes, but results in a linear function that solves much quicker and more reliably than the ACOPF. Since the DCOPF doesn't take into account voltage magnitudes there is no direct way of having voltage constraints in a system. The method in this paper describes a way of mapping a ii voltage limit in the ACOPF to a flow limit in the DCOPF. Constraining particular lines in the DCOPF model results in a solution of LMPs and dispatch that acts like it has a voltage constraint at a particular bus. These mappings of one limit to another are called proxy limits or the nomogram approach [1]. The method described in this paper will use a Mixed Integer Programming (MIP) technique to optimally choose lines needed to minimized the dispatch error, LMP error, or a combination of both. The technique was carried out with the modified 30 bus system supplied by Matpower [2]. Results of minimizing the LMP error, dispatch error, and different combinations are shown below. Also shown, are how the lines chosen may achieve the voltage constraint mapped back to the ACOPF. Multiple constraints in the system and whether choosing from different subsets of lines has any effect on the system are also shown. Finally, results of how this method scales up or down with larger or smaller systems is examined.