Abstract
Modern electricity markets with large penetration of renewable energy resources require fair and accurate pricing methods to elicit generation flexibility and foster competition in electricity markets. This paper proposes the fundamental theory and closed-form formulas for continuous-time locational marginal price (LMP) of electricity, which more accurately integrates the spatio-temporal variations of load and operational constraints of power systems in the electricity price calculation. This paper first formulates the network-constrained generation scheduling and pricing problems as continuous-time optimal control problems using two methods for modeling transmission network, i.e., Theta and generation shift factor (GSF) methods. The continuous-time network-constrained scheduling and pricing problems minimize in their objective functional the total operation cost of power systems over the scheduling horizon subject to generation and transmission constraints. The closed-form continuous-time LMP formulas are derived for each transmission network model, which explicitly include terms that reflect the simultaneous spatio-temporal impacts of transmission flow limits and intertemporal generation ramping constraints in LMP formation. A scalable and computationally efficient function space solution method is proposed that converts the continuous-time problems into mixed integer linear programming problems with finite-dimensional decision space. The proposed solution method enables high-fidelity solution of transmission-constrained scheduling and pricing problems in higher dimensional spaces, while including as a special case the current discrete-time solutions. The proposed models are implemented on a three-bus system and the IEEE reliability test system, where the proposed models showcase more accuracy in reflecting the impacts of fast net-load variations over discrete-time counterparts.
Highlights
Evolving electricity markets require fair and accurate pricing methods to maintain market transparency and efficiency and foster competition
With the advancements in power systems operation and integration of emerging energy technologies, new challenges are introduced to pricing of electricity encouraging several lines of research to investigate the impact of non-convexities [5]–[9], transmission architecture [10], The associate editor coordinating the review of this manuscript and approving it for publication was Ton Do
A scalable and computationally efficient solution method is proposed to reduce the dimensionality of the continuous-time scheduling and pricing problems and convert them to instances of mixed integer linear programming (MILP) and LP problems
Summary
Evolving electricity markets require fair and accurate pricing methods to maintain market transparency and efficiency and foster competition. Locational marginal price of electricity [1], which represents the power system’s operation cost increment due to incremental changes in nodal loads, is ubiquitously implemented in pricing engines of the market operators [2]–[4]. With the advancements in power systems operation and integration of emerging energy technologies, new challenges are introduced to pricing of electricity encouraging several lines of research to investigate the impact of non-convexities [5]–[9], transmission architecture [10], The associate editor coordinating the review of this manuscript and approving it for publication was Ton Do. market operator’s objective function [11], [12], uncertainty of the renewable resources [13], [14], and data quality [15] on locational marginal prices (LMP). In [5], the non-convexities are priced as
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