相关论文: Dual first-order methods for efficient computation…

The presence of non-convexities in electricity markets has been an active research area for about two decades. The -- inevitable under current marginal cost pricing -- problem of guaranteeing that no market participant incurs losses in the…

In certain electricity markets, because of non-convexities that arise from their operating characteristics, generators that follow the independent system operator's (ISO's) decisions may fail to recover their cost through sales of energy at…

This paper presents a new dynamic pricing model (a.k.a. real-time pricing) that reflects startup costs of generators. Dynamic pricing, which is a method to control demand by pricing electricity at hourly (or more often) intervals, has been…

Electricity prices determined by economic dispatch that do not consider fixed costs may lead to significant uplift payments. However, when fixed costs are included, prices become non-monotonic with respect to demand, which can adversely…

This paper introduces a computationally efficient comparative approach to classical pricing rules for day-ahead electricity markets, namely Convex Hull Pricing, IP Pricing and European-like market rules, in a Power Exchange setting with…

We consider a general power market with price-sensitive consumer bids and non-convexities originating from supply (start-up and no-load costs, nonzero minimum output limits of generating units, etc.) and demand. The convex hull…

In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…

The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…

In this note we observe that for constrained convex minimization problems $\min_{x \in P}f(x)$ over a polytope $P$, dual prices for the linear program $\min_{z \in P} \nabla f(x) z$ obtained from linearization at approximately optimal…

We consider fixed load power market with non-convexities originating from start-up and no-load costs of generators. The convex hull (minimal uplift) pricing method results in power prices minimizing the total uplift payments to generators,…

We develop a novel randomised block coordinate primal-dual algorithm for a class of non-smooth ill-posed convex programs. Lying in the midway between the celebrated Chambolle-Pock primal-dual algorithm and Tseng's accelerated proximal…

The system operator's scheduling problem in electricity markets, called unit commitment, is a non-convex mixed-integer program. The optimal value function is non-convex, preventing the application of traditional marginal pricing theory to…

The start up costs in many kinds of generators lead to complex cost structures, which in turn yield severe market loopholes in the locational marginal price (LMP) scheme. Convex hull pricing (a.k.a. extended LMP) is proposed to improve the…

Market equilibrium is a solution concept with many applications such as digital ad markets, fair division, and resource sharing. For many classes of utility functions, equilibria can be captured by convex programs. We develop simple…

Synchronous Generators (SGs) currently provide important levels of Short-Circuit Current (SCC), a critical ancillary service that ensures line protections trip during short-circuit faults. Given the ongoing replacement of SGs by…

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

Primal-Dual Hybrid Gradient (PDHG) and Alternating Direction Method of Multipliers (ADMM) are two widely-used first-order optimization methods. They reduce a difficult problem to simple subproblems, so they are easy to implement and have…

Electricity market operators worldwide use mixed-integer linear programming to solve the allocation problem in wholesale electricity markets. Prices are typically determined based on the duals of relaxed versions of this optimization…

We develop a simple yet efficient Lagrangian method for computing equilibrium prices in a mean-field game price-formation model. We prove that equilibrium prices are optimal in terms of a suitable criterion and derive a primal-dual…