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Convex Hull (CH) pricing, used in US electricity markets and raising interest in Europe, is a pricing rule designed to handle markets with non-convexities such as startup costs and minimum up and down times. In such markets, the market…

We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…

Electricity prices in liberalized markets are determined by the supply and demand for electric power, which are in turn driven by various external influences that vary strongly in time. In perfect competition, the merit order principle…

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…

We analyze pricing mechanisms in electricity markets with AC power flow equations that define a nonconvex feasible set for the economic dispatch problem. Specifically, we consider two possible pricing schemes. The first among these prices…

For the case of inflexible demand and considering network constraints, we introduce a Cost Minimisation (CM) based market clearing mechanism, and a model representing the standard Social Welfare Maximisation mechanism used in European Day…

In this paper, we propose a two-stage electricity market framework to explore the participation of distributed energy resources (DERs) in a day-ahead (DA) market and a real-time (RT) market. The objective is to determine the optimal bidding…

Locational Marginal Price (LMP) is a dual variable associated with supply-demand matching and represents the cost of delivering power to a particular location if the load at that location increases. In recent times it become more volatile…

This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer…

Due to its theoretical virtues, several recent works propose the use of the incentive-compatible Vickrey-Clarke-Groves (VCG) mechanism for electricity markets. Coalitions of participants, however, can influence the VCG outcome to obtain…

This paper describes a method for computing price signals for prosumers, incentivizing them to adjust their consumption according to the constraints of the distribution grids to which they are connected, thereby preventing voltage…

Decarbonizing electric grids is a crucial global endeavor in the pursuit of carbon neutrality. Taking carbon emissions from generation into account when pricing electricity usage is an essential way to achieve this goal. However, such…

Some consumers, particularly households, are unwilling to face volatile electricity prices, and they can perceive as unfair price differentiation in the same local area. For these reasons, nodal prices in distribution networks are rarely…

A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing…

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

This paper investigates the feasibility of using a discriminate pricing scheme to offset the inconvenience that is experienced by an energy user (EU) in trading its energy with an energy controller in smart grid. The main objective is to…

Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and…

This study investigates how Multi-Agent Reinforcement Learning (MARL) can improve dynamic pricing strategies in supply chains, particularly in contexts where traditional ERP systems rely on static, rule-based approaches that overlook…

Recently, the volatility associated with marginal prices has increased due to large scale integration of renewable generation. Price volatility is undesirable from a consumer perspective. To address this issue, we present a framework for…