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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…
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…
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…
Reducing uplift payments has been a challenging problem for most wholesale markets in US. The main difficulty comes from the unit commitment discrete decision makings. Recently convex hull pricing has shown promises to reduce the uplift…
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…
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,…
The increase of renewables in the grid and the volatility of the load create uncertainties in the day-ahead prices of electricity markets. Adaptive robust optimization (ARO) and stochastic optimization have been used to make commitment and…
A power market with non-convexities may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, the market players are entitled to receive the uplift payments that…
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…
Maintaining the stability of renewable-dominant power systems requires the procurement of virtual inertia services from non-synchronous resources (e.g., batteries, wind turbines) in addition to inertia traditionally provided by synchronous…
We consider the resource allocation problem and its numerical solution. The following constructions are demonstrated: 1) Walrasian price-adjustment mechanism for determining the equilibrium; 2) Decentralized role of the prices; 3) Slater's…
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…
To maintain frequency stability in decarbonized power systems, inertia services from synchronous generators (SGs) and inverter-based resources must be procured. However, designing an inertia-aware system operation poses significant…
In the presence of non-convexities, the power market may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, to achieve an economically stable outcome, the uplift…
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…
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly…
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…
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…
In safety-critical applications, reinforcement learning (RL) needs to consider safety constraints. However, theoretical understandings of constrained RL for continuous control are largely absent. As a case study, this paper presents a…
We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected…