Youfei Liu

Impacts of network constraints on electricity market equilibrium

Nash equilibrium is usually used as the solution of generators strategic bidding in electricity markets. The available literatures have demonstrated by simulation that multiple market equilibria or no pure equilibrium may be induced with the inclusion of network constraints (e.g. transmission constraints). This paper presents a systematical analysis of the impacts of network constraints on the market equilibrium in oligopolistic electricity markets. In our modeling, the ISO dispatches generation and determines nodal prices via solving an OPF problem; and the individual generator optimizes its supply function with Nash-Cournot strategy, after taking into account of the ISOs decision making process on dispatched generation and nodal prices. The conditions for the existence of equilibrium are given, and it is shown that there may be multiple equilibria; and the equilibrium, if exists, will be at a point where generators pay no congestion charge

Generator bidding in oligopolistic electricity markets using optimal control: fundamentals and application

In this paper, optimal control is applied to study generator bidding in an oligopolistic electricity market. The repeated bidding process in (hourly-based) real-time electricity markets is modeled as a dynamic feedback system; an optimal control problem is then formulated to explore individual generators long-term/multiperiod optimization behavior. Particularly in our formulation, the periodic property of the system demand is considered. Several lemmas are included for concerning system stability. Based on the necessary conditions for optimality from the Pontryagin maximum principle, a sweeping method is proposed, and an optimal state-feedback control rule is then obtained via backward induction. Numerical results suggest that the generator who unilaterally applies optimal control for generation decisions will obtain more profits. A sensitivity analysis is also performed, identifying these market factors that affect the performance of optimal control.

Existence, uniqueness, stability of linear supply function equilibrium in electricity markets

In this paper, an explicit mathematic proof is presented on the existence and uniqueness of non-cooperative equilibrium with linear supply functions in electricity markets. A rational adjustment model is proposed for the adjustment dynamics, which can be used to calculate the equilibrium efficiently. Based on the dynamic adjustment model, the equilibrium stability is studied. Some intuitive discussions are given such as how players in the market can find the equilibrium through learning based on the market information. Numerical test results support the analytical conclusions very well.

Control theory application in power market stability analysis

This paper proposes a new framework to model the system dynamics and study the system stability for the quantity bidding competition in power market. From the viewpoint of control theory, the quantity bidding competition is modeled as close-loop dynamic system, where market price is the system feedback signal. Based on the objective of maximizing individual profit in a shot-game, a general dynamic process is given to describe suppliers adjustment behavior, which can be used to model all classical bidding and CV-based bidding strategies. With the application of control theory, sufficient stability conditions and market equilibrium is presented. Computer test results support the analytic conclusion very well.

Optimal control of nonlinear system for generator bidding in deregulated power markets

In this paper, considering generators long-term optimization behavior, the generator bidding problem is studied using optimal control theory. In particular, the system demand is treated as a periodic function, and the competition process is then modeled as a dynamic, nonlinear and feedback system with periodic parameters, where the publicly known market clearing price (MCP) is the system output and the feedback signal, and suppliers outputs are the state variables. A software package MSIER3 for numerically solving the general optimal control problem is used for simulation. The performance of the optimal control is investigated, and a sensitivity analysis of system parameters is done through simulation.

Generator bidding in oligopolistic electricity markets using optimal control: Fundamentals and application

In this paper, optimal control is applied to study generator bidding in an oligopolistic electricity market. The repeated bidding process in (hourly-based) real-time electricity markets is modeled as a dynamic feedback system; an optimal control problem is then formulated to explore individual generators long-term/multiperiod optimization behavior. Particularly in our formulation, the periodic property of the system demand is considered. Several lemmas are included for concerning system stability. Based on the necessary conditions for optimality from the Pontryagin maximum principle, a sweeping method is proposed, and an optimal state-feedback control rule is then obtained via backward induction. Numerical results suggest that the generator who unilaterally applies optimal control for generation decisions will obtain more profits. A sensitivity analysis is also performed, identifying these market factors that affect the performance of optimal control

Transmission rights and generator's strategic bidding in electricity markets

In this paper, the interaction between generators strategic bidding and transmission rights holding is explored. It is shown that holding transmission rights further reconfigures generators strategic behavior and thus influence market equilibrium. It is then demonstrated that holding transmission rights may mitigate generators market power in some situation (with a positive PTDF), whilst exacerbate market power in another situation (with a negative PTDF)