David Pozo

A Three-Level Static MILP Model for Generation and Transmission Expansion Planning

We present a three-level equilibrium model for the expansion of an electric network. The lower-level model represents the equilibrium of a pool-based market; the intermediate level represents the Nash equilibrium in generation capacity expansion, taking into account the outcomes on the spot market; and the upper-level model represents the anticipation of transmission expansion planning to the investment in generation capacity and the pool-based market equilibrium. The demand has been considered as exogenous and locational marginal prices are obtained as endogenous variables of the model. The three-level model is formulated as a mixed integer linear programming (MILP) problem. The model is applied to a realistic power system in Chile to illustrate the methodology and proper conclusions are reached.

A Chance-Constrained Unit Commitment With an

This paper presents a new approach for the joint energy and reserves scheduling and unit commitment with n-K reliability constraints for the day-ahead market. The proposed method includes a novel n-K criterion where demand must be met with a specified probability under any simultaneous loss of K generating units. A chance-constrained method is proposed with an α-quantile measure to determine the confidence level to meet the demand under K simultaneous contingencies. The chance-constrained optimization problem is recast as a mixed integer linear programming optimization problem. Wind and demand uncertainty are included into the model. The methodology proposed is illustrated with several case studies where the effect of increasing wind power penetration is analyzed showing the performance of our model.

n-K

Intermittence and variability of renewable resources is often a barrier to their large scale integration into power systems. We propose a stochastic real-time unit commitment to deal with the stochasticity and intermittence of non-dispatchable renewable resources including ideal and generic energy storage devices. Firstly, we present a mathematical definition of an ideal and generic storage device. This storage device definition has some mathematical advantages: 1) it can be easily integrated within complex optimization problems, 2) it can be modeled using linear programming, suitable for practical large-scale cases. Secondly, a stochastic unit commitment with ideal and generic storage devices and intermittent generation is proposed to solve the joint energy-and-reserves scheduling and real-time power balance problem, reflecting the minute-by-minute intermittent changes and the stochasticity of renewable resources. We also compare our results with those obtained using a deterministic unit commitment with perfect information. The proposed model is illustrated with a 24-bus system.

Security Criterion and Significant Wind Generation

A mixed integer nonlinear programming (MINLP) model for scheduling of the short-term integrated operation of a series of price-taker hydroelectric plants (H-GENCO) along a cascaded reservoir system in a pool-based electricity market is presented. The objective of the H-GENCO can be either to maximize profit, taking into account technical efficiency, or to maximize technical efficiency, maintaining a profit level. In both cases, the efficiency can be accurately obtained using the “Hill diagram” supplied by turbine manufacturers. A multiple nonlinear regression analysis of the units technical efficiency is estimated as a quadratic function of net head and water discharge. Several case studies of realistic dimensions are described, where results indicate that a profit-based MINLP produces better results compared to an MILP model, on the other hand, higher efficiencies and water savings are obtained in the efficiency-based model.

Unit Commitment With Ideal and Generic Energy Storage Units

Summary form only given. Intermittence and variability of renewable resources is often a barrier to their large scale integration into power systems. We propose a stochastic real-time unit commitment to deal with the stochasticity and intermittence of non-dispatchable renewable resources including ideal and generic energy storage devices. Firstly, we present a mathematical definition of an ideal and generic storage device. This storage device definition has some mathematical advantages: 1) it can be easily integrated within complex optimization problems, 2) it can be modeled using linear programming, suitable for practical large-scale cases. Secondly, a stochastic unit commitment with ideal and generic storage devices and intermittent generation is proposed to solve the joint energy-and-reserves scheduling and real-time power balance problem, reflecting the minute-by-minute intermittent changes and the stochasticity of renewable resources. We also compare our results with those obtained using a deterministic unit commitment with perfect information. The proposed model is illustrated with a 24-bus system.

Optimal Scheduling of a Price-Taker Cascaded Reservoir System in a Pool-Based Electricity Market

We present a compact formulation to find all pure Nash equilibria in a pool-based electricity market with stochastic demands. The equilibrium model is formulated as a stochastic equilibrium problem subject to equilibrium constraints (EPEC). The problem is based on a Stackelberg game where the generating companies (GENCOs) optimize their strategic bids anticipating the solution of the independent system operator (ISO) market clearing. A finite strategy approach both in prices and quantities is applied to transform the nonlinear and nonconvex set of Nash inequalities into a mixed integer linear problem (MILP). A procedure to find all Nash equilibria is developed by generating “holes” that are added as linear constraints to the feasibility region. The result of the problem is the set of all pure Nash equilibria and the market clearing prices and assigned energies by the ISO. A case study illustrates the methodology and proper conclusions are reached.

Unit commitment with ideal and generic energy storage units

In competitive electricity markets, companies simultaneously offer their productions to obtain the maximum profits on a daily basis. In the long run, the strategies utilized by the electric companies lead to various long-term equilibria that can be analyzed with the appropriate tools. We present a methodology to find plausible long-term Nash equilibria in pool-based electricity markets. The methodology is based on an iterative market Nash equilibrium model in which the companies can decide upon their offer strategies. An exponential smoothing of the bids submitted by the companies is applied to facilitate the convergence of the iterative procedure. We introduce the concept of meta-game equilibrium strategies to allow companies to have a range of offer strategies where several pure and mixed meta-game Nash equilibria are possible. The application of the proposed methodology is illustrated with a realistic case study to illustrate the effect on equilibria, prices and profits of different offer strategies and coalitions of generating companies. Pure and mixed Nash equilibria for short- and long-term periods are obtained and discussed.

Finding Multiple Nash Equilibria in Pool-Based Markets: A Stochastic EPEC Approach

Decision making in the operation and planning of power systems is, in general, economically driven, especially in deregulated markets. To better understand the participants’ behavior in power markets, it is necessary to include concepts of microeconomics and operations research in the analysis of power systems. Particularly, game theory equilibrium models have played an important role in shaping participants’ behavior and their interactions. In recent years, bilevel games and their applications to power systems have received growing attention. Bilevel optimization models, Mathematical Program with Equilibrium Constraints and Equilibrium Problem with Equilibrium Constraints are examples of bilevel games. This paper provides an overview of the full range of formulations of non-cooperative bilevel games. Our aim is to present, in an unified manner, the theoretical foundations, classification and main techniques for solving bilevel games and their applications to power systems.

Short- and long-term Nash equilibria in electricity markets

We present a three-level equilibrium model for the expansion of an electric network. The lower-levelmodel represents the equilibrium of a pool-based market; the intermediate level represents the Nash equilibrium in generation capacity expansion, taking into account the outcomes on the spot market; and the upper-level model represents the anticipation of transmission expansion planning to the investment in generation capacity and the pool-based market equilibrium. The demand has been considered as exogenous and locational marginal prices are obtained as endogenous variables of the model. The three-level model is formulated as a mixed integer linear programming (MILP) problem. The model is applied to a realistic power system in Chile to illustrate the methodology and proper conclusions are reached.

Basic theoretical foundations and insights on bilevel models and their applications to power systems

This paper proposes a risk-based mixed integer quadratically-constrained programming model for the long-term VAr planning problem. Risk aversion is included in the proposed model by means of regret-based optimization to quantify the load shedding risk because of a reactive power deficit. The expected operation and expansion costs of new installed reactive power sources and load shedding risk are jointly minimized. Uncertainty in the active and reactive load demands has been included in the model. An