Learning the LMP-Load Coupling From Data: A Support Vector Machine Based Approach

This paper investigates the fundamental coupling between loads and locational marginal prices (LMPs) in security-constrained economic dispatch (SCED). Theoretical analysis based on multi-parametric programming theory points out the unique one-to-one mapping between load and LMP vectors. Such one-to-one mapping is depicted by the concept of system pattern region (SPR) and identifying SPRs is the key to understanding the LMP-load coupling. Built upon the characteristics of SPRs, the SPR identification problem is modeled as a classification problem from a market participant's viewpoint, and a Support Vector Machine based data-driven approach is proposed. It is shown that even without the knowledge of system topology and parameters, the SPRs can be estimated by learning from historical load and price data. Visualization and illustration of the proposed data-driven approach are performed on a 3-bus system as well as the IEEE 118-bus system

A Holistic Approach to Forecasting Wholesale Energy Market Prices

Electricity market price predictions enable energy market participants to shape their consumption or supply while meeting their economic and environmental objectives. By utilizing the basic properties of the supply-demand matching process performed by grid operators, known as Optimal Power Flow (OPF), we develop a methodology to recover energy market's structure and predict the resulting nodal prices by using only publicly available data, specifically grid-wide generation type mix, system load, and historical prices. Our methodology uses the latest advancements in statistical learning to cope with high dimensional and sparse real power grid topologies, as well as scarce, public market data, while exploiting structural characteristics of the underlying OPF mechanism. Rigorous validations using the Southwest Power Pool (SPP) market data reveal a strong correlation between the grid level mix and corresponding market prices, resulting in accurate day-ahead predictions of real time prices. The proposed approach demonstrates remarkable proximity to the state-of-the-art industry benchmark while assuming a fully decentralized, market-participant perspective. Finally, we recognize the limitations of the proposed and other evaluated methodologies in predicting large price spike values.Comment: 14 pages, 14 figures. Accepted for publication in IEEE Transactions on Power System

Congestion and Price Prediction in Locational Marginal Pricing Markets Considering Load Variation and Uncertainty

This work investigates the prediction of electricity price and power transmission network congestions under load variation and uncertainty in deregulated power systems. The study is carried out in three stages. In the first stage, the mathematical programming models, which produce the generation dispatch solution, the Locational Marginal Price (LMP), and the system statuses such as transmission congestions, are reviewed. These models are often referred to as Optimal Power Flow (OPF) models, and can be categorized into two major groups: Alternating Current OPF (ACOPF) and Direct Current OPF (DCOPF). Due to the convergence issue with the ACOPF model and the concern of inaccuracy with the DCOPF model, a new DCOPF-based algorithm is proposed, using a fictitious nodal demand (FND) model to represent power losses at each individual line. This is an improvement over the previous work that assigns losses to a few user-defined buses, and is capable of achieving a better tradeoff between computational effectiveness and the accuracy of the results. In the second stage, the solution features are explored for each of the three OPF models to predict critical load levels where a step change of LMP occurs due to the change of binding constraints. After careful examinations of the mathematical relationship of the OPF solutions, nodal prices, and congestions, with respect to load variation, simplex-like method, quadratic interpolation method, and variable substitution method are proposed for each of the three OPF models respectively in order to predict price changes and system congestion. In the last stage, the probabilistic feature of the forecasted LMP is investigated. Due to the step change characteristic of the LMP and uncertainty in load forecasting, the forecasted LMP represents only a certain possibility in a lossless DCOPF framework. Additional possible LMP values exist, other than the deterministically forecasted LMP. Therefore, the concept of Probabilistic LMP is introduced and a systematic approach to quantify the probability of the forecasted LMP, with respect to load variation, is proposed. Similar concepts and methodology have been applied to the ACOPF and FND-based DCOPF frameworks, which can be useful for power market participants in making financial decisions

Probabilistic Forecasting and Simulation of Electricity Markets via Online Dictionary Learning

The problem of probabilistic forecasting and online simulation of real-time electricity market with stochastic generation and demand is considered. By exploiting the parametric structure of the direct current optimal power flow, a new technique based on online dictionary learning (ODL) is proposed. The ODL approach incorporates real-time measurements and historical traces to produce forecasts of joint and marginal probability distributions of future locational marginal prices, power flows, and dispatch levels, conditional on the system state at the time of forecasting. Compared with standard Monte Carlo simulation techniques, the ODL approach offers several orders of magnitude improvement in computation time, making it feasible for online forecasting of market operations. Numerical simulations on large and moderate size power systems illustrate its performance and complexity features and its potential as a tool for system operators

Advanced Studies on Locational Marginal Pricing

The effectiveness and economic aspect of Locational Marginal Price (LMP) formulation to deal with the power trading in both Day-Ahead (DA) and Real-Time (RT) operation are the focus of not only the system operator but also numerous market participants. In addition, with the ever increasing penetration of renewable energy being integrated into the grid, uncertainty plays a larger role in the process of market operation. The study is carried out in four parts. In the first part, the mathematical programming models, which produce the generation dispatch solution for the Ex Post LMP, are reviewed. The existing approach fails to meet the premise that Ex Post LMP should be equal to Ex Ante LMP when all the generation and load combinations in RT operation remain the same as in DA market. Thus, a similar yet effective approach which is based on a scaling factor applied to the Ex Ante dispatch model is proposed. In the second part, the step change characteristic of LMP and the Critical Load Level (CLL) effect are investigated together with the stochastic wind power to evaluate the impacts on the market price volatility. A lookup table based Monte Carlo simulation has been adopted to capture the probabilistic nature of wind power as well as assessing the probabilistic distribution of the price signals. In the third part, a probability-driven, multilayer framework is proposed for ISOs to schedule intermittent wind power and other renewables. The fundamental idea is to view the intermittent renewable energy as a product with a lower quality than dispatchable power plants, from the operator’s viewpoint. The new concept used to handle the scheduling problem with uncertainty greatly relieves the intensive computational burden of the stochastic Unit Commitment (UC) and Economic Dispatch (ED). In the last part, due to the relatively high but similar R/X ratio along the radial distribution feeder, a modified DC power flow approach can be used to simplify the computational effort. In addition, distribution LMP (DLMP) has been formulated to have both real and reactive power price, under the linearized optimal power flow (OPF) model

Bi-Level Optimization Considering Uncertainties of Wind Power and Demand Response

Recently, world-wide power systems have been undergone a paradigm change with increasing penetration of renewable energy. The renewable energy is clean with low operation cost while subject to significant variability and uncertainty. Therefore, integration of renewables presents various challenges in power systems. Meanwhile, to offset the uncertainty from renewables, demand response (DR) has gained considerable research interests because of DR’s flexibility to mitigate the uncertainty from renewables. In this dissertation, various power system problems using bi-level optimization are investigated considering the uncertainties from wind power and demand response. In power system planning, reactive power planning (RPP) under high-penetration wind power is studied in this dissertation. To properly model wind power uncertainty, a multi-scenario framework based on alternating current optimal power flow (ACOPF) considering the voltage stability constraint under the worst wind scenario and transmission N-1 contingency is developed. The objective of RPP in this work is to minimize the VAR investment and the expected generation cost. Benders decomposition is used to solve this model with an upper level problem for VAR allocation optimization and generation cost minimization as a lower problem. Then, several problems related wind power and demand response uncertainties under power market operation are investigated. These include: an efficient and effective method to calculate the LMP intervals under wind uncertainty is proposed; the load serving entities’ strategic bidding through a coupon-based demand response (CBDR) with which a load serving entity (LSE) may participate in the electricity market as strategic bidders by offering CBDR programs to customers; the impact of financial transmission right (FTR) with CBDR programs is also studied from the perspective of LSEs; and the stragegic scheduling of energy storages owned by LSEs considering the impact of charging and discharging on the bus LMP. In these problems, a bi-level optimization framework is presented with various objective functions representing different problems as the upper level problems and the ISO’s economic dispatch (ED) as the lower level problem. The bi-level model is addressed with mathematic program with equilibrium constraints (MPEC) model and mixed-integer linear programming (MILP), which can be easily solved with the available optimization software tool