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

Power System Operations with Probabilistic Guarantees

This study is motivated by the fact that uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electrical grids. Among various tools for decision making in uncertain environments, this study focuses on chance-constrained optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-constrained optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. In this work, we provide a detailed tutorial on existing algorithms and a survey of major theoretical results of chance-constrained optimization theory. Data-driven methods, which are not constrained by any specific distributions of the underlying uncertainties, are of particular interest. Built upon chance-constrained optimization, we propose a three-stage power system operation framework with probabilistic guarantees: (1) the optimal unit commitment in the operational planning stage; (2) the optimal reactive power dispatch to address the voltage security issue in the hours-ahead adjustment period; and (3) the secure and reliable power system operation under uncertainties in real time. In the day-ahead operational planning stage, we propose a chance-constrained SCUC (c-SCUC) framework, which ensures that the risk of violating constraints is within an acceptable threshold. Using the scenario approach, c-SCUC is reformulated to the scenario-based SCUC (s-SCUC) problem. By choosing an appropriate number of scenarios, we provide theoretical guarantees on the posterior risk level of the solution to s-SCUC. Inspired by the latest progress of the scenario approach on non-convex problems, we demonstrate the structural properties of general scenario problems and analyze the specific characteristics of s-SCUC. Those characteristics were exploited to benefit the scalability and computational performance of s-SCUC. In the adjustment period, this work first investigates the benefits of look-ahead coordination of both continuous-state and discrete-state reactive power support devices across multiple control areas. The conventional static optimal reactive power dispatch is extended to a “moving-horizon” type formulation for the consideration of spatial and temporal variations. The optimal reactive power dispatch problem is further enhanced with chance constraints by considering the uncertainties from both renewables and contingencies. This chance-constrained optimal reactive power dispatch (c-ORPD) formulation offers system operators an effective tool to schedule voltage support devices such that the system voltage security can be ensured with quantifiable level of risk. Security-constrained Economic Dispatch (SCED) lies at the center of real-time operation of power systems and modern electricity markets. It determines the most cost-efficient output levels of generators while keeping the real-time balance between supply and demand. In this study, we formulate and solve chance-constrained SCED (c-SCED), which ensures system security under uncertainties from renewables. The c-SCED problem also serves as a benchmark problem for a critical comparison of existing algorithms to solve chance-constrained optimization problems

Understanding the LMP-Load Coupling: Theory, Examples and an SVM-Based Data-Driven Approach

This thesis 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. The SPR identification problem is considered from a market participant's viewpoint. Built upon the characteristics of SPRs, this paper proposes a data-driven approach to identifying SPRs. 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. A 3-bus system serves as an illustrative example. SPRs and posterior probabilities are visualized and discussed in details for better understandings. The proposed data-driven approach is also examined on the IEEE 24-bus system and 118-bus system. The simulation results on both systems illustrate that the proposed method is effective, and some computational issues are discussed

Robust Look-ahead Three-phase Balancing of Uncertain Distribution Loads

Increasing penetration of highly variable components such as solar generation and electric vehicle charging loads pose significant challenges to keeping three-phase loads balanced in modern distribution systems. Failure to maintain balance across three phases would lead to asset deterioration and increasing delivery losses. Motivated by the real-world needs to automate and optimize the three-phase balancing decision making, this paper introduces a robust look-ahead optimization framework that pursues balanced phases in the presence of demand-side uncertainties. We show that look-ahead moving window optimization can reduce imbalances among phases at the cost of a limited number of phase swapping operations. Case studies quantify the improvements of the proposed methods compared with conventional deterministic phase balancing. Discussions on possible benefits of the proposed methods and extensions are presented