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Xinbo Geng

Publications and source records attributed to Xinbo Geng.

13 recordsLinked to original sources
arXiv2022

Stochastic Uncertainty Propagation in Power System Dynamics using Measure-valued Proximal Recursions

We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm takes advantage of the exact nonlinearity structures in the trajectory-level dynamics of the networked power systems, and is nonparametric. Lifting the dynamics to the space of probability measures allows us to design a scalable algorithm that obviates gridding the underlying high dimensional state space which is computationally prohibitive. The proximal recursion implements a generalized infinite dimensional gradient flow, and evolves probability-weighted scattered point clouds. We clarify the theoretical nuances and algorithmic details specific to the power system nonlinearities, and provide illustrative numerical examples.

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arXiv2021

Two-stage Robust Energy Storage Planning with Probabilistic Guarantees: A Data-driven Approach

This paper addresses a central challenge of jointly considering shorter-term (e.g. hourly) and longer-term (e.g. yearly) uncertainties in power system planning with increasing penetration of renewable and storage resources. In conventional planning decision making, shorter-term (e.g., hourly) variations are not explicitly accounted for. However, given the deepening penetration of variable resources, it is becoming imperative to consider such shorter-term variation in the longer-term planning exercise. By leveraging the abundant amount of operational observation data, we propose a scenario-based robust planning framework that provides rigorous guarantees on the future operation risk of planning decisions considering a broad range of operational conditions, such as renewable generation fluctuations and load variations. By connecting two-stage robust optimization with the scenario approach theory, we show that with a carefully chosen number of scenarios, the operational risk level of the robust solution can be adaptive to the risk preference set by planners. The theoretical guarantees hold true for any distributions, and the proposed approach is scalable towards real-world power grids. Furthermore, the column-and-constraint generation algorithm is used to solve the two-stage robust planning problem and tighten theoretical guarantees. We substantiate this framework through a planning problem of energy storage in a power grid with deep renewable penetration. Case studies are performed on large-scale test systems (modified IEEE 118-bus system) to illustrate the theoretical bounds as well as the scalability of proposed algorithm.

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arXiv2021

Deferrable Load Scheduling under Demand Charge: A Block Model-Predictive Control Approach

Optimal scheduling of deferrable electrical loads can reshape the aggregated load profile to achieve higher operational efficiency and reliability. This paper studies deferrable load scheduling under demand charge that imposes a penalty on the peak consumption over a billing period. Such a terminal cost poses challenges in real-time dispatch when demand forecasts are inaccurate. A block model-predictive control approach is proposed by breaking demand charge into a sequence of stage costs. The problem of charging electric vehicles is used to illustrate the efficacy of the proposed approach. Numerical examples show that the block model-predictive control outperforms benchmark methods in various settings.

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arXiv2020

Probabilistic Hosting Capacity Analysis via Bayesian Optimization

This paper studies the probabilistic hosting capacity analysis (PHCA) problem in distribution networks considering uncertainties from distributed energy resources (DERs) and residential loads. PHCA aims to compute the hosting capacity, which is defined as the maximal level of DERs that can be securely integrated into a distribution network while satisfying operational constraints with high probability. We formulate PHCA as a chance-constrained optimization problem, and model the uncertainties from DERs and loads using historical data. Due to non-convexities and a substantial number of historical scenarios being used, PHCA is often formulated as large-scale nonlinear optimization problem, thus computationally intractable to solve. To address the core computational challenges, we propose a fast and extensible framework to solve PHCA based on Bayesian Optimization (BayesOpt). Comparing with state-of-the-art algorithms such as interior point and active set, numerical results show that the proposed BayesOpt approach is able to find better solutions (25% higher hosting capacity) with 70% savings in computation time on average.

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arXiv2020

Computing Essential Sets for Convex and Non-convex Scenario Problems: Theory and Application

The scenario approach is a general data-driven algorithm to chance-constrained optimization. It seeks the optimal solution that is feasible to a carefully chosen number of scenarios. A crucial step in the scenario approach is to compute the cardinality of essential sets, which is the smallest subset of scenarios that determine the optimal solution. This paper addresses the challenge of efficiently identifying essential sets. For convex problems, we demonstrate that the sparsest dual solution of the scenario problem could pinpoint the essential set. For non-convex problems, we show that two simple algorithms return the essential set when the scenario problem is non-degenerate. Finally, we illustrate the theoretical results and computational algorithms on security-constrained unit commitment (SCUC) in power systems. In particular, case studies of chance-constrained SCUC are performed in the IEEE 118-bus system. Numerical results suggest that the scenario approach could be an attractive solution to practical power system applications.

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arXiv2019

Chance-constrained Unit Commitment via the Scenario Approach

Keeping the balance between supply and demand is a fundamental task in power system operational planning practices. This task becomes particularly challenging due to the deepening penetration of renewable energy resources, which induces a significant amount of uncertainties. In this paper, we propose a chance-constrained Unit Commitment (c-UC) framework to tackle challenges from uncertainties of renewables. The proposed c-UC framework seeks cost-efficient scheduling of generators while ensuring operation constraints with guaranteed probability. We show that the scenario approach can be used to solve c-UC despite of the non-convexity from binary decision variables. We reveal the salient structural properties of c-UC, which could significantly reduce the sample complexity required by the scenario approach and speed up computation. Case studies are performed on a modified 118-bus system.

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arXiv2019

Data-driven Decision Making with Probabilistic Guarantees (Part 2): Applications of Chance-constrained Optimization in Power Systems

Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper 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. Part I of this two-part paper reviews three categories of existing methods to chance-constrained optimization: (1) scenario approach; (2) sample average approximation; and (3) robust optimization based methods. Data-driven methods, which are not constrained by any particular distributions of the underlying uncertainties, are of particular interest. Part II of this two-part paper provides a literature review on the applications of chance-constrained optimization in power systems. Part II also provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system test cases.

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arXiv2019

Data-driven Decision Making with Probabilistic Guarantees (Part 1): A Schematic Overview of Chance-constrained Optimization

Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper 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. Part I of this two-part paper reviews three categories of existing methods to chance-constrained optimization: (1) scenario approach; (2) sample average approximation; and (3) robust optimization based methods. Data-driven methods, which are not constrained by any particular distributions of the underlying uncertainties, are of particular interest. Part II of this two-part paper provides a literature review on the applications of chance-constrained optimization in power systems. Part II also provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system test cases.

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arXiv2018

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.

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arXiv2018

Optimal Power Consumption for Demand Response of Thermostatically Controlled Loads

We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads. This is motivated by the problem of synthesizing the demand response for a load serving entity (LSE) serving a population of such customers. We show how the LSE can opportunistically design the aggregate reference consumption to minimize its energy procurement cost, given day-ahead price, load and ambient temperature forecasts, while respecting each individual load's comfort range constraints. The resulting synthesis problem is shown to be amenable to optimal control techniques, but computationally difficult otherwise. Numerical simulations elucidate how the LSE can use the optimal aggregate power consumption trajectory thus computed, for the purpose of demand response.

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arXiv2018

Mean Field Games in Nudge Systems for Societal Networks

We consider the general problem of resource sharing in societal networks, consisting of interconnected communication, transportation, energy and other networks important to the functioning of society. Participants in such network need to take decisions daily, both on the quantity of resources to use as well as the periods of usage. With this in mind, we discuss the problem of incentivizing users to behave in such a way that society as a whole benefits. In order to perceive societal level impact, such incentives may take the form of rewarding users with lottery tickets based on good behavior, and periodically conducting a lottery to translate these tickets into real rewards. We will pose the user decision problem as a mean field game (MFG), and the incentives question as one of trying to select a good mean field equilibrium (MFE). In such a framework, each agent (a participant in the societal network) takes a decision based on an assumed distribution of actions of his/her competitors, and the incentives provided by the social planner. The system is said to be at MFE if the agent's action is a sample drawn from the assumed distribution. We will show the existence of such an MFE under different settings, and also illustrate how to choose an attractive equilibrium using as an example demand-response in energy networks.

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arXiv2016

Architecture and Algorithms for Privacy Preserving Thermal Inertial Load Management by A Load Serving Entity

Motivated by the growing importance of demand response in modern power system's operations, we propose an architecture and supporting algorithms for privacy preserving thermal inertial load management as a service provided by the load serving entity (LSE). We focus on an LSE managing a population of its customers' air conditioners, and propose a contractual model where the LSE guarantees quality of service to each customer in terms of keeping their indoor temperature trajectories within respective bands around the desired individual comfort temperatures. We show how the LSE can price the contracts differentiated by the flexibility embodied by the width of the specified bands. We address architectural questions of (i) how the LSE can strategize its energy procurement based on price and ambient temperature forecasts, (ii) how an LSE can close the real time control loop at the aggregate level while providing individual comfort guarantees to loads, without ever measuring the states of an air conditioner for privacy reasons. Control algorithms to enable our proposed architecture are given, and their efficacy is demonstrated on real data.

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arXiv2016

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.

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