The ever-increasing integration of stochastic renewable energy sources into power systems operation is making the supply-demand balance more challenging. While joint chance-constrained methods are equipped to model these complexities and uncertainties, solving these models using the traditional iterative solvers is time-consuming and can hinder real-time implementation. To overcome the shortcomings of today's solvers, we propose a fast, scalable, and explainable machine learning-based optimization proxy. Our solution, called Learning to Optimize the Optimization of Joint Chance-Constrained Problems (LOOP-JCCP), is iteration-free and solves the underlying problem in a single-shot. Our model uses a polyhedral reformulation of the original problem to manage constraint violations and ensure solution feasibility across various scenarios through customizable probability settings. To this end, we build on our recent deterministic solution (LOOP-LC 2.0) by incorporating a set aggregator module to handle uncertain sample sets of varying sizes and complexities. Our results verify the feasibility of our near-optimal solutions for joint chance-constrained power dispatch scenarios. Additionally, our feasibility guarantees increase the transparency and interpretability of our method, which is essential for operators to trust the outcomes. We showcase the effectiveness of our model in solving the stochastic energy management problem of Virtual Power Plants (VPPs). Our numerical findings complement our theoretical justifications and demonstrate great flexibility in parameter tuning, adaptability to diverse datasets, and increased computational speed.
The issues of uncertainty and frequency security could become significantly serious in power systems with the high penetration of volatile inverter-based renewables (IBRs). These issues make it necessary to consider the uncertainty and frequency-related constraints in the economic dispatch (ED) programs. However, existing ED studies rarely proactively optimize the control parameters of inverter-based resources related to fast regulation (e.g., virtual inertia and droop coefficients) in cooperation with other dispatchable resources to improve the system frequency security and dispatch reliabili…
This paper considers a security constrained dispatch problem involving generation and line contingencies in the presence of the renewable generation. The uncertainty due to renewables is modeled using joint chance-constraint and the mismatch caused by contingencies and renewables are handled using reserves. We consider a distributionally robust approach to solve the chance-constrained program. We assume that samples of the uncertainty are available. Using them, we construct a set of distributions, termed ambiguity set, containing all distributions that are close to the empirical distribution u…
Economic Load Dispatch depicts a fundamental role in the operation of power systems, as it decreases the environmental load, minimizes the operating cost, and preserves energy resources. The optimal solution to Economic Load Dispatch problems and various constraints can be obtained by evolving several evolutionary and swarm-based algorithms. The major drawback to swarm-based algorithms is premature convergence towards an optimal solution. Fitness Dependent Optimizer is a novel optimization algorithm stimulated by the decision-making and reproductive process of bee swarming. Fitness Dependent O…
This thesis explores a particular class of distributed optimization methods for various separable resource allocation problems, which are of high interest in a wide array of multi-agent settings. A distinctly motivating application for this thesis is real-time power dispatch of distributed energy resources for providing frequency control in a distribution grid or microgrid with high renewable energy penetration. In this application, it is paramount that agent data be shared as sparsely as possible in the interest of conserving user privacy, and it is required that algorithms scale gracefully a…
Reinforcement learning has been found useful in solving optimal power flow (OPF) problems in electric power distribution systems. However, the use of largely model-free reinforcement learning algorithms that completely ignore the physics-based modeling of the power grid compromises the optimizer performance and poses scalability challenges. This paper proposes a novel approach to synergistically combine the physics-based models with learning-based algorithms using imitation learning to solve distribution-level OPF problems. Specifically, we propose imitation learning based improvements in deep…
We consider the problem of look-ahead economic dispatch (LAED) with uncertain renewable energy generation. The goal of this problem is to minimize the cost of conventional energy generation subject to uncertain operational constraints. The risk of violating these constraints must be below a given threshold for a family of probability distributions with characteristics similar to observed past data or predictions. We present two data-driven approaches based on two novel mathematical reformulations of this distributionally robust decision problem. The first one is a tractable convex program in w…
Given the increased percentage of wind power in power systems, chance-constrained optimal power flow (CC-OPF) calculation, as a means to take wind power uncertainty into account with a guaranteed security level, is being promoted. Compared to the local CC-OPF within a regional grid, the global CC-OPF of a multi-regional interconnected grid is able to coordinate across different regions and therefore improve the economic efficiency when integrating high percentage of wind power generation. In this global problem, however, multiple regional independent system operators (ISOs) participate in the …
The development of miniaturized nuclear power (NP) units and the improvement of the carbon trading market provide a new way to realize the low-carbon operation of integrated energy systems (IES). In this study, NP units and carbon trading mechanisms are introduced into the IES to build a new low-carbon scheduling model. In view of the decrease in system operation flexibility caused by the introduction of NP unit, on the one hand, the heating renovation of the NP unit is carried out to make it a cogeneration unit, to expand its operating range and improve its operating flexibility; on the other…
This work presents an optimization framework to aggregate the power and energy flexibilities in an interconnected power distribution systems. The aggregation framework is used to compute the day-ahead dispatch plans of multiple and interconnected distribution grids operating at different voltage levels. Specifically, the proposed framework optimizes the dispatch plan of an upstream medium voltage (MV) grid accounting for the flexibility offered by downstream low voltage (LV) grids and the knowledge of the uncertainties of the stochastic resources. The framework considers grid, i.e., operationa…
Uncertainty in renewable energy generation and load consumption is a great challenge for microgrid operation, especially in islanded mode as the microgrid may be small in size and has limited flexible resources. In this paper, a multi-timescale, two-stage robust unit commitment and economic dispatch model is proposed to optimize the microgrid operation. The first stage is a combination of day-ahead hourly and real-time sub-hourly model, which means the day-ahead dispatch result must also satisfy the real-time condition at the same time. The second stage is to verify the feasibility of the day-…
As renewable energy sources replace traditional power sources (such as thermal generators), uncertainty grows while there are fewer controllable units. To reduce operational risks and avoid frequent real-time emergency controls, a preparatory schedule of renewable generation curtailment is required. This paper proposes a novel two-stage robust generation dispatch (RGD) model, where the preparatory curtailment schedule is optimized in the pre-dispatch stage. The curtailment schedule will then influence the variation range of real-time renewable power output, resulting in a decision-dependent un…
In light of a reliable and resilient power system under extreme weather and natural disasters, networked microgrids integrating local renewable resources have been adopted extensively to supply demands when the main utility experiences blackouts. However, the stochastic nature of renewables and unpredictable contingencies are difficult to address with the deterministic energy management framework. The paper proposes a comprehensive distributionally robust joint chance-constrained (DR-JCC) framework that incorporates microgrid island, power flow, distributed batteries and voltage control constr…
Multi-Transmission Node DER Aggregation: Chance-Constrained Unit Commitment with Bounded Hetero-Dimensional Mixture Model for Uncertain Distribution Factors
针对覆盖多输电节点的 DER 聚合难题，提出基于 BHMM 表征不确定分布因子的机会约束机组组合模型，并以场景随机形式和 Benders 分解求解。
A probabilistic performance-oriented control design optimization approach is introduced for flight systems. Aiming at estimating rare-event probabilities accurately and efficiently, subset simulation is combined with surrogate modeling techniques to improve efficiency. At each level of subset simulation, the samples that are close to the failure domain are employed to construct a surrogate model. The existing surrogate is then refined progressively. In return, seed and sample candidates are screened by the updated surrogate, thus saving a large number of calls to the true model and reducing th…
School of Vehicle and Mobility, Tsinghua University（清华大学车辆与 Mobility学院）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）
Safety is essential for reinforcement learning (RL) applied in real-world situations. Chance constraints are suitable to represent the safety requirements in stochastic systems. Previous chance-constrained RL methods usually have a low convergence rate, or only learn a conservative policy. In this paper, we propose a model-based chance constrained actor-critic (CCAC) algorithm which can efficiently learn a safe and non-conservative policy. Different from existing methods that optimize a conservative lower bound, CCAC directly solves the original chance constrained problems, where the objective…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where the constraints are required to hold for a family of distributions constructed from the observed realizations of the uncertainty via the Wasserstein distance. Our main results establish that if the samples are drawn independently from an underlying distribution and the problems satisfy suitable technical assumptions, then the optimal value and optimizers of …
To manage huge amount of flexible distributed energy resources (DERs) in the distribution networks, the virtual power plant (VPP) is introduced in industry. The VPP can optimally dispatch these resources in a cluster way and provide flexibility for the power system operation as a whole. Most existing works formulate the equivalent power flexibility of the aggregating DERs as deterministic optimization models without considering their uncertainties. In this paper, we introduce the stochastic power flexibility range (PFR) to describe the power flexibility of VPP, which is formulated as a chance …
