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 which the uncertain constraints are defined via the distributionally robust conditional-value-at-risk. The second one is a scalable robust optimization program that yields an approximate distributionally robust chance-constrained LAED. Numerical experiments on the IEEE 39-bus system with real solar production data and forecasts illustrate the effectiveness of these approaches. We discuss how system operators should tune these techniques in order to seek the desired robustness-performance trade-off and we compare their computational scalability.
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…
Load forecasting is one of the most important and studied topics in modern power systems. Most of the existing researches on day-ahead load forecasting try to build a good model to improve the forecasting accuracy. The forecasted load is then used as the input to generation scheduling with the ultimate goal of minimizing the cost of generation schedules. However, existing day-ahead load forecasting models do not consider this ultimate goal at the training/forecasting stage. This paper proposes a task-based day-ahead load forecasting model labeled as LfEdNet that combines two individual layers …
To address the challenge of the renewable energy uncertainty, the ISO New England (ISO-NE) has proposed to apply do-not-exceed (DNE) limits, which represent the maximum nodal injection of renewable energy the grid can accommodate. Unfortunately, it appears challenging to compute DNE limits that simultaneously maintain the system flexibility and incorporate a large portion of the available renewable energy at the minimum cost. In addition, it is often challenging to accurately estimate the joint probability distribution of the renewable energy. In this paper, we propose a two-stage distribution…
A high number of electric vehicles (EVs) in the transportation sector necessitates an advanced scheduling framework for e-mobility ecosystem operation as a whole in order to overcome range anxiety and create a viable business model for charging stations (CSs). The framework must account for the stochastic nature of all stakeholders' operations, including EV drivers, CSs, and retailers and their mutual interactions. In this paper, a three-layer joint distributionally robust chance-constrained (DRCC) model is proposed to plan grid-to-vehicle (G2V) and vehicle-to-grid (V2G) operation in day-ahead…
We present modeling and analysis of day-ahead spatio-temporal energy markets in which each competitive aggregator aims at making the highest profit by managing a complex mixture of different energy resources, such as conventional generators, storage batteries, and uncertain renewable resources. First, we develop an energy market model in terms of an adjustable robust convex program. This market modeling is novel in the sense that the prosumption cost function of each aggregator, which evaluates the cost to realize an amount of spatio-temporal energy prosumption, is a multi-variable function re…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of stochastic parameters can be inferred from historical data, and then employed to model the set of probability distributions. The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints, and we show that it can be recast as a mixed-integer semidefinite programming (MI-SDP) with finite constraints. The solut…
The Russian wholesale electricity market started to operate in its present form since 2006. Its unique specificity is the AC-based economic dispatch model underlying the market applications. Solution method for the day-ahead and balancing market applications was developed and implemented. Now it is employed by the commercial operator and the system operator of the Russian energy system. It is proved to be an adequate and reliable scheduling market technology
The participation of renewable, energy storage, and resources with limited fuel inventory in electricity markets has created the need for optimal scheduling and pricing across multiple market intervals for resources with intertemporal constraints. In this paper, a new multi-period market model is proposed to enhance the efficiency of markets with such type of resources. It is also the first market design that links a forward market and a spot market through the coordination of schedule and price under the multi-period paradigm, achieving reliability, economic efficiency and dispatch-following …
In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide a tractable reformulation of the proposed distributionally robust chance-constrained…
To effectively enhance the integration of distributed and renewable energy sources in future smart microgrids, economical energy management accounting for the principal challenge of the variable and non-dispatchable renewables is indispensable and of significant importance. Day-ahead economic generation dispatch with demand-side management for a microgrid in islanded mode is considered in this paper. With the goal of limiting the risk of the loss-of-load probability, a joint chance constrained optimization problem is formulated for the optimal multi-period energy scheduling with multiple wind …
We present a distributionally robust optimization (DRO) approach for the transmission expansion planning problem, considering both long- and short-term uncertainties on the system demand and non-dispatchable renewable generation. On the long-term level, as is customary in industry applications, we address the deep uncertainties arising from social and economic transformations, political and environmental issues, and technology disruptions by using long-term scenarios devised by experts. In this setting, many exogenous long-term scenarios containing partial information about the random paramete…
The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for m…
The increasing penetration of Renewable Energy Sources (RES) requires more Flexibility Resources (FR), generally thermal units and storages, must be kept in the system to accommodate the uncertainties from RES. The challenge is how the system can survive when the RES level is very high. In this paper, RESs are considered as full-role market participants. They can bid in the day-ahead market, and the powers they deliver to the market are controllable up to their maximum available powers. Therefore, RESs are effectively dispatchable and can function as FR providers. To integrate dispatchable ren…
Energy storage is a key enabler towards a low-emission electricity system, but requires appropriate dispatch models to be economically coordinated with other generation resources in bulk power systems. This paper analyzes how different dispatch models and bidding strategies would affect the utilization of storage with various durations in deregulated power systems. We use a dynamic programming model to calculate the operation opportunity value of storage from price predictions, and use the opportunity value result as a base for designing market bids. We compare two market bidding and dispatch …
Currently, system operators implement demand response by dispatching controllable loads for economic reasons in day-ahead scheduling. Particularly, demand shifting from peak hours when the cost of electricity is higher to non-peak hours to maintain system reliability by flattening the load profile. However, the system flexibility and economic benefits of such action in post-contingency scenarios are not explicitly considered in short-term operations. Hence, this paper highlights the benefits of demand response as a corrective action for potential post-contingency emergencies in day-ahead sched…
The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem is in e…
This paper studies the behavior of a strategic aggregator offering regulation capacity on behalf of a group of distributed energy resources (DERs, e.g. plug-in electric vehicles) in a power market. Our objective is to maximize the aggregator's revenue while controlling the risk of penalties due to poor service delivery. To achieve this goal, we propose data-driven risk-averse strategies to effectively handle uncertainties in: 1) The DER parameters (e.g., load demands and flexibilities) and 2) sub-hourly regulation signals (to the accuracy of every few seconds). We design both the day-ahead and…
Strategic Pricing in Electricity Markets with Pollution Constraints
Univ. Lille, Inria, CNRS, Centrale Lille（里尔大学、法国国家信息与自动化研究所、法国国家科学研究中心、里尔中央理工学院）；Depto de Ingeniería Matemática and CMM, Universidad de Chile（智利大学数学工程系和CMM）
In this paper, we consider the day-ahead operational planning problem of a radial distribution network hosting Distributed Energy Resources (DERs) including rooftop solar and storage-like loads, such as electric vehicles. We present a novel decomposition method that is based on a centralized AC Optimal Power Flow (AC OPF) problem interacting iteratively with self-dispatching DER problems adapting to real and reactive power Distribution Locational Marginal Costs. We illustrate the applicability and tractability of the proposed method on an actual distribution feeder, while modeling the full com…
