Asynchronous Lagrangian scenario decomposition

Owing to the massive deployment of renewablepower production units over the last couple of decades, the useof stochastic optimization methods to solve the unit commitmentproblem has gained increasing attention. Solving stochastic unitcommitment problems in large-scale power systems requires high computational power, as stochastic models are dramaticallymore complex than their deterministic counterparts. This paperprovides new insight into the potential of Progressive Hedgingto decrease the solution time of the stochastic unit commitmentproblem with a relatively small trade-off in terms of thesuboptimality of the solution. Computational studies show thatthe run-time is at most half of what is needed to solve theoriginal extensive formulation of the problem, when more thanten wind power scenarios are utilized. These studies demonstrategreat potential for solving real-world stochastic unit commitmentproblems using the Progressive Hedging algorithm.

We develop a Design and Analysis of the Computer Experiments (DACE) approach to the stochastic unit commitment problem for power systems with significant renewable integration. For this purpose, we use a two-stage stochastic programming formulation of the stochastic unit commitment-economic dispatch problem. Typically, a sample average approximation of the true problem is solved using a cutting plane method (such as the L-shaped method) or scenario decomposition (such as Progressive Hedging) algorithms. However, when the number of scenarios increases, these solution methods become computationally prohibitive. To address this challenge, we develop a novel DACE approach that exploits the structure of the first-stage unit commitment decision space in a design of experiments, uses features based upon solar generation, and trains a multivariate adaptive regression splines model to approximate the second stage of the stochastic unit commitment-economic dispatch problem. We conduct experiments on two modified IEEE-57 and IEEE-118 test systems and assess the quality of the solutions obtained from both the DACE and the L-shaped methods in a replicated procedure. The results obtained from this approach attest to the significant improvement in the computational performance of the DACE approach over the traditional L-shaped method.

In this paper, we consider stochastic unit commitment problems where power demand and the output of some generators are random variables. We represent stochastic unit commitment problems in the form of factored Markov decision process models, and propose an approximate algorithm to solve such models. By incorporating a risk component in the cost function, the algorithm can achieve a balance between the operational costs and blackout risks. The proposed algorithm outperformed existing non-stochastic approaches on several problem instances, resulting in both lower risks and operational costs.

Independent System Operators (ISOs) worldwide face the ever-increasing challenge of coping with uncertainties, which requires sophisticated algorithms for solving unit-commitment (UC) problems of increasing complexity in less-and-less time. Hence, decomposition methods are appealing options to produce easier-to-handle problems that can hopefully return good solutions at reasonable times. When applied to two-stage stochastic models, decomposition often yields subproblems that are embarrassingly parallel. Synchronous parallel-computing techniques are applied to the decomposable subproblem and frequently result in considerable time savings. However, due to the inherent run-time differences amongst the subproblem’s optimization models, unequal equipment, and communication overheads, synchronous approaches may underuse the computing resources. Consequently, asynchronous computing constitutes a natural enhancement to existing methods. In this work, we propose a novel extension of the asynchronous level decomposition to solve stochastic hydrothermal UC problems with mixed-integer variables in the first stage. In addition, we combine this novel method with an efficient task allocation to yield an innovative algorithm that far outperforms the current state-of-the-art. We provide convergence analysis of our proposal and assess its computational performance on a testbed consisting of 54 problems from a 46-bus system. Results show that our asynchronous algorithm outperforms its synchronous counterpart in terms of wall-clock computing time in 40% of the problems, providing time savings averaging about 45%, while also reducing the standard deviation of running times over the testbed in the order of 25%.

Time-domain scheduling simulation is the most effective tool for predicting the operational costs in wind-integrated power systems, because it can represent the inter-temporal constraints that limit the balancing actions of the thermal plant, storage, and demand-side measures. High wind penetrations demand just-in-time commitment decisions that reflect the uncertainties in the wind infeed, so that it is desirable to generate the scheduling decisions using stochastic unit commitment (SUC) with rolling planning. However, the computational burden can make such methods impractical in long simulations. We present an efficient formulation of the SUC problem that is designed for use in scheduling simulations of single-bus power systems. Unlike traditional SUC techniques, the proposed formulation uses a quantile-based scenario tree structure that avoids the need for exogenous operating reserves. We compare the performance of various tree topologies in year-long simulations of a large system. Simple quantile-based trees give statistically significant cost improvements over fixed-quantile deterministic methods and compare favorably with trees based on Monte Carlo-generated scenarios.

A Scalable Bounding Method for Multi-Stage Stochastic Integer Programs

Managing solar uncertainty in microgrid systems with stochastic unit commitment

Asynchronous grid computation for American options derivatives

In this paper we are interested in studying the development of parallel algorithms to solve nonlinear wave equations. Both synchronous and asynchronous algorithms contexts are considered. The solver is based on the multisplitting Newton method that provides a coarse-grained scheme. Experiments are carried out in both homogeneous and heterogeneous grid environments. According to the configuration environment, the behaviors of parallel synchronous and asynchronous algorithms are analyzed. Experiments allow us to draw some conclusions about the use of parallel iterative algorithms in grid computing environment.

A high level of renewable resource penetration could lead to displacement of conventional synchronous generators from dispatch, and consequently, reduce the system inertia. The decline in the system inertia will increase the primary frequency response (PFR) need requiring to maintain grid frequency stability. This study proposes a new market design to co‐optimise energy, inertia and PFR while considering uncertainties in renewable energy productions. A full dynamic model of Electric Reliability Council of Texas (ERCOT) interconnection is used to quantify the PFR requirement for the system inertia. The proposed method explicitly incorporates frequency dynamics and uncertainties in energy production from renewable resources in the scheduling process, which is formulated as a stochastic unit commitment problem. A case study of ERCOT grid demonstrated that the proposed stochastic scheduling of energy, inertia and PFR could yield a more cost‐effective solution than the traditional deterministic formulation for the grids with a high penetration of renewable resources.

Scenario tree reductions of multi-period stochastic processes have been used as an important technique in obtaining good approximate solutions of multi-period convex stochastic programs. The scenario reduction step is aimed often at optimal approximation of the underlying stochastic process. We provide a new fast computationally cheap scenario tree reduction procedure and describe its approximation capabilities. Our context is the stochastic Unit Commitment Problem, the stochastic version of a problem that is at the heart of many modern energy markets. Its solution determines wholesale contracts between energy producers and energy consumers a day before actual transactions. We show that the new technique performs better than earlier prescriptions in obtaining approximations to the original program. However, these techniques of approximating only the underlying distributions without attention to the cost functions may produce weaker approximations of the optimal solution value; we provide a couple of illustrations to this point. 1

This paper presents a stochastic cost model and a solution technique for optimal scheduling of the generators in a wind integrated power system considering the demand and wind generation uncertainties. The proposed robust unit commitment solution methodology will help the power system operators in optimal day-ahead planning even with indeterminate information about the wind generation. A particle swarm optimization based scenario generation and reduction algorithm is used for modeling the uncertainties. The stochastic unit commitment problem is solved using a new parameter free self adaptive particle swarm optimization algorithm. The numerical results indicate the low risk involved in day-ahead power system planning when the stochastic model is used instead of the deterministic model.

In Japan, the electric power market has been fully deregulated since April 2016, and many Independent Power Producers have entered the electric power market. Companies participating in the market, conduct transactions between market participants to maximize their profits. When companies consider maximization of their profit, it is necessary to optimize operation of generators in consideration of market transactions. However, it is not easy to consider trading in the market because the market contains many complex and uncertain factors. Even now, the number of participating companies is increasing, and research on operation of generators in consideration of market transactions is an important field. In the power market, there are various markets such as a day-ahead market and an adjustment market, and various transactions are performed between market participants. In this study, we discuss the day-ahead market trading. In the day-ahead market, power prices and demands vary greatly depending on the trends in power sell and purchase bidding. It is necessary for business operators to set operational schedules that takes into account fluctuations in power prices and demand. We consider an optimization model of generator operation considering market transactions and apply stochastic programming to solve the problem. In addition, we show that scheduling based on the stochastic programming method is better than conventional deterministic planning.

Scenario tree reductions of multi-period stochastic processes have been used as an important technique in obtaining good approximate solutions of multi-period convex stochastic programs. The scenario reduction step is aimed often at optimal approximation of the underlying stochastic process. We provide a new fast computationally cheap scenario tree reduction procedure and describe its approximation capabilities. Our context is the stochastic Unit Commitment Problem, the stochastic version of a problem that is at the heart of many modern energy markets. Its solution determines wholesale contracts between energy producers and energy consumers a day before actual transactions. We show that the new technique performs better than earlier prescriptions in obtaining approximations to the original program. However, these techniques of approximating only the underlying distributions without attention to the cost functions may produce weaker approximations of the optimal solution value; we provide a couple of illustrations to this point.

Astochastic, mixed-integer program (MIP) involving joint chance constraints is developed that generates least-cost vehicle redistribution plans for shared-vehicle systems such that a proportion of all near-term demand scenarios are met. The model aims to correct short-term demand asymmetry in shared-vehicle systems, where flow from one station to another is seldom equal to the flow in the opposing direction. The model accounts for demand stochasticity and generates partial redistribution plans in circumstances when demand outstrips supply. This stochastic MIP has a nonconvex feasible region. A novel divide-and-conquer algorithm for generating p-efficient points, used to transform the problem into a set of disjunctive, convex MIPs and handle dual-bounded chance constraints, is proposed. Assuming independence of random demand across stations, a faster cone-generation method is also presented. In a real-world application for a system in Singapore, the potential of redistribution as a fleet management strategy and the value of accounting for inherent stochasticities are demonstrated.