A Joint Chance-Constrained Stochastic Programming Approach for the Integrated Predictive Maintenance and Operations Scheduling Problem in Power Systems
Bahar Cennet Okumusoglu, Beste Basciftci, Burak Kocuk
Maintenance planning plays a key role in power system operations under uncertainty by helping system operators ensure a reliable and secure power grid. This paper studies a short-term condition-based integrated maintenance planning with operations scheduling problem while considering the unexpected failure possibilities of generators as well as transmission lines. We formulate this problem as a two-stage stochastic mixed-integer program with failure scenarios sampled from the sensor-driven remaining lifetime distributions of the individual system elements whereas a joint chance-constraint consisting of Poisson Binomial random variables is introduced to account for failure risks. Because of its intractability, we develop a cutting-plane method to obtain an exact reformulation of the joint chance-constraint by proposing a separation subroutine and deriving stronger cuts as part of this procedure. To solve large-scale instances, we derive a second-order cone programming based safe approximation of this constraint. Furthermore, we propose a decomposition-based algorithm implemented in parallel fashion for solving the resulting stochastic program, by exploiting the features of the integer L-shaped method and the special structure of the maintenance and operations scheduling problem to derive stronger optimality cuts. We further present preprocessing steps over transmission line flow constraints to identify redundancies. To illustrate the computational performance and efficiency of our algorithm compared to more conventional maintenance approaches, we design a computational study focusing on a weekly plan with daily maintenance and hourly operational decisions involving detailed unit commitment subproblems. Our computational results on various IEEE instances demonstrate the computational efficiency of the proposed approach with reliable and cost-effective maintenance and operational schedules.
This paper considers the simultaneous high-speed train assignment and maintenance scheduling problem. For the maintenance scheduling module, our focus is the second-level maintenance, which is carried out once a month on average. We propose a binary non-linear programming model to mathematically describe the problem. The objective aims to minimize the mileage losses for all high-speed trains and the constraints cover various operational requirements and capacity restrictions. To model the difficult operational requirements, a novel cumulative mileage update function is developed; meanwhile, to…
During the life of a wind farm, various types of costs arise. A large share of the operational cost for a wind farm is due to maintenance of the wind turbine equipment; these costs are especially pronounced for offshore wind farms and provide business opportunities in the wind energy industry. An effective scheduling of the maintenance activities may reduce the costs related to maintenance. We combine mathematical modelling of preventive maintenance scheduling with corrective maintenance strategies. We further consider different types of contracts between the wind farm owner and a maintenance …
We suggest a mathematical model for computing and regularly updating the next preventive maintenance plan for a wind farm. Our optimization criterium takes into account the current ages of the key components, the major maintenance costs including eventual energy production losses as well as the available data monitoring the condition of the wind turbines. We illustrate our approach with a case study based on data collected from several wind farms located in Sweden. Our results show that preventive maintenance planning gives some effect, if the wind turbine components in question live significa…
We consider a problem concerning a network and a set of maintenance requests to be undertaken. We wish to schedule the maintenance in such a way as to minimise the impact on the total throughput of the network. We apply disaggregated Benders cuts and lazy constraints to solve the problem to optimality, as well as exploring the strengths and weaknesses of the technique. We prove that our Benders cuts are pareto optimal. Solutions to the LP relaxation also provide further valid inequalities to reduce total solve time. We implement these techniques on simulated data presented in previous papers, …
We consider a problem that marries network flows and scheduling, motivated by the need to schedule maintenance activities in infrastructure networks, such as rail or general logistics networks. Network elements must undergo regular preventive maintenance, shutting down the arc for the duration of the activity. Careful coordination of these arc maintenance jobs can dramatically reduce the impact of such shutdown jobs on the flow carried by the network. Scheduling such jobs between given release dates and deadlines so as to maximize the total flow over time presents an intriguing case to study t…
Optimizing maintenance scheduling is a major issue to improve the performance of hydropower plants. We study a system of several physical components of the same family: either a set of turbines, a set of transformers or a set of generators. The components share a common stock of spare parts and experience random failures that occur according to known failure distributions. We seek a deterministic preventive maintenance strategy that minimizes an expected cost depending on maintenance and forced outages of the system. The Auxiliary Problem Principle is used to decompose the original large-scale…
This paper proposes a dynamic game-based maintenance scheduling mechanism for the asset owners of the natural gas grid and the power grid by using a bilevel approach. In the upper level, the asset owners of the natural gas grid and the power grid schedule maintenance to maximize their own revenues. This level is modeled as a dynamic game problem, which is solved by the backward induction algorithm. In the lower level, the independent system operator (ISO) dispatches the system to minimize the loss of power load and natural gas load in consideration of the system operating conditions under main…
A large part of the operational cost for a wind power farm is due to the cost of equipment maintenance, especially for offshore wind farms. How to reduce the maintenance cost, and hence increase profitability, is this article's focus. It presents a binary linear optimization model whose solution may suggest the wind turbine owners which components, and when, should undergo the next preventive maintenance (PM) replacements. The suggested short-term scheduling strategy takes into account eventual failure events of the multi-component system, in that after the failed system is repaired, the previ…
The approach presented in this article is a contribution to research relating to the optimization of the scheduling of the spots of maintenance. This work answers the following objectives: Decision in time-reality (planning and scheduling), Allowance/assignment of resources, To ensure a minimum availability required, To minimize times delay while inserting the dynamic tasks "corrective maintenance"
Due to increasing railway use, the capacity at railway yards and maintenance locations is becoming limiting. Therefore, the scheduling of rolling stock maintenance and the choice regarding optimal locations to perform maintenance is increasingly complicated. This research introduces a Maintenance Scheduling and Location Choice Problem (MSLCP). It simultaneously determines maintenance locations and maintenance schedules of rolling stock, while it also considers the available capacity of maintenance locations, measured in the number of available teams. To solve the MSLCP, an optimization framewo…
Wind power is one of the most important sources of renewable energy. A large part of the wind energy cost is due to the cost of maintaining the wind power equipment. To further reduce the maintenance cost, one can improve the design of the wind turbine components. One can also reduce the maintenance costs by optimal scheduling of the component replacements. The latter task is the main motivation for this paper. When a wind turbine component fails to function, it might need to be replaced under less than ideal circumstances. This is known as corrective maintenance. To minimize the unnecessary c…
We investigate a novel scheduling problem which is motivated by an application in the Australian railway industry. Given a set of maintenance jobs and a set of train paths over a railway corridor with bidirectional traffic, we seek a schedule of jobs such that a minimum number of train paths are cancelled due to conflict with the job schedule. We show that the problem is NP-complete in general. In a special case of the problem when every job under any schedule just affects one train path, and the speed of trains is bounded from above and below, we show that the problem can be solved in polynom…
Despite the promising outlook, the numerous economic and environmental benefits of offshore wind energy are still compromised by its high operations and maintenance (O&M) expenditures. On one hand, offshore-specific challenges such as site remoteness, harsh weather, transportation requirements, and production losses, significantly inflate the O&M costs relative to land-based wind farms. On the other hand, the uncertainties in weather conditions, asset degradation, and electricity prices largely constrain the farm operator's ability to identify the time windows at which maintenance is possible,…
The integration of distributed renewable generation (DRG) in distribution networks can be effectively promoted by scheduling flexible resources such as heating, ventilation, and air conditioning (HVAC) loads. However, finding the optimal scheduling for them is nontrivial because DRG outputs are highly uncertain. To address this issue, this paper proposes a learning-based joint chance-constrained approach to coordinate HVAC loads with DRG. Unlike cutting-edge works adopting individual chance constraints to manage uncertainties, this paper controls the violation probability of all critical const…
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…
Behind the concept of Industry 4.0, there are a number of principles and ideas; one of them is the integration of problems of different decision levels. In this work, we integrate maintenance with planning problems, aiming to take full advantage of the production capacity providing immediate delivery of products to customers and avoiding failures. We propose a hybrid approach for solving a maintenance problem integrated with the lot-sizing and scheduling problems. The approach is based on the concepts of robustness and simheuristics, considering preventive, predictive and corrective maintenanc…
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 …
Redox Flow Batteries are a promising option for large-scale stationary energy storage. The vanadium redox flow battery is the most widely commercialized system thanks to its chemical stability and performance. This work aims to optimize the scheduling of a vanadium flow battery that stores energy produced by a renewable power plant, keeping into account a thorough characterization of the battery performance, with variable efficiencies and capacity fade effects. A detailed characterization of the battery performance improves the calculation of the optimal number of cycles and revenue associated…
Power systems are shifted from conventional bulk generation toward renewable generation. This trend leads to the frequency security problem due to the decline of system inertia. On the other hand, natural gas-fired units are frequently scheduled to provide operational flexibility due to their fast adjustment ability. The interdependence between power and natural gas systems is thus intensified. In this paper, we study the frequency constrained scheduling problem from the perspective of an integrated electricity-gas system under variable wind power. We propose a distributionally robust (DR) cha…
This paper presents a techno-economic optimisation tool to study how the power system expansion decisions can be taken in a more economical and efficient way, by minimising the consequent costs of network reinforcement and reconfiguration. Analyses are performed to investigate how the network reinforcement and reconfiguration should be planned, within a time horizon of several years, by continuously keeping the network feasibility and ability to satisfy the load. The main contribution of this study is the inclusion of key features within the mathematical model to enhance the investment decisio…
The number of cancer cases per year is rapidly increasing worldwide. In radiation therapy (RT), radiation from linear accelerators is used to kill malignant tumor cells. Scheduling patients for RT is difficult both due to the numerous medical and technical constraints, and because of the stochastic inflow of patients with different urgency levels. In this paper, a Column Generation (CG) approach is proposed for the RT patient scheduling problem. The model includes all the constraints necessary for the generated schedules to work in practice, including for example different machine compatibilit…
By modeling the uncertainty of spinning reserves provided by energy storage with probabilistic constraints, a new optimal scheduling mode is proposed for minimizing the operating costs of an isolated microgrid (MG) by using chance-constrained programming. The model is transformed into a readily solvable mixed integer linear programming (MILP) formulation in GAMS via a proposed discretized step transformation (DST) approach and finally solved by applying the CPLEX solver. By properly setting the confidence levels of the spinning reserve probability constraints, the MG operation can be achieved …
Insufficient flexibility in system operation caused by traditional "heat-set" operating modes of combined heat and power (CHP) units in winter heating periods is a key issue that limits renewable energy consumption. In order to reduce the curtailment of renewable energy resources through improving the operational flexibility, a novel optimal scheduling model based on chance-constrained programming (CCP), aiming at minimizing the lowest generation cost, is proposed for a small-scale integrated energy system (IES) with CHP units, thermal power units, renewable generations and representative auxi…
Microsoft Research（微软研究院）；Peking University（北京大学）；Microsoft 365（微软365）；Microsoft Azure（微软Azure）
This paper investigates a critical resource allocation problem in the first party cloud: scheduling containers to machines. There are tens of services and each service runs a set of homogeneous containers with dynamic resource usage; containers of a service are scheduled daily in a batch fashion. This problem can be naturally formulated as Stochastic Bin Packing Problem (SBPP). However, traditional SBPP research often focuses on cases of empty machines, whose objective, i.e., to minimize the number of used machines, is not well-defined for the more common reality with nonempty machines. This p…
In this paper, we present a novel approach for solving a maintenance scheduling problem from the French electricity grid company RTE, as presented in the ROADEF 2020 challenge. Our approach combines constraint generation with a new family of cutting planes to address the nonconvexity of the problem. We provide mathematical proofs and separation algorithms for the cutting planes and study the practical impact of our approach on the challenge instances. This method is applicable to a wide range of problems involving the modeling of uncertainty, and is shown to improve results significantly on re…
The community integrated energy system (CIES) is an essential energy internet carrier that has recently been the focus of much attention. A scheduling model based on chance-constrained programming is proposed for integrated demand response (IDR)-enabled CIES in uncertain environments to minimize the system operating costs, where an IDR program is used to explore the potential interaction ability of electricity-gas-heat flexible loads and electric vehicles. Moreover, power to gas (P2G) and micro-gas turbine (MT), as links of multi-energy carriers, are adopted to strengthen the coupling of diffe…
Polytechnique Montréal（蒙特利尔理工学院）；GERAD（GERAD 运筹学研究中心）；Canada Excellence Research Chair in Data Science for Real-Time Decision-Making, Polytechnique Montréal（加拿大数据科学实时决策卓越研究教席，蒙特利尔理工学院）
Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is divided between these two parts. In routing or scheduling applications, the problems are mostly defined on a network, and the PP is usually an NP-hard shortest path problem with resource constraints. In this work, we propose a new heuristic pricing algorithm based on machine learning. By taking advantage of the data collected during previous executions, the ob…
