Multi-Stage Stochastic Programming For Condition-Based Power System Maintenance Scheduling

Within the context of condition-based maintenance,making equipment maintenance decision from the perspective of system operation,namely condition-based power system maintenance scheduling(in this paper,power system refers to the systems with power background,such as power generation system,power transmission system,power generation and transmission system,power distribution system),can make full use of equipment condition information from system decision-making level and maximize the potential of equipment condition monitoring and evaluation technology at the decision-making application level,which has important theoretical and practical significance for improving the equipment asset management and operating reliability of the power system.The current condition-based power system maintenance scheduling model obtains a fixed maintenance scheduling in the planning horizon,which lacks a response strategy for the potential new equipment condition information.These models are reasonable within the context of offline monitoring because the obtained condition information is limited and therefore it is impossible to make a complete maintenance strategy.However,the equipment condition monitoring technology is developing from offline monitoring to online monitoring rapidly,which makes that the gradual realization process of equipment condition can be continuously observed during the planning horizon.The impact on the decision-making application level is that the amount of available condition information during the planning horizon will increase dramatically,which provides a basis for formulating a complete maintenance strategy.From the perspective of stochastic optimization theory,the current condition-based power system maintenance scheduling model belongs to two-stage stochastic optimization,in which the first-stage maintenance decision needs to be made before the realization of the uncertainty in the planning horizon.To obtain a power system maintenance strategy which is adaptive to the gradual realization of the observable equipment condition during the planning horizon,it is necessary to research the condition-based power system maintenance scheduling problem under the framework of multi-stage stochastic programming theory.To this end,we focus on the multi-stage stochastic programming for condition-based power system maintenance scheduling.The purpose is to apply the multi-stage stochastic programming theory to the condition-based power system maintenance scheduling within the context of online condition monitoring,which can obtain a power system maintenance strategy.The strategy is adaptive to the observable condition dynamics,which can fully take advantage of online condition monitoring and improve the efficiency of maintenance scheduling.Therefore,it can improve power system asset management and operating reliability.The contributions of this paper are as follows:(1)The problem formulation of multi-stage stochastic programming for condition-based power system maintenance scheduling is introduced.Firstly,the multi-stage stochastic optimization theory is introduced.Then,the problem formulation of the multi-stage stochastic programming for condition-based power system maintenance scheduling is introduced,which contains four parts:1)two decision-making problems are constructed,including maintenance decision-making and operation decision-making;2)the multi-stage decision process is established;3)the multi-stage stochastic programming model is formulated;4)the rolling decision-making framework is considered.The problem formulation lays a theoretical foundation for the specific works below.(2)A two-stage robust-stochastic optimization model for condition-based power system maintenance scheduling with N-K security criterion is proposed.The proposed method aims to minimize the sum of preventive costs and expected corrective maintenance costs over the planning horizon while satisfying N-K security criterion in each period.To tackle the computational intractability of enumerating contingencies,we propose a two-stage robust optimization framework embedded with a stochastic maintenance optimization,namely the two-stage robust-stochastic optimization.The first-stage problem determines sequential maintenance schedules of all periods,and the second-stage problem determines non-sequential dispatch decisions separately in periods.The column-and-constraint generation procedure is employed to solve the problem.To accelerate the convergence,we propose an enhanced procedure that generates additional valid variables and constraints in each iteration.Finally,two case studies are presented to verify the validity of the proposed method.(3)A multi-stage stochastic optimization model based on the maintenance threshold decision rule is proposed.To prevent the scenarios in which the failure occurs before the prescheduled maintenance task,we introduce the concept of maintenance threshold into the existing two-stage stochastic optimization model.The maintenance threshold decision rule consists of the maintenance threshold and the prescheduled maintenance task,which establishes a mapping from the states to maintenance decisions.Therefore,the maintenance threshold decision rule can capture the dynamics of unfolding uncertainties over time and adjust decisions dynamically,which improve the existing two-stage stochastic optimization model to the multi-stage stochastic optimization model.When the state measurement of a device is identified to reach the maintenance threshold,the prescheduled maintenance task should be executed ahead of time to prevent failures.Based on this,the expected equipment corrective maintenance cost and the expected system interruption cost considering prescheduled maintenance tasks and maintenance thresholds are expressed.Then,an optimization model is formulated to minimize the sum of the expected equipment corrective maintenance cost and the expected system interruption cost through co-optimizing prescheduled maintenance tasks and maintenance thresholds.Furthermore,a decomposition algorithm based on genetic algorithm is designed to solve the optimization model.Finally,two case studies are presented to verify the validity of the proposed method.(4)An adaptive multi-stage stochastic model is proposed.The model aims to provide a maintenance strategy which is not restricted by any decision rules and adaptive to the dynamics of unfolding uncertainties over time.Firstly,we establish the complete adaptive multi-stage stochastic programming based on the multi-stage decision process.The proposed model needs to provide a decision in each node of the scenario tree,which is computationally intractable.To tackle the computational intractability,we reconstruct the problem in the Markov decision process form,which avoids providing decisions based on the nodes.However,it suffers the well-known the curses of dimensionality.To avoid the curses,we employ approximate dynamic programming,which contains four steps:1)reconstruction using post-decision state variable;2)forward dynamic programming;3)Using the sample outcome space to substitute the true outcome space;4)value function approximation.Finally,three case studies are presented to verify the validity of the proposed method.