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Register a new userCondition-based maintenance at both scheduled and unscheduled opportunities
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Motivated by original equipment manufacturer (OEM) service and maintenance practices we consider a single component subject to replacements at failure instances and two types of preventive maintenance opportunities: scheduled, which occur due to periodic system reviews of the equipment, and unscheduled, which occur due to failures of other components in the system. Modelling the state of the component appropriately and incorporating a realistic cost structure for corrective maintenance as well as condition-based maintenance (CBM), we derive the optimal CBM policy. In particular, we show that the optimal long-run average cost policy for the model at hand is a control-limit policy, where the control limit depends on the time until the next scheduled opportunity. Furthermore, we explicitly calculate the long-run average cost for any given control-limit time dependent policy and compare various policies numerically.
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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 significantly shorter than the turbine itself.
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 maintenance plans from the asset owners in the upper level. This is modeled as a mixed integer linear programming problem. For the model of the natural gas grid, a piecewise linear approximation associated with the big-M approach is used to transform the original nonlinear model into the mixed integer linear model. Numerical tests on a 6-bus system with a 4-node gas grid show the effectiveness of the proposed model.
Whereas maintenance has been recognized as an important and effective means for risk management in power systems, it turns out to be intractable if cascading blackout risk is considered due to the extremely high computational complexity. In this paper, based on the inference from the blackout simulation data, we propose a methodology to efficiently identify the most influential component(s) for mitigating cascading blackout risk in a large power system. To this end, we first establish an analytic relationship between maintenance strategies and blackout risk estimation by inferring from the data of cascading outage simulations. Then we formulate the component maintenance decision-making problem as a nonlinear 0-1 programming. Afterwards, we quantify the credibility of blackout risk estimation, leading to an adaptive method to determine the least required number of simulations, which servers as a crucial parameter of the optimization model. Finally, we devise two heuristic algorithms to find approximate optimal solutions to the model with very high efficiency. Numerical experiments well manifest the efficacy and high efficiency of our methodology.
Let $z=(x,y)$ be coordinates for the product space $mathbb{R}^{m_1}times mathbb{R}^{m_2}$. Let $f:mathbb{R}^{m_1}times mathbb{R}^{m_2}rightarrow mathbb{R}$ be a $C^1$ function, and $ abla f=(partial _xf,partial _yf)$ its gradient. Fix $0<alpha <1$. For a point $(x,y) in mathbb{R}^{m_1}times mathbb{R}^{m_2}$, a number $delta >0$ satisfies Armijos condition at $(x,y)$ if the following inequality holds: begin{eqnarray*} f(x-delta partial _xf,y-delta partial _yf)-f(x,y)leq -alpha delta (||partial _xf||^2+||partial _yf||^2). end{eqnarray*} When $f(x,y)=f_1(x)+f_2(y)$ is a coordinate-wise sum map, we propose the following {bf coordinate-wise} Armijos condition. Fix again $0<alpha <1$. A pair of positive numbers $delta _1,delta _2>0$ satisfies the coordinate-wise variant of Armijos condition at $(x,y)$ if the following inequality holds: begin{eqnarray*} [f_1(x-delta _1 abla f_1(x))+f_2(y-delta _2 abla f_2(y))]-[f_1(x)+f_2(y)]leq -alpha (delta _1|| abla f_1(x)||^2+delta _2|| abla f_2(y)||^2). end{eqnarray*} We then extend results in our recent previous results, on Backtracking Gradient Descent and some variants, to this setting. We show by an example the advantage of using coordinate-wise Armijos condition over the usual Armijos condition.
We investigate a two-player zero-sum differential game with asymmetric information on the payoff and without Isaacs condition. The dynamics is an ordinary differential equation parametrised by two controls chosen by the players. Each player has a private information on the payoff of the game, while his opponent knows only the probability distribution on the information of the other player. We show that a suitable definition of random strategies allows to prove the existence of a value in mixed strategies. Moreover, the value function can be characterised in term of the unique viscosity solution in some dual sense of a Hamilton-Jacobi-Isaacs equation. Here we do not suppose the Isaacs condition which is usually assumed in differential games.
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