stochastic dynamic programming

In this paper, a single-product, single-machine system under Markovian deterioration of machine condition and demand uncertainty is studied. The objective is to find the optimal intervals for inspection and preventive maintenance (PM) activities in a condition-based maintenance planning with discrete monitoring (CBMDM) framework. At first, a stochastic dynamic programming model whose state variable is the machine status is presented. This model whose objective is minimizing inspection, preventive maintenance and lost production costs due to the difference in actual capacity with nominal capacity, does not take into account demand. Then, demand is appended to the state variable in the second model and the average cost of lost production which is due to the difference in actual production capacity with demand is replaced in the first model correspondingly. Finally, to validate and analyze the proposed models, an application of the models in wind turbines is prepared. The numerical results show that replacing demand by nominal capacity in simultaneous inspection and preventive maintenance planning, the average total costs consist of inspection and preventive maintenance in the planning horizon are reduced in the planning horizon.

Attention has been paid to the Demand Response (DR) programs in recent years to improve the power system operation. Demand Response affects market clearing price، which is the main motivation for investment، and thus the trend of investment on generation expansion will be affected. So far، the demand has been considered inelastic for modeling the investment on generation expansion. However، increasing the deployment of smart grid has waived this assumption. In this paper، we have used stochastic dynamic programming for modeling the generation expansion problem. We have considered both the renewable resources and demand response in modeling. In the proposed model، the uncertainty in generation and the accuracy of the price responsive demand performance are considered. In this regard، the market clearing price is determined by interaction between price and the price responsive demand. Some long-term indices are proposed and using the simulation results، they are evaluated. The achieved results، quantitatively confirm that the demand response results in decreasing the price and the outages and therefore improving the reliability.