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This paper designs an optimization model for Unit Commitment Problem (UCP) which is formulated as a Non Linear Programming Problem (NLPP) with respect to various constraints. The model can be solved by Lagrangian Decomposition (LD) problem and it is obtained by relaxing the constraints from NLPP using Lagrangian Relaxation Method. Generation scheduling is used to find the maximum demand utilized in the planning horizon by the minimum generation cost. It reveals the fact that Maximum profit can be achieved for power generating utility in order to supply the load in a reliable manner. Based on the numerical calculations and graphical representations, the optimum value is obtained by the proposed model for electrical power system cycles.

Background/objectives: Wireless sensor network (WSN) has sensor nodes; may failure happen because of hardware failure, communication error, energy depletion, and malicious attack. So there is a need to identify the problem and take necessary action to avoid performance degradation. The main objective of this research work is to enhance the performance and improves the network life time. Methods/statistical analysis: The proposed method discusses the faulty sensor node and the type of fault that may be transient, intermittent, and permanent compares it with the other network which has the same type of faulty node. It considers both the hard fault and soft fault and also it detects the fault easily. Findings: The fault node is identified from the neighbor using nodes and when the information is received from the exterior passed to the sink. Tables in this article show that the sensor which is detected has a permanent, transient, or intermittent fault in three WSNs with a common mode of fault. Novelty: The enhanced method saves the energy sources and finds the fault that occurs in common mode failure nodes in the WSNs.