Distributed generations (DGs) introduce significant uncertainties to restoration of active distribution networks, in addition to roughly estimated load demands. An adjustable robust restoration optimization model with a two-stage objective is proposed in this paper, involving the uncertain DG outputs and load demands. The first stage generates optimal strategies for recovery of outage power and the second stage seeks the worst-case fluctuation scenarios. The model is formulated as a mixed-integer linear programming problem and solved using the column-and-constraint generation method. The feasibility and reliability of the strategies obtained via this robust optimization model can be guaranteed for all cases in the predefined uncertainty sets with good performance. A technique known as the uncertainty budget is used to adjust the conservativeness of this model, providing a tradeoff between conservativeness and robustness. Numerical tests are carried out on the modified PG&E 69-bus system and a modified 246-bus system to compare the robust optimization model against a deterministic restoration model, which verifies the superiority of this proposed model.

Robust Restoration Method for Active Distribution Networks

During system restoration, it is critical to utilize the available black-start (BS) units to provide cranking power to non-black-start (NBS) units in such a way that the overall system generation capability will be maximized. The corresponding optimization problem is combinatorial with complex practical constraints that can vary with time. This paper provides a new formulation of generator start-up sequencing as a mixed integer linear programming (MILP) problem. The linear formulation leads to an optimal solution to this important problem that clearly outperforms heuristic or enumerative techniques in quality of solutions or computational speed. The proposed generator start-up strategy is intended to provide an initial starting sequence of all BS or NBS units. The method can provide updates on the system MW generation capability as the restoration process progresses. The IEEE 39-Bus system, American Electric Power (AEP), and Entergy test cases are used for validation of the generation capability optimization. Simulation results demonstrate that the proposed MILP-based generator start-up sequencing algorithm is highly efficient.

Optimal Generator Start-Up Strategy for Bulk Power System Restoration

This paper solves the distribution system restoration problem using dynamic programming with state reduction. The algorithm is an operator-permissive, automated approach to the restoration of distribution systems after a blackout. The timing and selection of feeders to be energized are represented as states in a dynamic programming formulation. An enhanced dynamic programming method reduces the number of states by grouping states that are close to each other and selecting the best state. The algorithm was tested on an 8 feeder/32 load distribution system. The method is applicable to radially configured systems.

Optimal Restoration of Distribution Systems Using Dynamic Programming

Energy constraint is an important issue in wireless sensor networks. This paper proposes a distributed energy optimization method for target tracking applications. Sensor nodes are clustered by maximum entropy clustering. Then, the sensing field is divided for parallel sensor deployment optimization. For each cluster, the coverage and energy metrics are calculated by grid exclusion algorithm and Dijkstra's algorithm, respectively. Cluster heads perform parallel particle swarm optimization to maximize the coverage metric and minimize the energy metric. Particle filter is improved by combining the radial basis function network, which constructs the process model. Thus, the target position is predicted by the improved particle filter. Dynamic awakening and optimal sensing scheme are then discussed in dynamic energy management mechanism. A group of sensor nodes which are located in the vicinity of the target will be awakened up and have the opportunity to report their data. The selection of sensor node is optimized considering sensing accuracy and energy consumption. Experimental results verify that energy efficiency of wireless sensor network is enhanced by parallel particle swarm optimization, dynamic awakening approach, and sensor node selection.

Distributed Energy Optimization for Target Tracking in Wireless Sensor Networks

Xue Wang *, Jun-Jie Ma , Sheng Wang and Dao-Wei Bi State Key Laboratory of Precision Measurement Technology and Instrument, Department of Precision Instruments, Tsinghua University, Beijing 100084, P. R. China; E-mails: {mjj, wang_sheng00, bdw02} @mails.tsinghua.edu.cn. * Author to whom correspondence should be addressed; E-mail: wangxue@mail.tsinghua.edu.cn. Received: 25 April 2007 / Accepted: 8 May 2007 / Published: 10 May 2007 Abstract: The limited energy supply of wireless sensor networks poses a great challenge for the deployment of wireless sensor nodes. In this paper, we focus on energy-efficient coverage with distributed particle swarm optimization and simulated annealing. First, the energy-efficient coverage problem is formulated with sensing coverage and energy consumption models. We consider the network composed of stationary and mobile nodes. Second, coverage and energy metrics are presented to evaluate the coverage rate and energy consumption of a wireless sensor network, where a grid exclusion algorithm extracts the coverage state and Dijkstra’s algorithm calculates the lowest cost path for communication. Then, a hybrid algorithm optimizes the energy consumption, in which particle swarm optimization and simulated annealing are combined to find the optimal deployment solution in a distributed manner. Simulated annealing is performed on multiple wireless sensor nodes, results of which are employed to correct the local and global best solution of particle swarm optimization. Simulations of wireless sensor node deployment verify that coverage performance can be guaranteed, energy consumption of communication is conserved after deployment optimization and the optimization performance is boosted by the distributed algorithm. Moreover, it is demonstrated that energy efficiency of wireless sensor networks is enhanced by the proposed optimization algorithm in target tracking applications. Keywords: Wireless sensor network, deployment optimization, energy efficiency, particle swarm optimization, simulated annealing.

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Distributed Particle Swarm Optimization and Simulated Annealing for Energy-efficient Coverage in Wireless Sensor Networks

The power quality service is necessary demand in near future of the customer's. The fast service restoration has been a hot issue with fault tolerable distribution system in maintaining power quality. When a fault takes place, it results in the isolation of some portion of the feeder downstream from the affected areas. So this paper describes a high speed-switching algorithm for a distribution network that has been developed with the aim of reducing the time of the restoration and maximizes the amount of power restored. The algorithm developed isolates only the fault section and restores the power supply to normal sections after a fault takes place. The algorithm developed is based on network reduction and determination of the optimal configuration of the reduced network by using Dijkstra's algorithm. The developed algorithm is tested on a standard system and then it is applied for practical systems.

http://ieeexplore.ieee.org/iel5/9877/31408/01460073.pdf

Supply restoration in distribution networks using Dijkstra's algorithm

Whenever a fault occurs in a distribution network and on isolation of the fault some of the loads get disconnected and are left unsupplied. Hence service should be restored to these load points as quickly as possible through a network reconfiguration. But the restoration of supply is a large-scale combinatorial problem, which puts the control operators under pressure to find a restoration solution quickly. This paper presents a new technique, which is based on minimum number of switching operations and minimum losses. The main contribution of this paper is to convert a complicated network into a simple one, by using network reduction technique and then applying the developed algorithm for the reduced network to get an optimal configuration after the occurrence of the faults. The developed algorithm is tested on a standard system and then it is applied for a practical system.

S.M.R. Slochanal

Papers

Supply restoration in distribution networks using Dijkstra's algorithm

Heuristic based strategy for the restoration problem in electric power distribution systems