I have been working on a tree message passing algorithm which uses dynamic programming to calculate optimal power flow in a tree network given an number of loads and generation units. Leaf nodes start by constructing a number of elements that contain a particular flow, carbon intensity and resulting carbon emission. They calculate it based on whether there is flow coming in from their parent, flow going out to their parent or whether there is no resultant flow between them and their parent. The leaf nodes send these elements to their parents and the parents then construct their own set of elements by merging the results from their children. This continues all the way up to the root of the tree, at which point the root can calculate the optimum state it should be in to produce the minimum carbon emission. This optimum state is propagated back down the tree and each node uses backtracking to determine what state they should be in given and optimum state from their parent. Once messages have propagated to the leaf nodes the algorithm terminates and each node will be outputting a certain power that satisfies loads in the tree and minimises carbon emissions.
The algorithm has nearly been fully implemented, I just need to code the merging of the elements for the root node and the decisions it has to make. I also need to thoroughly test this.
Showing posts with label power flow. Show all posts
Showing posts with label power flow. Show all posts
Thursday, 31 March 2011
Tuesday, 15 March 2011
Direction of research: Distributed Optimal Power Flow
I have just read the following papers on distributed optimal power flow:
1. Kim BH, Baldick R. Coarse-grained distributed optimal power flow. IEEE Transactions on Power Systems. 1997:932-939.
This paper provides a distributed approach to optimal power flow based on an objective function. It involves splitting the network into a variety of regions each with its own set of buses and transmission lines. Regions which have a transmission line between them share variable values by using a dummy bus. The variables are then duplicated for that dummy bus and each region uses their version of the variables to solve their power flow. For each iteration, regions exchange their shared variables and update them until convergence is experienced.
The distributed equations involve using lagrangians to solve and update the shared variables. This paper provides some very good reasons for decentralised power flow and promising test results. As future work it suggests a number of possibilities which could be used. For example make use of previous iterations to avoid having to refactorise certain equations.
2. Baldick R, Kim BH, Chase C, Luo Y. A fast distributed implementation of optimal power flow. IEEE Transactions on Power Systems. 1999:858-864.
This paper is a fast implementation of [1] using techniques from:
3. Wu Y-C, Debs AS, Marsten RE. A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows. IEEE Transactions on Power Systems. 1994:876-883.
This is one direction that my research is heading. I am very interested in distributed optimal power flow and how this can be used in conjunction with reducing overloaded lines within a network whilst minimising carbon emissions.
1. Kim BH, Baldick R. Coarse-grained distributed optimal power flow. IEEE Transactions on Power Systems. 1997:932-939.
This paper provides a distributed approach to optimal power flow based on an objective function. It involves splitting the network into a variety of regions each with its own set of buses and transmission lines. Regions which have a transmission line between them share variable values by using a dummy bus. The variables are then duplicated for that dummy bus and each region uses their version of the variables to solve their power flow. For each iteration, regions exchange their shared variables and update them until convergence is experienced.
The distributed equations involve using lagrangians to solve and update the shared variables. This paper provides some very good reasons for decentralised power flow and promising test results. As future work it suggests a number of possibilities which could be used. For example make use of previous iterations to avoid having to refactorise certain equations.
2. Baldick R, Kim BH, Chase C, Luo Y. A fast distributed implementation of optimal power flow. IEEE Transactions on Power Systems. 1999:858-864.
This paper is a fast implementation of [1] using techniques from:
3. Wu Y-C, Debs AS, Marsten RE. A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows. IEEE Transactions on Power Systems. 1994:876-883.
This is one direction that my research is heading. I am very interested in distributed optimal power flow and how this can be used in conjunction with reducing overloaded lines within a network whilst minimising carbon emissions.
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