Implementation Details

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.

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.

Simplex Methods

This week I have been researching the Simplex method and how it can solve linear programming problems. I have specifically been looking at whether a decentralised version exists that could be applied to the generator coordination domain. However so far I think the decentralised version still requires all nodes to know the global objective function and thus still contains centralised elements. I am also looking at whether a message passing algorithm can be applied in order to coordinate generators, however so far I have concluded that each generator must know about all the loads within the network in order to collectively coordinate their outputs. This week I have also applied to IBM and Google for summer internships. I have had two telephone interviews with Google where they asked me some technical questions regarding algorithms.

Video Demo

I've created a short video of my centralised demo. It doesn't have any audio or captions explaining what's going on because I would normally use it during presentations where I explain what's happening.Here's an explanation: To start with the network is working normally, loads and output are balanced and no transmission lines are overloaded. The green node is a generator that has been nominated to follow the load within the network and will ramp up/down accordingly. As the red nodes's load increases the nominated generator will ramp up its output to compensate, however this overloads two transmission lines on the network. In order to reduce the overload, the generators must be coordinated such that they reconfigure there outputs. The objective function is minimising carbon emissions but it is also making sure that the distance between a generators current output and the output it is changing to is minimal.