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Game Theoretic Methods of the Smart Grid Network

Game Theory has featured as an interesting technique to help people make rational decisions based on the variety of pay-offs on offer. At its core, Game Theory helps the world make decisions, providing a concrete framework to solve problems that involve allocating resources effectively or making decisions intelligently. Hence, it seems only natural that Game Theory has the potential to play an integral part in simplifying and improving the functioning of one of the most complex and most crowded networks of all—the Electricity Grid.  As worldview shifts its focus to Demand-side Management of resources (related to power), instead of the conventional focus on increasing the Supply of resources, the Power Industry for the past couple of years has sought to implement, what they call, “the Smart Grid Network to offer a reliable, robust and intelligent system to provide/allocate power effectively. As envisaged by various researchers, governments and multi- national corporations, the core of the Smart Grid Development lies in ability to carry out intelligent two-way Communication across the network.  And, this is where Game Theory enters the picture for us; it becomes a tool that helps us to simplify and determine the Best Responses to the various decisions and strategies that the Electricity Transmission and Distribution formulate.

Before presenting some of the information and insight gained from W. Saad, Z. Han, H. V. Poor, and T. Basar’s paper on “Game theoretic methods for the Smart Grid, it would be useful to take a general view of what the Smart Grid Network—including the nodes and edges– looks like, along with a brief look at what the structure of this decision- based Game that arises for both the distributor of electricity and the specific nodes (power consumers) in the system that systematically collaborate to allocate power and make intelligent decisions to distribute the generated power amongst themselves. Let us take a closer look at the image representing a Cooperative Smart Grid Network of Generators and Transmissions of Power, below:

Screen Shot 2014-09-19 at 8.17.49 am

Source: http://arxiv.org/pdf/1202.0452.pdf

Typically, the nodes represent as Micro grids that Transmit, generate power and consume power (we are looking at the Grid from a Macro level; there are interesting game theoretic applications at the Micro level as well but it is easier to focus on just the Macro level for the moment). And, the edges represent the two- way communication between these micro grids to enhance/develop an intelligent network.  The graph (or network of nodes formed) formed is bipartite, in that divides the consumers and generators (leaving a matching problem, but we will not discuss this in more detail; more information on this can be found at: http://arxiv.org/pdf/1202.0452.pdf). Instead, we will focus on the application of Game Theory, to optimally distribute electricity between power generators to power consumers. The two-way communication (as represented in the diagram above by two-sided arrows) will play an integral part in the optimal distribution of power, as all of the nodes (suppliers and consumers) will come together through the two-way communication channels to distribute the power effectively.

Generally speaking, power generation grids are not able exactly to match their entire demand (some grids produce more and others produce less than their demand); hence, it only makes sense for them to collaborate and exchange power between them to optimally allocate the power distributed (otherwise the extra generation of power will be wasted if a micro grid has extra power). A simple game of this form would look at a number of micro- grids (the players) that could potentially collaborate with another outside Utility (say MicroGrid 3) and their strategies would concern whether they should collaborate or not. A sample payoff matrix (payoffs measure monetary gain, but really it could be anything else as well) for the game looks as follows:

Screen Shot 2014-09-19 at 3.18.45 pm 

 

By determining, the mixed Nash Equilibrium from the above payoff matrix (there is no pure Nash Equilibria in the case above), it can be easily bee seen how the two Micro Grid’s should choose to collaborate. Obviously, this is a very simple game, and in fact it does not take into account the Peak-Demand consumption and generation, but from this game it is easy to see how the firms can choose to allocate their resources to achieve a reliable, robust and efficient Grid that reduces Transmission & Distribution Losses. And, since this is a collaborative game (mostly the State’s own Distribution Companies), the State will try to find the strategy with the best payoff, considering that they want to optimize the Smart Grid.

To bring it all together, I feel that the smart grid network utilizes most of the tools to model and understand networks that we have discussed in class. Although some of the concepts of Strong- Triadic Closure may not be as applicable, everything from Game Theory to Auctions and Matching Problems can be integral to the setup of the Smart Grid Network. Game Theory, as illustrated, would help us to determine if MicroGrids should collaborate to match their actual demand, in order to reduce losses. And, with different households consuming different amounts of power may involve some sort of an auction. Finally, the power generation companies must match themselves with power consumers in a way that every consumer is able receive the power that they demand. Although my discussion has mainly focused on the Game Theory concepts applicable to the Smart Grid Network, all of the aforementioned concepts are addressed in the following papers (and there is a wealth of information online):

http://arxiv.org/pdf/1202.0452.pdf

http://smartgrids.newmexicoconsortium.org/Talks/Poor.pdf

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