## Areas of Research include:

### Direction 1: A Methodology to Minimize Cascading of Failures

A major problem in today’s power infrastructure is that it was not designed to deal with sudden supply disruptions due to failures, as was evident in the Northeast blackout of 2003. The key technical problem is that when supply is unexpectedly disrupted, there is an immediate imbalance between energy supply and demand. If the imbalance is not remedied quickly, equipment is shut down by automatic control systems to meet design limitations. Shutting down equipment can further disrupt the supply and lead to a cascade of failures. Also, interrupting supply to certain critical customers, such as nuclear power generators, may disrupt other energy supplies downstream.

Deciding exactly where to reduce energy delivery in order to balance supply against demand can have a dramatic effect on the economic impact. For example, if a gas pipeline cuts delivery to a power generation facility serving a metropolitan area, the economic impact may be much greater than cutting delivery to a manufacturing plant. There are many factors in such a decision, including limitations of equipment and facilities, contractual obligations, and anticipated costs to groups of customers. And the decision must be made quickly.

In this project we propose to (1) develop a detailed methodology to prevent cascade of failures while minimizing negative economic impact, (2) further develop a Decision-Guidance Management System and an optimization solution for minimizing economic impact, and (3) develop a market-based economic impact model to be used by the optimization solution, and (4) Extend the Methodology to Vulnerability Assessment and Mitigation.

We propose a methodology based on two key components: (1) automated decision optimization at the time of failure to respond quickly to reduced supply, and (2) a market-based mechanism to determine in advance the true cost to various customers of a local supply interruption.

We propose to address this difficult decision problem through optimization. We will develop quantitative models of the facilities, the financial contracts, and the economic impact to customers. We will use proven optimization algorithms to search through the many combinations of alternative supplies, routes, and deliveries, and to balance the energy supply and demand while minimizing the overall economic impact. This is in fact a large and complex optimization problem. Below, we explain the technology used to solve it.

In addition, determining the economic impact of a chosen supply structure is quite challenging. There are many diverse participants affected by a supply reduction, and their interdependencies are numerous and complex. Imagine trying to predict the full economic cost of a traffic jam. Furthermore, even if we were to develop a direct estimate of global economic impact, it would be very challenging to induce energy suppliers to structure supply so as to minimize the global economic impact rather than their own economic interests.

Instead of directly estimating economic impact, we propose using a market-based approach that allows the participants to indicate the true costs they expect from a local energy supply interruptions. As energy suppliers and their customers participate in a market for contingent contracts, the customers negotiate to protect themselves from potential future power interruptions. As a result, the customers reveal their preferences with respect to energy price and energy interruption. At the same time, the energy suppliers gain knowledge and incentives to supply exactly those customers that indicate the highest economic impact from future power interruptions.

### Direction 2: An Optimization Solution to Minimizing Economic Impact

Our methodology for minimizing cascade of failures calls for automated optimization of a complex decision problem. The problem is to activate alternative supply sources, reroute supply, and strategically reduce delivery so as to minimize overall economic impact.

A typical Operations Research (OR) approach to this sort of problem involves building a global mathematical model, consisting of a set of constraint inequalities, a set of decision variables, and an objective function to maximize. This approach works very well for relatively small and simple optimization problems. However, the problems of critical infrastructure protection are typically large and diverse, with very complex rules such as engineering constraints, laws of physics, etc.

As a result, a global mathematical model for critical infrastructure protection would be huge. It would consist of thousands of complex mathematical equations. It would resemble the spaghetti-like software code written in the early days of computing: thousands of cryptic instructions, which can only be interpreted by the original author (at best).

It takes a long time to develop a global mathematical model directly. In order to avoid overwhelming complexity, simplification is necessary, which reduces the accuracy of the model. Furthermore, it is extremely difficult to validate and debug such a model, as well as to modify or extend it without rebuilding from scratch.

We propose to develop and utilize a Decision Guidance Management System (DGMS) , being developed at GMU. The DGMS approach involves a paradigm shift, from monolithic mathematical models to modular local models. The DGMS automatically constructs a global mathematical model from modular local models at run-time. As a result, both the problem and the results are expressed in terms relevant to the business. The drawbacks of directly developing and solving a global mathematical model are largely avoided. The table below summarizes the technical advantages of the DGMS Technology:

Current optimization approaches | DGMS Optimization |
---|---|

Models are monolithic, complex problems are very difficult to model, modify or extend |
Models are local and modular, DGMS automatically constructs global models from local model instances at run-time |

"Black-box" solutions can’t be easily changed or customized |
New business rules and factors are easy to add |

Simplifying assumptions required to model very complex value/supply chain |
No simplifying assumptions are necessary due to relative simplicity of local models. |

Enterprise-wide optimization is often simplified with a series of silo optimizations |
DGMS performs enterprise-wide optimization |

Models described in mathematical terms |
Decision models described in business level terms |

Each problem starts from scratch |
Models and algorithms can be shared across multiple problems |

Optimization algorithms do not scale well in the presence of very large amounts of data |
DGMShandles large numbers of factors due to constraint database indexing and filtering |

### Direction 3: A Market-Based Economic Impact Model

Our methodology for minimizing cascading failures calls for a quantitative model of overall economic impact. As noted above, this is very difficult to estimate directly. Instead, we use a market-based approach to gather information about the expected costs of future supply interruptions. The information revealed through market trading prior to a supply failure is used to structure supply at the time of a supply failure.

The project will use state of the art market design principles to create a dynamic feedback system that will enhance the outcomes of the optimization process. The test bed will create a prototype market and contract form that will be integrated with the design of the optimization algorithm to minimize the economic impact of network failures and cascades. This will be of direct application to system operators of electric power grids who must make decisions about shutdown without having to make spot market queries about potential values. Since there are many ways to reduce the load on a system, the information contained in a market process will provide generators and systems operators with the trade-offs required to make optimal decisions. In addition, the compensation schemes will provide the direct incentives to reveal the true value of the shutdowns.

Given that the system is closed in terms of the compensation among users, there is no need to have swings in the revenues of the producers. The prices generated from the market will provide valuable information to the generators, transmission owners and system operators of where the best investment should be made in the system to get the most economic worth. The design and issues found in an electric power network could be tailored to any network with interactive components including, gas and communication networks.

### Direction 4: A Methodology to Vulnerability Assessment & Mitigation

The same quantitative models developed to minimize cascade failures can also be used to answer other questions. All of the facilities models, the contract models, and supplier and customer models remain the same. The only difference is the metric that we minimize during optimization. Rather than minimizing the economic impact, we can *maximize* the economic impact, or we can *minimize* the *maximum* economic impact.

To identify the most critical vulnerabilities in the infrastructure, we adopt the perspective of an attacker, and we solve quantitatively for the maximum economic impact that can be inflicted. In this case, we allow the optimizer to vary certain parameters of the attack, so as to find the largest possible economic impacts. The result is a set of vulnerabilities, as well as a specific attack that can exploit each vulnerability.

Having identified the most critical vulnerabilities in the infrastructure, we can proceed to improve the infrastructure to reduce the vulnerabilities. In this case, we allow the optimizer to vary certain characteristics of the infrastructure facilities. We minimize a metric that corresponds to the maximum economic damage that can be inflicted. In this case, the optimizer assumes the roles of both the infrastructure improver and the attacker. The optimizer determines the result of a formal game played between these two adversaries. Furthermore, we can account for the cost of each improvement, and can find the most cost effective improvements.