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This book showcases the strengths of Linear Programming models for Cyber Physical Systems (CPS), such as the Smart Grids. Cyber-Physical Systems (CPS) consist of computational components interconnected by computer networks that monitor and control switched physical entities interconnected by physical infrastructures. A fundamental challenge in the design and analysis of CPS is the lack of understanding in formulating constraints for complex networks. We address this challenge by employing collection of Linear programming solvers that models the constraints of sub-systems and micro grids in a distributed fashion.
The book can be treated as a useful resource to adaptively schedule resource transfers between nodes in a smart power grid. In addition, the feasibility conditions and constraints outlined in the book will enable in reaching optimal values that can help maintain the stability of both the computer network and the physical systems. It details the collection of optimization methods that are reliable for electric-utilities to use for resource scheduling, and optimizing their existing systems or sub-systems. The authors answer to key questions on ways to optimally allocate resources during outages, and contingency cases (e.g., line failures, and/or circuit breaker failures), how to design de-centralized methods for carrying out tasks using decomposition models; and how to quantify un-certainty and make decisions in the event of grid failures.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
The worldwide electric-power industry is undergoing a transformation unlike anything that it has seen in over a century. The entire supply chain for electricity, including how the power is generated, transmitted, distributed, and consumed, is being overhauled with the goal of establishing a more sustainable energy future. Adopting new technologies and the associated market restructuring are a complex undertaking that requires knowledge about the many interacting variables and the conflicting cost functions for various market participants, such as power producers, system operators, load-serving entities, regulators, aggregators, service providers, and consumers. The smart grid is an information-enriched energy network, and it is going to require substantial information processing, storage, and data-mining resources. An entirely new software sector is being created to meet the challenges and to fill the many needs resulting from smart grid’s arrival. Spending for the Smart grid is estimated to be $165 billion over the next 20 years, and a good portion of this cost will be for software and data services [RPT07, AW05]. The Smart grid is a complex, highly networked system that must operate in diverse, often-challenging environments that combine large and complex facilities with vast numbers of edge nodes, e.g., the smart meters that are grid’s consumer-fronting boundary. The smart meters require sophisticated software in order to operate efficiently. Upgrading utility information and control infrastructure is critical to maintain the electric distribution system’s reliability at a time of rising costs.
Prakash Ranganathan, Kendall E. Nygard

Chapter 2. Literature Review

Abstract
The goal of this chapter is to provide prior work done with linear-programming approaches for the resource-allocation problem. Operations-research (OR) modeling often concerns finding the best quantitative solution for management problems [HL01, Mom01]. The OR methods include mathematical-optimization modeling as simulation, and using OR methods has grown significantly since their origination during World War II. Templeman [Tem91] describes quantitative OR methods for designing and controlling industrial and economical operations. Many private and government organizations have improved their operations by successfully using mathematical programming [Wad83, Aro02, Chv83, Dan63, SS85]. This book focuses on a resource-allocation problem and applies linear programming for the solution approach.
Prakash Ranganathan, Kendall E. Nygard

Chapter 3. Energy Reallocation in a Smart Grid

Abstract
When a malfunction occurs in a smart-grid electricity-provisioning system, it is vitally important to quickly diagnose the problem and to take corrective action. The self-healing problem refers to the need to take action in near real time in order to reallocate power to minimize the disruption. To address this need, we present a collection of integer linear programming (ILP) models that are designed to identify the optimal combinations of supply sources, the demand sites for generators to serve, and the pathways along which the reallocated power should flow. The models explicitly support multiple time periods and the uncertainty associated with alternative sources such as wind power. Model solutions are evaluated using a simulator configured with multiple, intelligent, distributed software agents.
Prakash Ranganathan, Kendall E. Nygard

Chapter 4. Resource Allocation Using Branch and Bound

Abstract
The chapter describes a resource-allocation problem in a smart-grid application that is formulated and solved as a binary integer-programming model. To handle power outages from the main distribution circuit, the Smart grid’s intelligent agents have to utilize and negotiate with distributed-energy resource agents that act on behalf of the grid’s local generators in order to negotiate power-supply purchases to satisfy shortages. We develop a model that can optimally assign these DERs to the available multiple regional utility areas (RUAs) or units that are experiencing power shortages. This type of allocation is a resource-assignment problem. The DERs in our model depict the behavior of power created with a wind turbine, solar generation, or other renewable generation units, and the region or area refers to a centralized distribution unit. The integer-programming approach is called Capacity-Based Iterative Binary Integer Linear Programming (C-IBILP). All simulation results are computed using the optimization tool box in MATLAB. Computation results exhibit very good performance for the problem instances tested and validate the assumptions made.
Prakash Ranganathan, Kendall E. Nygard

Chapter 5. Resource Allocation Using DW Decomposition

Abstract
Dantzig-Wolfe decomposition is a technique for dealing with linear- and integer-programming problems that have embedded substructures that permit efficient solution. The technique has been successfully applied in a variety of contexts [Dan63, Chv83, BJN98]. Implementing DW-decomposition-based algorithms poses various challenges. The primary constraint revolves around convergence of the dual-bound computations and, in the context of integer programming, the enforcement of integrality restrictions. The standard view of DW decomposition is that it exploits the linear-programming formulation of the Lagrangian dual. This so-called master linear program has an exponential number of variables that are handled using dynamic column generation. An alternative view is that DW is a reformulation technique that gives rise to a mixed-integer master program. Viewing DW as a reformulation technique allows for the development of a theoretical framework that facilitates the handling of branching decisions and cutting planes in the master program.
Prakash Ranganathan, Kendall E. Nygard

Chapter 6. Implementation and Testing of the Dantzig-Wolfe Procedure

Abstract
This chapter discusses the AMPL implementation and results for running the IEEE 14-bus and IEEE 30-bus systems. The environment for the AMPL modeling software is discussed regarding how to specify the model, data, and run-file information.
Prakash Ranganathan, Kendall E. Nygard

Chapter 7. Remarks About the Dantzig-Wolfe Scheme

Abstract
A distributed linear-programming model has been created, developed, implemented, and tested. Two standard IEEE bus systems are modeled and successfully decomposed, in multiple ways, into sub-problems. The problem is solved iteratively in each case and directly supports resource allocation in a Smart-grid environment. I have shown that the LP-based design using the Dantzig-Wolfe decomposition can execute and can quickly determine the primary resource scheduling and allocation issues if a failure occurs in the grid. The decomposition procedure can easily be managed by system operators. In the study using the 4-bus, 14-bus, and 30-bus systems, the results indicate that the computational benefits of the Dantzig-Wolfe approach enable fast responses on the order of a millisecond to a few seconds as network size increases. Although the 30-bus system is not a large bus network, the results clearly indicate a faster computation time if an appropriate Dantzig-Wolfe structure is formulated. This approach can enable system operators in the electric grid to respond to any allocation request for resources in the event of outages or line failures. The book’s key contribution is the design, development, and testing of a procedure that successfully decomposes an optimization problem that is defined over a large grid but can be solved in regional pieces.
Prakash Ranganathan, Kendall E. Nygard

Chapter 8. A Linear Classifier for Decision Support in a Smart Grid

Abstract
Because electric-grid sensor data originating from several sensors, such as the phasor measurement units (PMUs); intelligent relays; and the new installation of smart meters, Plug-in Hybrid Electric Vehicles (PHEV), or Gridable Vehicles (GV), are exponentially growing, the Smart Grid’s data-analytic platform has huge potential (generation, transmission, or distribution) and can play a significant role in the decision-making process for meaningful data interpretation in order to act promptly or to automate the grid process to avoid any failures or grid instability. This chapter focuses on identifying the variables of interest that are important for the electric grid that is embedded in distributed real-time data engines which will help with the system operators’ decision-support process. More specifically, the applicability and performance of the M5 model and J48 decision-tree machine-learning technique are investigated using real electric-grid data. We have presented how a decision-tree model, such as M5P, can support system operators in making effective decisions in the Smart Grid. Two sets of test data are used in this chapter; the first data set is taken from a 10-unit commitment with a 50,000 Gridable Vehicle, and the latter one analyzes weekly New York City (NYC) demand data from NYISO.
Prakash Ranganathan, Kendall E. Nygard

Chapter 9. Maximization of the Utility Function, Time-Dependent Energy Allocation, and Fuzzy-Logic Resource-Allocation Models

Abstract
Today’s and tomorrow’s smart-grid systems are made more efficient, cleaner, and reliable with “smart” control mechanisms and decision models that deliver information to consumers so that they can better manage energy resources. The rapidly changing needs and opportunities of today’s electric-grid market require unprecedented levels of inter-operability in order to integrate diverse information systems to share knowledge and to collaborate among the grid’s sub-devices or sub-systems. This chapter focuses on the optimal mathematical models for resource allocation. A series of mathematical models is presented for solving large-scale energy-allocation problems with partially observable states, utility functions and constrained action is introduced. The techniques use a linear-programming (LP) approach to determine resource allocations among a set of fuzzy rules that allocate Distributed Energy Resources (DERs) or power sources/sinks and uses to determine improved resource management.
Prakash Ranganathan, Kendall E. Nygard

Chapter 10. Placement of Synchrophasors Using Linear Programming and Zero-Injection Constraints

Abstract
This chapter presents a linear-programming-based optimal solution for an Optimal Placement Problem (OPP) of Synchrophasors or Phasor Measurement Units (PMU). With the increasing use of Synchrophasors for smart-grid monitoring and control, the problem with PMU placement has become a major concern due to its large installation costs. This chapter utilizes an Integer Linear Programming (ILP) approach to find optimal solutions. We show that the performance of our LP constraints and the formulation makes the ILP approach very attractive for smaller utilities that have limited budgets. This is shown using with and without zero-injection cases in programmed AMPL language using CPLEX solver. We also propose an Optimal Redundancy Criterion (ORC) which assists utilities with providing redundant observability for critical buses in the system. Our approach yields full and redundant observabilities within a few milliseconds for different cases, such as IEEE 300 test systems and an Indian power grid.
Prakash Ranganathan, Kendall E. Nygard

Chapter 11. Unbiased Optimal Power Flow (OPF) for Power Systems with Wind-Power Generation

Abstract
Wind-power plants that are connected to power systems are often unable to utilize all available power due to transmission constraints.
Prakash Ranganathan, Kendall E. Nygard

Chapter 12. Smart-Grid Optimization Using A Capacitated Transshipment Problem Solver

Abstract
Creating an autonomous, self-healing electrical grid is one of the most important challenges facing electric-energy providers. Such a system, known as the “smart grid,” must interweave a multitude of systems, both software and hardware, in order to form a complete solution that is capable of meeting the requirements outlined by the United States Department of Energy (DOE). According to the DOE [LSC05], “It is a colossal task. But it is a task that must be done.”
Prakash Ranganathan, Kendall E. Nygard

Chapter 13. Decomposition of Microgrids in Large-Scale Electric Test Beds for Economic Dispatch Optimization

Abstract
Microgrid decomposition (partitioning, splitting, and clustering) or otherwise determining community structures within a power transmission network is important to optimal management of the transmission system. Power transmission system decomposition is not itself a novel concept. Similar concepts have been utilized dating back to the 1950s for various reasons [kro63]. There are very limited existing literatures that use clustering for grid decomposition.
Prakash Ranganathan, Kendall E. Nygard

Backmatter

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