A Network Graph-based Framework for Modeling, Calculating and Controlling Feasible AC Electric Power Delivery
Creators: name: Hsu, Andrew
Publisher: name: Carnegie Mellon University
Year: 2015
Subjects: subject: 90699 Electrical and Electronic Engineering not elsewhere classified
subject: FOS: Electrical engineering, electronic engineering, information engineering
subject: FOS: Electrical engineering, electronic engineering, information engineering

description: An influx of technology has changed the traditional, top-down approach to electric power systems,into an interconnected electrical and informations network with large generators, intermittent renewables, storage, and demand response. The transmission network has seen its fair share of innovation, as new hardware is introduced for both monitoring and control purposes. For example, distributed line rating units (DLRs) are used to determine a more accurate thermal rating for transmission lines. Flexible AC Transmission Systems (FACTS) devices are capable of adjusting the reactance of lines using power electronics switching. Even newer technologies, like distributed series reactances (DSRs) are offering similar adjustment capabilities at lower cost. How can these devices be coordinated to run the electric power system more efficiently and reliably?<br>This thesis proposes a framework for modeling power systems using a graph representation.This localizes each individual component's behavior and only interconnects the system through thepower and voltages of the components, over a network graph that obeys Kirchhoff's laws. Usingthis framework, a number of new formulations for the power flow problem are introduced. <br>The first formulation poses the conventional power flow problem, in terms of nodal voltage magnitude and phase angle, as a complex-value domain problem in terms of complex-valued nodalvoltages, for systems with only a slack bus and PQ buses.<br>Secondly, the complex-value domain power flow problem has been reposed in terms of the branchvoltages, or voltage difference across the lines of the network. By combining this with the S-E graphmodel, a pi model of transmission lines, a set of power flow equations was formulated in terms ofthe power transferred through each line, and the voltage across each line.<br>However, the branch-based formulation of power flow is more difficult to solve using the conventional numerical methods, especially Jacobi method. Therefore, a new optimization-based formulation of power ow is developed, in terms of branch variables. This thesis shows how distributedpower flow calculation, performed by smart wires and buses, can be performed through only communication with neighbors. This new formulation is also instrumental in deriving methods for ensuring feasible power delivery.<br>If there is no power flow solution, there is no equilibrium value for the voltages of the network, and will lead to voltage collapse. To ensure that power is successfully delivered across the network, the components of the network must adjust so that there is a valid power flow solution. This thesis proposes two methods of ensuring feasible power delivery; targeted load shedding, and adjustmentof line reactances. <br>By using Lagrangian relaxation to solve the new optimization-based power flow problem, theset of possible solutions is expanded beyond just the possibly power flow solutions of the network. Ifthere is no valid power flow solution, then the optimization problem can still converge to a solution.The Lagrange multipliers, which correspond to physical constraints, such as nodal power balance,therefore becomes a measure of power mismatch at each bus. Using the numerical results of theLagrange multipliers, adjustments to load can be made, allowing targeted load shedding.<br>Another method of reaching a feasible power flow solution is by adjusting the parameters ofthe lines connecting the generators and loads. It may be less desirable to shed load, which woulddisconnect customers from power, than to use devices such as DSRs and FACTS devices to changethe reactance of lines. By using the mathematical closed form power flow solution of a two-buspower system, the conditions for feasible power delivery across one line can be derived. Extendingthis to the multi-bus network allows each line to determine whether it should adjust, to reach avalid power flow solution.<br>Finally, proof of concept simulations show the distributed calculation of power flow, targetedload adjustment and line reactance adjustment on 3 bus, 14 bus, and 45 bus systems. An object-oriented programming platform is used to simulate power systems in an actual distributed environment, with separate Matlab processes communicating between one another. The distributed power flow algorithm has been implemented for the 3 and 14 bus networks on this platform.