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Über dieses Buch

This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds.

The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system.

This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.

Inhaltsverzeichnis

Chapter 1. Introduction

Abstract
The goal of this research review is to describe advances in the state of the art with regard to power system reliability [1] and voltage (in)stability [2,3]. We consider a given network configuration in the sense of statistical mechanics and examine the domains of (in)stability from the standpoint of intrinsic geometry. We introduce the geometric theory of statistical stability for power networks. In this respect, it is well known that, for effective power system planning, the appropriate reactive compensation [4] is essential with a suitable set of network parameters (resistance $$R$$ and reactance $$X$$) and associated planning issues [5,6]. With a given network as the statistical system, such planning helps to reduce the apparent power by cutting reactive power losses in the network.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 2. Proposed Methodology

Abstract
In this chapter, we recall the mathematical preliminaries and the flow properties of power networks. The method used here is to eliminate the effect of voltage fluctuation about an equilibrium.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 3. Intrinsic Geometric Characterization

Abstract
In this chapter, we offer a concise account of network power flow and stability criteria arising from real intrinsic Riemannian geometry. We begin by considering a brief review of the flow equations and related concepts, for use in the later chapters.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 4. A Test of Network Reliability

Abstract
In this chapter, we focus on the aforementioned techniques of network theory and real intrinsic geometry. In order to carry out this investigation, we first formulate the problem as in the previous chapter. We then describe the details of this innovation for two-parameter single-component networks and show in the sequel that the method works in general. In particular, we evaluate the network reliability and test the results in order to demonstrate the accuracy of the proposed solution.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 5. A Test of Voltage Stability

Abstract
In this chapter, we extend the techniques of intrinsic geometry and examine the problem of voltage stability in network theory. In order to carry out this investigation, we determine stability domains by first specifying the three-parameter model for the reformulation of the problem. We then consider single-component LCR networks, showing how voltage stability is achieved according to the results of the present model. From the outset of the present investigation, we offer specific remarks and outlook for future research.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 6. Phases of Power Network

Abstract
In this chapter, we describe the intrinsic geometric design of power flow and the parametric stability of power networks by focusing our attention on the admissible values of the parameters $$\{L, C, R\}$$ for the real power flow, the imaginary power flow, and their arbitrary linear combinations as the unified description of the network power flow. In the context of the power flow equations [1, 2], the usefulness of the present investigation may appear to be somewhat limited. However, we shall show how our proposal could in principle be generically applied to all electrical networks, in order to achieve a better understanding of the phenomenon and importance of controlled power flow and network analysis. Intrinsic geometric considerations can provide strategic planning criteria for the effective use of power systems and voltage stability. We show that this notion follows from the standard laws of electrical circuits (for a review, see [2]). For an additional component, the criteria of voltage stability can then be used for optimal selection of the network parameters.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 7. Phase Shift Correction

Abstract
In the context of network planning, equipment and load dynamics are of course the driving force behind phase shift voltage instability. In this chapter, for the 2-bus systems in a connected power system, we show that the voltage of all relevant buses (i.e., both bus-1 and bus-2) varies in the same way as the transmitted power. In the sequel, we examine the state-space formulation pertaining to voltage regulation and phase-shift correction. In the state-space formulation, some assumptions are made, i.e., shunt admittance has been neglected, there is no reactive support on the load bus, and the generator terminal voltage phasor is assumed to coincide with the rotor position, the load being defined by the real and reactive power demand. We anticipate further that the incorporation of shunt admittance, reactive support on the load bus, and the generator terminal voltage phasor will involve a sub-dominant correction.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 8. Complex Power Optimization

Abstract
In this chapter, we analyze the voltage instability pertaining to the maximum deliverable power for a given load. We thus illustrate the role of state-space geometry in complex power flow optimization. In the rapidly growing and competitive power market, optimization is crucial in order to define the loadability limit of the power network, where not only the real power is considered, but the reactive support is also involved.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 9. Large Scale Voltage Instability

Abstract
In this chapter, we apply the methods of state-space geometry to the issue of complex power optimization in a non-steady state regime by incorporating the intrinsic state-space geometry. Considering the power flow between two arbitrary points along the chosen transmission line, we compute the stability domains for a large voltage instability problem. In the proposed formulation of this problem, some assumptions are made, i.e., shunt admittance has been neglected, we assume that there is no reactive support on the load bus, the generator terminal voltage phasor is assumed to coincide with the rotor position, and the load is defined by the real and reactive power demand.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

Chapter 10. Conclusion and Outlook

Abstract
The present research concerns the problem of planning in the power industry.The issues of network reliability and bus voltage stability have been examined from the perspective of engineering applications to planning and operation using intrinsic geometric considerations. Specifically, we have considered an intrinsic geometric model for the limiting reliability and limiting voltage stability analysis of electrical networks. The correlation model has been converted into an intrinsic geometric model in order to cater for the non-linear effects of stochastic nature encoded in power systems with an appropriate optimization of the components. The robustness of the proposed model is illustrated by introducing variations of the circuit parameters. In this model, reliability and stability of a component are directly accomplished through the framework of intrinsic Riemannian geometry.
Stefano Bellucci, Bhupendra Nath Tiwari, Neeraj Gupta

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