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Power system modelling and scripting is a quite general and ambitious title. Of course, to embrace all existing aspects of power system modelling would lead to an encyclopedia and would be likely an impossible task. Thus, the book focuses on a subset of power system models based on the following assumptions: (i) devices are modelled as a set of nonlinear differential algebraic equations, (ii) all alternate-current devices are operating in three-phase balanced fundamental frequency, and (iii) the time frame of the dynamics of interest ranges from tenths to tens of seconds. These assumptions basically restrict the analysis to transient stability phenomena and generator controls. The modelling step is not self-sufficient. Mathematical models have to be translated into computer programming code in order to be analyzed, understood and “experienced”. It is an object of the book to provide a general framework for a power system analysis software tool and hints for filling up this framework with versatile programming code. This book is for all students and researchers that are looking for a quick reference on power system models or need some guidelines for starting the challenging adventure of writing their own code.

Inhaltsverzeichnis

Frontmatter

Introduction

Frontmatter

Power System Modelling

Abstract
This chapter introduces basic modelling concepts that are used throughout the book. Section 1.1 defines a power system and provides most relevant references related to power system analysis. Section 1.2 states the philosophical background of the book and general motivations. Section 1.3 presents programmatic assumptions and the proposed methodological approach for power system modelling. Finally, Section 1.4 defines the general equations that are used for modelling power systems.
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Power System Architecture

Abstract
The main concept that is developed in the chapter is that any complex project can be conveniently handled if correctly planned and structured. With this aim, Section 2.1 discusses the fragmentation of software packages. An example is also given in this section. Section 2.2 describes the main components that compose a general-purpose software package, namely classes and procedures, while Section 2.3 introduces the concept of modularity. A simple example on how organizing a modular software package is also provided in Section 2.3. Section 2.3 also discusses the modularity of power system structure. Finally, Section 2.4 applies the concepts previously discussed and proposes the structure of a general power system analysis tool.
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Power System Scripting

Abstract
The topics of this chapter are threefold. The first topic is to find the most adequate scenario for a didactic and research-oriented programming environment (Section 3.1). With this aim, the concepts of open and closed software as well as the differences between traditional programming and scripting are introduced and discussed (Sections 3.2 and 3.3, respectively). The second topic is to describe the minimal features that a computer language should have to be suitable for power system analysis and simulation (Section 3.4). Comparisons among various modern programming languages commonly used in computational science is given. Finally, the chapter introduces the Python programming language and provides a complete simple example of modular application implemented in this language (Section 3.5).
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Power System Analysis

Frontmatter

Power Flow Analysis

Abstract
This chapter describes the power flow analysis from both analytic and algorithmic viewpoints. Section 4.1 introduces the power flow problem through a simple example and clarifies the differences between power flow and circuit analysis. Section 4.2 provides a taxonomy of the power flow problem, while Section 4.3 presents the standard power flow equations. Section 4.4 describes the most common algorithms used for solving this problem. These are the Gauss-Seidel’s method, the Newton’s method and its variants, the fast decoupled power flow and the dc power flow. A discussion about the single and distributed slack bus models and a comparative example are also included in Section 4.4. Section 4.5 provides a general mathematical framework for the power flow problem based on the continuous Newton’s method. Finally, Section 4.6 summarizes the most relevant concepts provided in this chapter.
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Continuation Power Flow Analysis

Abstract
This chapter describes a variety of techniques used for determining the point of collapse of power flow equations with particular emphasis on continuation power flow analysis. Section 5.1 introduces the maximum loading condition problem using a didactic 2-bus system. Section 5.2 defines the general model for the maximum loading condition. Section 5.3 describes direct methods for computing saddle-node bifurcation and limit-induced bifurcation points while Section 5.4 describes the continuation power flow technique. Section 5.4 also explains the conceptual differences, advantages and drawbacks of continuation (or homotopy) methods with respect to direct ones. Subsections 5.4.4 and 5.4.5 discuss the analogy between the continuous Newton’s method and the homotopy approach and the N-1 contingency analysis, respectively. Finally, Section 5.5 summarizes the main concepts of the continuation power flow analysis.
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Optimal Power Flow Analysis

Abstract
This chapter describes the optimal power flow problem. Section 6.1 provides the background of the OPF problem and justifies the need for numerical methods. Section 6.2 provides a general nonlinear programming model for the OPF problem. A variety of examples are also provided in this section. Section 6.3 describes two solver methods for tackling the OPF problem, namely the generalized reduced gradient and the primal-dual interior-point methods. For the latter method, the Python implementation and numerical results are also provided. Finally, Section 6.4 summarizes common parameters of the interior point method.
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Eigenvalue Analysis

Abstract
This chapter describes various aspects of eigenvalues analysis. Section 7.1 provides the background of modal analysis using a simple one-machine infinite-bus example. Section 7.2 describes the small signal stability analysis for dynamical power systems and outlines the properties of equilibrium points, including bifurcation points commonly shown by power systems, participation factors and the Z-domain transformation. Section 7.3 describes a variety of methods for computing a reduced set of eigenvalues and introduces the singular value decomposition. Section 7.4 describes the modal analysis applied to the power flow Jacobian matrix. Finally, Section 7.5 summarizes most relevant concepts related to eigenvalue analysis.
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Time Domain Analysis

Abstract
This chapter describes numerical integration methods for transient stability analysis. Section 8.1 provides a qualitative justification of the need for numerical integration and describes intrinsic limitations of Lyapunov’s direct method. Section 8.2 describes two common models for time domain analysis, namely the current-injection and the power-injection models. Section 8.3 outlines a variety of explicit and implicit numerical methods, paying particular attention to the accuracy and the stability of these methods. Section 8.4 provides a complete numerical integration routine and discusses related issues such as the choice of the step length, disturbances and stop criteria, including the SIME method. Sections 8.5 and 8.6 briefly describes numerical methods for electro-magnetic as well as long-term transients, respectively. Finally Section 8.7 summarizes most relevant concepts given in this Chapter.
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Device Models

Frontmatter

Device Generalities

Abstract
This chapter is about modelling and scripting of general purpose devices. Section 9.1 defines the mathematical model of an as general as possible device, while Section 9.2 provides the conceptual basis for implementing a device as a class. Subsection 9.2.1 presents a Python example of a base device class, while Subsection 9.2.3 provides an example of specific device methods, namely the two-axis model of the synchronous machine.
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Power Flow Devices

Abstract
This chapter describes topological elements as well as standard shunt (i.e., connected to a single bus) devices for power flow analysis. The most important topological element is the bus, while standard devices are constant υΘ generators, PV generators, PQ generators, PQ loads and constant and switched shunt admittances.
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Transmission Devices

Abstract
This chapter describes the models of standard series devices, namely transmission lines (Section 11.1) and transformers (Section 11.2). In particular, Subsection 11.2.1 presents static two-winding transformers, Subsections 11.2.2 and 11.2.3 present under load tap changers and phase shifters, respectively, and Subsection 11.2.4 describes three-winding transformers. Finally, Section 11.3 discusses efficient vectorial computation for static series devices.
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OPF Devices

Abstract
The object of this chapter are the models that define the objective function and inequality constraints for the optimal power flow analysis discussed in Chapter 6. Sections 12.1 describes typical network security constraints. Section 12.2 describes technical limits and offering functions of generators. Finally Section 12.3 describes technical limits and bidding functions of loads.
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Faults and Protections

Abstract
This chapter describes symmetrical three phase faults (Section 13.1), breakers (Section 13.2) and relays (Section 13.3). The chapter also describes measurement devices of non-standard quantities during time domain simulations, namely the Phasor Measurement Unit (Section 13.4) and the bus frequency measurement (Section 13.5).
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Loads

Abstract
This chapter describes static and dynamic nonlinear loads. Since traditional loads used in power flow and transient analysis are constant PQ and shunt admittances, the loads described in this chapter are also called non-conforming loads. These are the voltage dependent load (Section 14.1), the ZIP load (Section 14.2), the frequency dependent load (Section 14.3), the exponential recovery load (Section 14.5), the thermostatically controlled load (Section 14.6), the Jimma’s load (Section 14.7), and the mixed load (Section 14.8).
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Alternate-Current Machines

Abstract
This chapter describes the two most important alternate-current machines used in power systems, namely the synchronous machine and the induction machine. Section 15.1 provides a detailed taxonomy of synchronous machine models, as well as a discussion about saturation models, the center of inertia and the sub-synchronous resonance phenomenon. Section 15.2 describes various induction machine models and provides an example about the induction motor start-up transient.
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Synchronous Machine Regulators

Abstract
This chapter describes the most relevant synchronous machines primary regulators and limiters. These are the turbine governor, the automatic voltage regulator and the over- and under-excitation limiters. These regulators are the dynamic counterpart of the static capability curve described in Section 12.2.1 of Chapter 12. Furthermore, this chapter also describes the power system stabilizer that allows efficiently damping synchronous machine rotor oscillations. Figure 16.1 provides a synoptic scheme of the synchronous machine regulators described in this chapter.
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Direct-Current Devices

Abstract
This chapter describes dc devices used for modelling hybrid electro-magnetic and electro-mechanical power system models. The devices included in this chapter are: dc nodes (Section 17.1), common interface equations for dc devices (Section 17.2), ideal generators (Section 17.3) and basic components such as RLC circuits (Section 17.4), dc machines (Section 17.5), and unconventional dc generators, namely solid oxide fuel cell, solar photovoltaic cell and energy battery (Section 17.6).
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AC/DC Devices

Abstract
This chapter describes the two most common ac/dc devices, namely the highvoltage dc transmission system (Section 18.1) and the voltage source converter (Section 18.2). Each section provides the detailed device model and control scheme examples.
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FACTS Devices

Abstract
This chapter describes Thyristor Controlled Reactor (TCR) and Voltage Sourced Converter (VSC) based Flexible AC Transmission System (FACTS) devices. In particular, the considered TCR-based FACTS devices are the static var compensator (Section 19.1) and the thyristor controlled series compensator (Section 19.2), whereas VSI-based FACTS devices are the static synchronous compensator (Section 19.3), the static synchronous series compensator (Section 19.4) and the unified power flow controller (Section 19.5).
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Wind Power Devices

Abstract
This chapter presents wind speed and wind turbine models. Wind power is particularly interesting from the modelling viewpoint since it combines stochastic models (i.e., wind speed), mechanics (i.e., wind turbine), electrical machines, power electronics (i.e., VSC devices) and controls. For this reason, wind power models conclude this part dedicated to power system modelling.
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Spare Material and Concluding Remarks

Frontmatter

Data Formats

Abstract
This chapter provides a taxonomy of existing data formats for power power system analysis. These include most commonly used formats of free and proprietary software packages as well as the IEC common information model. The chapter is completed by a discussion about the desirable features of a data format for power system analysis.
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Visualization Matters

Abstract
This chapter discusses visualization matters related to power system analysis. In particular, the aspects covered in the chapter are the adequacy of graphical user interfaces versus the command line usage (Section 22.1) and available approaches for displaying results (Section 22.2). The latter describes standard two-dimensional plots (Subsection 22.2.1), temperature maps (Subsection 22.2.2), three-dimensional plots (Subsection 22.2.3), and the integration of graphical information systems into power system analysis software packages (Subsection 22.2.4).
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Challenges of Scripting for Power System Education

Abstract
Most power system software packages are commercial proprietary products that require a generally costly license. This fact is implicitly accepted as normal in the power system community. However, there can be a reliable and costless alternative. This alternative is provided by Free and Open Source Software (FOSS). This chapter shows that FOSS is a valid platform to distribute educational and research-oriented tools for power system analysis as it has proved to be in several other scientific fields.
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Backmatter

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