Converter-Based Dynamics and Control of Modern Power Systems

By Antonello Monti, Federico Milano, Ettore Bompard and Xavier Guillaud

Converter-Based Dynamics and Control of Modern Power Systems addresses the ongoing changes and challenges in rotating masses of synchronous generators, which are transforming dynamics of the electrical system.

These changes make it more important to consider and understand the role of power electronic systems and their characteristics in shaping the subtleties of the grid and this book fills that knowledge gap.

Balancing theory, discussion, diagrams, mathematics, and data, this reference provides the information needed to acquire a thorough overview of resilience issues and frequency definition and estimation in modern power systems.

This book offers an overview of classical power system dynamics and identifies ways of establishing future challenges and how they can be considered at a global level to overcome potential problems. The book is designed to prepare future engineers for operating a system that will be driven by electronics and less by electromechanical systems.

• Includes theory on the emerging topic of electrical grids based on power electronics
• Creates a good bridge between traditional theory and modern theory to support researchers and engineers
• Links the two fields of power systems and power electronics in electrical engineering

• Language: English
• Publisher: Academic Press
• Release date: Oct 22, 2020
• ISBN: 9780128184929

Antonello Monti

Antonello Monti is currently the Director of the Institute for Automation of Complex Power Systems at the E.ON Energy Research Center at RWTH Aachen University and Scientist at Fraunhofer FIT as part of the Center for Digital Energy in Aachen. He has previously held positions at Politecnico di Milano, Italy, and at the University of South Carolina, USA. Antonello has been and is Associate Editor of several international journals edited by IEEE, Elsevier, and Springer. He has been the recipient of the 2017 IEEE Innovation in Societal Infrastructure Award.

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Chapter 1: Introduction

Antonello Montia; Ettore Bompardb; Xavier Guillaudc; Federico Milanod    a Institute for Automation of Complex Power Systems, RWTH Aachen University, Aachen, Germany

b Department of Energy Galileo Ferraris, Politecnico di Torino, Torino, Italy

c Laboratory of Electrical Engineering and Power Electronics, École Centrale de Lille, Lille, France

d School of Electrical and Electronic Engineering, University College Dublin, Dublin, Ireland

Abstract

Power Grids have evolved in the last 100 years without substantially changing the basic principles of operation. Since the end of the famous War of Currents, the key components have been the same and the principles of automation did not change significantly. Power Electronics is now changing significantly the characteristics of the power grids and it is now time to understand the consequences and what are the implications in terms of system dynamics.

Keywords

Power grids; Alternative current; Thermal dynamics; Electromechanical dynamics; Electromagnetic dynamics; Switching events and lightning; Power Electronics

1.1: Introduction

Power Grids have evolved in the last 100 years without substantially changing the basic principles of operation. Since the end of the famous War of Currents, the key components have been the same and the principles of automation did not change significantly.

Alternative current (AC) has been the main choice with few exceptions, and correspondingly AC generators, induction motors, and transformers have been the key components of such a system.

The main pillar of the power grid has been for about a century the synchronous machine and, consequently, the dynamics of the grid have been substantially determined by the physical characteristics of this component. At the same time, the prevalent use of thermal and hydro-power plants has pushed more and more towards a concentration in large generation units driven by consideration of efficiency and hence economy of scale.

Thanks to large thermal-driven power plants, it was possible to structure the study of a power system by separating some key categories of dynamics:

–Thermal dynamics: from minutes to hours

–Electromechanical dynamics: from milliseconds to seconds

–Electromagnetic dynamics: in the range of milliseconds

–Switching events and lightning: from microseconds to milliseconds

The availability of clear categories allowed the engineers to tackle the complexity of the power systems by selectively simplifying the models to target the specific timescale of a category of dynamics. Such a process of model reduction has some important consequences:

–A conventional dynamic model for angle and voltage transient stability analysis are reduced to their essentials and, sometimes, an analytical description is possible;

–Even when the analytical description is not viable, the computational burden for numerical analysis is significantly reduced.

This process has been a key element for the success of the development of a power system of the complexity of the continental Europe bringing to synchronism the operation of all the ENTSO-E operators. Growing knowledge in power systems dynamics and automation brought this infrastructure to be an extremely reliable system with an unprecedented level of power quality and security.

The main element of change that appeared in the last 30–40 years is power electronics.

Power electronics started penetrating the power system first of all at the load level. During the 1980s and 1990s most of the industrial processes started inserting variable speed drive as a mechanism to increase the flexibility of operation and also efficiency.

On the load side power electronics expanded then more and more also at the consumer level with the availability of low-cost inverters increasing the efficiency of everyday devices such as washing machine. During the first 10 years of the 21st century, this process has become massive making power electronics an obvious solution for a large majority of loads.

Another parallel development has been the introduction of high voltage direct current (HVDC) connection to reinforce part of the AC grid or to connect systems that are not synchronized. While first commercial implementations happened in the 1950s, the advent of silicon devices has been the major technological change that brought this technology to a new level of maturity in the 1980s. At the end of the 1990s, finally, the first application of voltage source converters (VSC) for HVDC gave a tremendous impulse to the development of this technology opening also the way for possible application of multiterminal solutions.

HVDC represents the first electronic technology able to interact with the electrical grid with an increased level of controllability and flexibility.

The move from current source to voltage source type of inverters allows also the inclusion of HVDC connectors in the provision of reactive power for voltage stability control.

The biggest change though is happening now at the generation level. The process of decarbonization of the energy system, in the framework of the energy transition, is aiming at substituting traditional power plants with renewable driven energy sources (RES). This change brings some significant changes from the power system dynamics perspective:

–RES may be also distributed and then we move away from the concept of having only large centralized power plants;

–RES are interconnected to the grid, in the majority of cases, through power electronics interfaces;

–RES (wind and solar) are driven by changing weather conditions that determine faster changes in the power input and introduce an unprecedented high level of stochasticity in the grid;

–Several novel technologies for energy storage devices are being developed and committed into the grid. Among these, power-electronic-based grid-connected lithium-ion and redox batteries are currently the most promising technologies.

All these three factors point in the same direction: dynamics of the grid is playing a new and more relevant role and the classical separation of categories is losing meaning. Thermal processes are substituted by intermittent and rapid changing patterns of wind and solar generation and slow electromechanical dynamics are substituted by fast electronic transients.

In a nutshell, future power grids are supposed to become a power-electronic-driven system in which renewable and distributed energy resource interact with smartly controlled (flexible) loads. If we consider that also transformers have the chance to become electronic devices, we have that the future grid will be completely a power electronics power system. While this evolution is also reopening the question DC versus AC, it is also in any case modifying the characteristics of the spectrum of interacting dynamics.

In effect, we can see the situation as a convergence of dynamics. This convergence of dynamics and Eigenvalues is definitely an element of complexity, but power electronics should be also considered as an opportunity. In the new scenario dynamics are the results of controllers that engineers have the freedom to design. This means that it is actually possible to reinvent the basic principle of grid interface with criteria that are totally different from the past.

The scope of this book is to take the reader through this transition. While traditional power systems dynamic is covered, main focus is given to the element of changes and the opportunities opened by the new technologies.

1.2: Book structure

The book can be fundamentally split into two parts. The first part deals mostly with methodologies and techniques that apply also to classical power systems, the second is vice versa concentrated on new or emerging solutions that are directly related to the idea of a power electronics power system.

Chapter 2 introduces the key elements of the classical power system dynamics theory. The key concept discussed is the idea of Swing equation (SE). SE is the cornerstone of power system dynamic theory condensing the interaction of the electromechanical system in a simple dynamic of power imbalance. Understanding the hypothesis of this approach is critical also to appreciate the role and impact of power electronics.

Still in the direction of classical theory, Chapter 3 extends the swing equations to the so-called modal analysis. Modal analysis is a small signal analysis of multibus system, still based on the electromechanical range of Eigenvalues and then still connected to the main hypothesis of the SE.

Chapter 4 moves from dynamics to automation presenting the basic principle of operation for voltage and frequency control. All the basic principles and criteria are reviewed and introduced.

Chapter 5 opens the new scenario of modern power electronics-based power system. It presents a brief introduction to power electronics and focus on the different mode of operation for inverters when used on the generation and load side. This chapter introduces different devices that can play a role in the dynamics of the grid and that are integrating part of the grid infrastructures. These include: FACTS, Smart Transformers, VSC-HVDC.

A key transformation given by the modern dynamics is the fact that also key quantities need new definition and measurement processes. Chapter 6, in particular, describes advanced methods for frequency definition introducing then the key challenges related to grids with low level of inertia.

From the definition to the automation, the following Chapter 7 uses the concept of the previous analysis to introduce modern approaches to frequency control and in particular the possibility to move from a strictly central approach to a distributed intelligence solution.

As mentioned in the previous section, in any case, the big change is introduced by the new dynamics in generation driven by power electronics. Chapter 8 discusses the control structure for different mode of operation of grid-connected inverters (Grid supporting, Grid feeding, etc.). In particular, the role of grid forming converters and of different algorithms and control schema show how to embed a frequency support with power electronics.

Chapter 9 introduces a possible futuristic approach in this direction called linear swing dynamics. The chapter shows how, thanks to the flexibility given by programmable control, the grid interface can dramatically change with respect to the case of a synchronous machine. The idea is to show how in the new scenario it is not necessary to replicate the past, but we can actually think freely and imagine a totally new power system for the future.

Of course, the new characteristics of the grid will affect not only frequency control but also voltage control. The last two chapters presents an overview of advanced method for voltage stability working at two different time scales. Chapter 10 focused on the steady-state characteristics and optimal coordination of control action in distribution networks, while Chapter 11 looks at voltage stability as a power electronic challenge introducing extension to power systems of theorems such as Middle brook criterion.

1.3: How to use the book

The book is intended for engineers that have already a background in power systems at least from the point of view of static analysis of grids.

The book is intended to complement master-level classes on power system dynamics. The content of the book is adequate for a full semester class for students focusing on energy and power grids. A prerequisite of a previous class on power system operation, modeling, and control is recommended.

The book can also represent a useful guide for practitioners to understand how the reality is changing day by day thanks to power electronics. Electrical engineers working for power system operators, for example, can find interesting information about the evolution of the dynamics they experience every day in their job.

Chapter 2: Review of the classical power system dynamics concepts*

Guilherme Pereiraa; Valentin Costana; Antoine Bruyèreb; Xavier Guillaudb    a Lab Paris-Saclay—Energy System Economics, Functioning and Studies (EFESE), EDF, Palaiseau, France

b Laboratory of Electrical Engineering and Power Electronics, École Centrale de Lille, Lille, France

Abstract

This chapter introduces the main elements of the traditional theory on the synchronous machine used as a generator of electricity connected to a large power system. A simplified model is proposed which grasps the dominant electromechanical behavior. Several comparisons are proposed between this simplified model and the more detailed models of the synchronous machine including progressively the major constituting elements of this complex system: Prime mover with its associated governor, various excitation systems and the voltage control, Power system Stabilizer.

Keywords

Synchronous machine; Swing equation; Governor; Excitation system; PSS

2.1: Introduction

Even with the fast increase of the renewable energy, synchronous machines are still the major way to produce electricity in the grid. They have been used for more than a hundred years for the production of electricity and they are still a very reliable and efficient part of the chain for the conversion of the energy coming from the primary source to the electrical energy delivered to the grid. Developed in the end of the 19th century, the production of electricity was based on the pure electromechanical concept which was emerging in these years. Even if the concept has not evaluated much since the beginning, the size has grown to reach huge power (1750 MW in Taishan power plant commissioned in 2018/2019).

The synchronous machine is composed of a stator made of three-phase windings connected to the AC grid and a rotor connected to a DC source. The rotating dc flux generates induced voltages in the stator windings, which is the base of the electromechanical conversion.

Synchronous machine theory and modeling are vastly addressed in the literature [1–6]. Several types of models have been developed and depending on the required analysis to be carried out, a specific representation may be more suitable than others.

In this chapter, the foundations of the classical EMT representation of the synchronous machine are first recalled and compared with a simplified electromechanical model. The different elements constituting the power conversion system are described. A short overview of the steam turbine is proposed. In the same time, the way to drive the power with the governor is recalled. Different types of excitation systems have been developed. They are presented and compared in terms of dynamics and performances and linked to the voltage regulation which is inherent to the synchronous machine operation. A Power System Stabilizer may be needed to damp the dynamic behavior of the electromechanical system, its principle is explained in the last part of this chapter.

With each element added to the detailed EMT model, a dynamic analysis is provided and the dominant oscillatory modes are compared with the one obtained from a simplified representation of the synchronous machine. In this model, the synchronous machine is represented by the internal voltage behind the transient reactance and the swing equation is used to describe its electromechanical dynamics.

2.2: Electromagnetic model of synchronous machines

According to [6], a model including two rotor circuits in each axis––one field circuit and one damper in the d-axis and two dampers in the q-axis––is recommended for use in more critical stability studies. The following paragraphs summarize the foundations used to establish this model. More details can be found in [1–3, 7].

Fig. 2.1A illustrates the equivalent electrical circuit of the synchronous machine. As previously mentioned, the rotor circuit is composed of four windings, whereas the stator circuit is composed of one winding for each phase of the system. The terminal voltage of each winding is expressed as the combined effect of an induced voltage and a voltage drop. According to Faraday’s law, the induced voltage is due to the variation of the linkage flux across the winding over time. From Fig. 2.1A, it can be observed the presence of two reference frames, where one is static and the other rotates over time. The major challenge related to that is the complexity of the equations describing the physical phenomena, which present multiple trigonometric terms.

Fig. 2.1 Equivalent circuit of the electromagnetic model of the synchronous machine. (A) abc frame. (B) dq frame.

To circumvent this issue, Blondel has proposed an elegant solution in [8], applying a rotating transformation on the quantities related to the stator. Because this transformation rotates at the angular frequency of the rotor at all times, in the rotor frame, all windings are stationary, which highly simplifies the problem. This transformation is known in the literature as abc to dq0 transformation or even, Park’s transformation after R. H. Park, who has generalized the method in [5]. The winding distribution after the application of Park’s transformation is illustrated in Fig. 2.1B. It should be highlighted that, under balanced sinusoidal conditions, the component 0 is null and, since only balanced operations are treated within this work, this component is not represented. Several variants of Park’s transformation exist. In the following model, the amplitude invariant transformation is used [1].

Therefore, Eqs. (2.1)–(2.6) express the terminal voltage of each winding of the synchronous machine considering the equivalent circuit illustrated in Fig. 2.1B.

Nota bene: Since the dampers of the synchronous machine are short-circuited, the terminal voltage of these windings are equal to zero. It should be highlighted that all electric equations of the synchronous machine are expressed in per unit using the conventions below:

   (2.1)

   (2.2)

   (2.3)

   (2.4)

   (2.5)

   (2.6)

where vd, vq, and vfd are the terminal voltages of the stator and field windings, Rs, Rfd, R1d, R1q, and R2q are the resistances of the windings, id, iq, ifd, i1d, i1q, i2q, and ψd, ψq, ψfd, ψ1d, ψ1q, and ψ2q are the currents and linkage fluxes across the stator, field and dampers windings, and ωr and ωb are the angular frequency and base angular frequency of the rotor.

The linkage fluxes are expressed in Eqs. (2.7)–(2.12). Since all windings along one axis are magnetically coupled, the linkage flux across one winding is composed both of the leakage flux induced by its self-inductance and of the mutual flux linking all inductances along the axis. Because d- and q-axes are perpendicular, there is no linkage between the windings of the axes:

   (2.7)

   (2.8)

   (2.9)

   (2.10)

   (2.11)

   (2.12)

where Lld, Llq, Llfd, Ll1d, Ll1q, and Ll2q are the leakage inductances of the stator, field and the dampers and Lad, Laq are the mutual inductances of d- and q-axes.

Fig. 2.2 illustrates a visual description of the equivalent circuits of the synchronous machine proposed from Eq. (2.1) to Eq. (2.12). From this representation, it is possible to determine the expressions of the so-called standard parameters of the synchronous machines, which translate their behaviors during transients, in which, the linkage fluxes are forced into high-reluctance paths by different induced currents, which decay in different periods of time [1, 3]. Depending on the decaying velocity of these components, the parameters associated to the phenomena are called, from the fastest to the slowest, subtransient, transient and synchronous, where the last one represents the steady state of the synchronous machine [1]. These parameters can be determined from experimental data obtained from short-circuit tests on unloaded machines [1, 9].

Fig. 2.2 Equivalent circuits of the dq -axes of the synchronous machine.

Regarding the mechanical modeling of the synchronous machine, the turbine-generator shaft is represented by a lumped single mass model, not displaying any torsional effect. Therefore, the variation of the angular frequency of the shaft is caused by the unbalance between the mechanical and electromagnetic torques applied on it. In per unit, the motion of the synchronous machine can be expressed as a function of the power unbalance. In the literature, Eq. (2.13) is also known as the swing equation:

   (2.13)

where △ ωr is the angular frequency deviation of the rotor in relation to the grid frequency (ωg), H and Kd are the coefficient of inertia and the damping factor of the rotating mass, Pm and Pe are the mechanical and electric powers at the shaft level and θ is the internal angle of the synchronous machine rotor. The coefficient of inertia (H) represents the amount of kinetic energy per rated power (MWs/MVA) stored into the turbine-generator shaft, and it is inherent to the physical construction of the machinery. Typical values of H are between 2.5 and 10 s, depending on the type of generating unit [1]. The damping factor (Kd) represents the damping related to the mechanics of the system (i.e., mechanical losses), and it can often be neglected for practical considerations [2]. To deduce Pe, the electric power at the stator level (Pt) is given in Eq. (2.14).

   (2.14)

Replacing Eqs. (2.1), (2.2) in (2.14):

   (2.15)

Rearranging the right side of Eq. (2.15):

   (2.16)

The right side terms of Eq. (2.16) correspond, respectively, to the rate of change of the magnetic energy stored in the armature, the electric power at the shaft level (Pe), which is also known as the power transferred across the air gap between the rotor and the stator of the synchronous machine, and the resistive losses at the stator level [1, 5].

2.3: E′X′H synchronous machine model

According to Refs.[1, 4], although simplified models of synchronous machines may conceal critical phenomena, they can still be considered acceptable for determined studies. In this section, a simplified model of the synchronous machine is proposed to determine the dominant dynamic of the system composed of a synchronous machine connected to an infinite bus. It is based on the simplest model used to represent synchronous machines during transients usually called constant voltage behind a single reactance associated with the swing equation, (2.13). This model is hereinafter referred to as E′X′H, referring to its electric and mechanical representations, where E′X′ and H are the main parameters of these models, respectively. The hypotheses considered to establish this model are listed below [1–3]:

•Considering that the variations of the angular frequency of the rotor are sufficiently small, ωr is assumed approximately equal to its nominal value (ω0), it does not present any impact on the stator voltages.

•The variations of the linkage fluxes of the stator (ψd and ψq) are also neglected. This neglects the electromagnetic transients of the stator of the synchronous machine, and, according to Ref. [1], the overlook of these phenomena can only be made if the same approximation is applied to the network equations, otherwise, the assumption is inconsistent.

•As previously mentioned, the armature flux is forced into high-reluctance paths outside the field winding by induced currents during transients. Since the subtransient stage decays much faster than the transient stage, the former (and its associated circuit) will be neglected. Furthermore, since the decay of the transient stage is slow––several seconds––the linkage fluxes are considered constant during all the transient period.

From these hypotheses, Eqs. (2.1)–(2.6) can be rewritten as given in Eqs. (2.17)–(2.19):

   (2.17)

   (2.18)

   (2.19)

By neglecting the flux in the dampers Eqs. (2.7), (2.9) can be simplified:

   (2.20)

   (2.21)

Defining ψad as:

   (2.22)

These equations are illustrated by Fig. 2.3. Isolating ifd in the second line of Eq. (2.22) and replacing in the first line, it is possible to rewrite ψad as:

   (2.23)