Source-Grid Interaction of Wind Power Integration Systems

By Da Xie, Xitian Wang, Yanchi Zhang and Chenghong Gu

Source-Grid Interaction of Wind Power Integration Systems systematically describes the problems of source-grid interactions of wind power grid-connected system, introducing related research methods and proposing a series of novel control methods for damping oscillations. The book presents problems to be solved, thus enabling easy understanding and perception, from detailed analysis of the problems, to mathematical derivations and simulation verification.

• Includes principles that can be used to analyze the operation and control of wind farms
• Presents models developed from basic to complex aspects that affect modeling accuracy
• Provides control methods and effectiveness verification based on rigorous theory and actual operational data

• Language: English
• Publisher: Elsevier Science
• Release date: Apr 29, 2023
• ISBN: 9780323951043

Da Xie

His major research interests include renewable energy, multi-vector energy system, system simulation, power electronic equipment, and smart grid.

Book preview

Source-Grid Interaction of Wind Power Integration Systems

Da Xie

Professor, Department of Electrical Engineering, Shanghai Jiao Tong University, P.R.China

Xitian Wang

Associate Professor, Department of Electrical Engineering, Shanghai Jiao Tong University, China

Yanchi Zhang

Professor, Department of Electrical Engineering, Shanghai Dian Ji University, China

Chenghong Gu

Reader, Department of Electronic and Electrical Engineering, University of Bath, UK

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Table of Contents

Cover image

Title page

Copyright

Chapter 1. Introduction

1.1. Overview of wind power development

1.2. Interaction between grid-connected wind power and power grid

1.3. Overview of research methods for the machine–grid interaction mechanism

1.4. Overview of control methods for machine–grid interaction

1.5. The main content of this book

Chapter 2. Small-signal model for grid-connected wind turbines

2.1. Small-signal analysis method for system dynamic stability

2.2. Small-signal wind turbine model—shafting part

2.3. Mathematical model of doubly-fed induction generator

2.4. Mathematical model of permanent magnet synchronous generator

2.5. Mathematical model of power grid

Chapter 3. Machine–grid interaction of wind power systems

3.1. Machine–network unified model of mainstream wind power systems

3.2. Initialization of small signal model

3.3. Machine–grid interaction of doubly-fed wind power generation system

3.4. Machine–grid interaction of permanent-magnet direct-drive wind power generation system

3.5. Influence of series compensation capacitor of transmission line on machine–grid interaction

Chapter 4. Equivalent method, oscillation propagation mechanism, and observability and controllability metrics for multimachine wind farm models

4.1. General structure of wind farm and double-machine small-signal wind turbine model

4.2. Small-signal model analysis of multimachine wind farm

4.3. Equivalence and reduced-order distributed cloud algorithm for large-scale wind power plants

4.4. Subsynchronous oscillation power propagation mechanism of wind power generation system

4.5. Controllability and observability metrics

Chapter 5. Impedance analysis of grid-connected wind turbines

5.1. Impedance analysis for dynamic system stability

5.2. Impedance model for doubly-fed wind turbines

5.3. Impedance model of permanent-magnet direct-drive wind turbine

5.4. Grid impedance model

5.5. Wind farm impedance model

5.6. Example of wind farm impedance modeling

5.7. Analysis of characteristics of the loop under subsynchronous interaction in wind power systems

Chapter 6. Suppression of source–grid interaction

6.1. Suppression strategy of wind turbine side

6.2. Suppression effect of reactive power compensation device

6.3. Suppression effect of high-voltage DC converter station on source–grid interaction

6.4. Suppression effect of energy storage system on the source–grid interaction

6.5. Additional power system stabilizer control for source–grid interaction suppression

Chapter 7. Online identification of wind turbine network interaction based on big data

7.1. Overview of wind power big data

7.2. Oscillation identification

7.3. Analysis of oscillation correlation factors

7.4. Research on location technology of oscillation disturbance source based on multisignal correlation analysis

Chapter 8. Power quality of wind farms

8.1. Overview

8.2. Detection of wind power quality

8.3. Measurement analysis of integer-order and high-order harmonics

8.4. Interharmonic analysis of wind power generation

8.5. Characteristic harmonic model of variable-speed constant-frequency wind turbine

8.6. Harmonic phase analysis of wind power generation

8.7. Flicker of wind power generation

Index

Copyright

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Chapter 1: Introduction

Abstract

It is a practical problem that must be solved in the planning, design, and operation of grid-connected wind farms to analyze and eliminate the complex oscillation in wind farms and power grid. This chapter summarizes the development of wind power generation, the structure of wind turbines, the interaction principle of grid-connected wind power and power grid, the research methods of source-grid interaction mechanism, and the control methods of source grid interaction and briefly introduces the main contents of this book.

Keywords

Control method; Source-grid interaction; Subsynchronous oscillaiton (SSO); Wind power generation; Wind turbine

1.1 Overview of wind power development

1.1.1 Overview of global wind power development

1.1.2 Overview of wind power generation technology

1.1.2.1 Wind turbine

1.1.2.2 Wind turbine generator

1.2 Interaction between grid-connected wind power and power grid

1.2.1 Overview of machine–grid interaction problems

1.2.2 Classification of machine–grid interactions

1.2.2.1 Institute of Electrical and Electronics Engineers definition and classification of subsynchronous resonance for conventional turbogenerators

1.2.2.2 Definition and classification of subsynchronous oscillation related to wind power systems in some studies

1.2.2.3 Relationships among various machine–grid interactions

1.3 Overview of research methods for the machine–grid interaction mechanism

1.3.1 Mechanism model analysis method

1.3.1.1 Complex torque coefficient method

1.3.1.2 Impedance analysis method

1.3.1.3 Small signal analysis method

1.3.2 Analysis method of electromagnetic transient simulation model

1.3.2.1 Frequency sweep method

1.3.2.2 Test signal method

1.3.2.3 Fast Fourier transform and Hilbert–Huang transform

1.3.2.4 Prony algorithm

1.4 Overview of control methods for machine–grid interaction

1.4.1 Damping control

1.4.2 Parameter optimization

1.4.2.1 Kharitonov's theorem

1.4.2.2 Analytic hierarchy process

1.4.3 Operating point adjustment

1.5 The main content of this book

Bibliography

1.1. Overview of wind power development

1.1.1. Overview of global wind power development

The statistical results from the Global Wind Energy Council in 2021 show the rapid development of wind power generation technology during the 20th century. Following 2011, as shown in Fig. 1.1A, newly built installed wind power capacity has been above 40GW each year, with a steadily increasing growth rate. Newly installed wind power capacity in 2020 reached 93GW, up 52.8% from 2019 and the highest level since 1997. Globally, cumulative installed wind power capacity reached an astonishing 742.689GW in 2020, a 14.2% increase over 2019.

Although wind power generation shows a rapid growth trend globally, the distribution in different countries and regions is quite different, as shown in Fig. 1.1B. More than 40% of the world's total wind power generation is in Asia. The regional distribution of wind power in Asia varies greatly, mostly among China, India, and Japan. Wind power in China accounts for 39%, or 285.77GW, of global wind power, far ahead of other countries. The wind power shares of European countries have a relatively average distribution, with Germany, Spain, and the United Kingdom having the largest shares. Wind power in North America is mainly in the United States, and newly installed capacity continues to lead in North America. North America (18.4%) overtook Europe (15.9%) as the second-largest region for new capacity additions, driven by a record year of new installations in the United States. In 2020, Latin America was the fourth-largest region for wind power growth (5.0%), followed by Africa and the Middle East (0.9%).

The Global Wind Report 2021, released by the Global Wind Energy Council in 2021, expects the global wind energy market to grow an average of 4% per year. By 2030, global installed wind power capacity is expected to exceed 2000GW, with wind power generation accounting for 17%–19% of all power generation capacity and carbon dioxide emissions reduced by up to 3 billion tons per year. By 2050, 25%–30% of electricity will be provided by wind power.

Figure 1.1  Global wind energy development. (A) Global installed wind capacity and development. (B) Top 10 cumulative capacity in 2020.

1.1.2. Overview of wind power generation technology

Compared with traditional thermal power units, hydropower units, and gas turbines, wind turbines are significantly different, mainly in the following: (1) The capacity of a single generator is small. The capacity of wind turbines commonly used at present is about 2MW, which is much lower than the other three types. (2) The structure is simple, and the wind turbine mainly consists of a drive system (blade), a speed-increasing system (gearbox), a power generation system, and a converter system. (3) It has obvious intermittent randomness, and wind power generation is greatly affected by wind conditions. Its power output is unstable. (4) The forms of access to the grid are diversified and include grid connection directly and through power electronic equipment such as converters.

The key wind power generation technologies are wind turbine maximum energy capture technology, rectification and inverter technology, wind power-friendly grid connection technology, and coordinated machine–grid and farm–grid control technology. Wind turbines usually comprise mechanical parts such as wind turbines and electrical parts such as generators, control systems, transformers, and lines.

1.1.2.1. Wind turbine

A wind turbine includes rotor blades, hubs, low-speed shafts, speed-increasing gearboxes, and high-speed shafts. The blades convert captured wind energy into mechanical energy for the rotation of the low-speed shaft. After acceleration by the gearbox, the high-speed shaft drives the generator to generate electricity. In a direct-drive wind turbine, the speed-up effect is achieved by increasing the number of generator pole pairs instead of through the gearbox. The output power of a wind turbine can be calculated by Eq. (1.1):

(1.1)

where C p (λ, β) is the wind energy utilization coefficient, and λ=ω w R/v w is the tip speed ratio, in which ω w is the angular velocity of the wind turbine, R is the radius of the wind rotor, and v w is the wind speed. β is the pitch angle, ρ is the density of the air, and A = πR ² is the area swept by the wind rotor. When the pitch angle is a fixed value, C p mainly depends on the tip speed ratio, λ, as shown in Eq. (1.2):

(1.2)

1.1.2.2. Wind turbine generator

At present, mainstream wind turbine generators are divided into two kinds: fixed-pitch stall wind turbine generators and variable-pitch variable-speed wind turbine generators.

In a fixed-pitch wind turbine generator, the blades are rigidly connected to the hub. When the wind speed is greater than the rated wind speed, a vortex forms on the surface of the blade, and wind energy utilization efficiency is automatically reduced, thereby ensuring that the output power of the generator is maintained near the rated value. The fixed-speed wind turbine is also called a stall wind turbine because of its stall adjustment characteristics. Contrary to the stall wind turbine, the blades of a variable-speed wind turbine can be adjusted through the pitch control system to achieve variable-speed operation, and power generation efficiency and flexibility are significantly improved. The variable-speed wind turbine can use various generators and converters, typically doubly-fed and permanent magnet wind turbines.

1.1.2.2.1. Fixed-speed induction generator

The fixed-speed induction generator (FSIG) generally adopts a squirrel-cage asynchronous motor and does not use power electronic equipment in the whole system. Its structure is shown in Fig. 1.2A. An FSIG comprises a wind turbine, asynchronous induction generator, transformer, and parallel compensation capacitor. Since the squirrel-cage induction generator has no external excitation, it consumes a great deal of reactive power during operation. Therefore, to improve its power factor, a capacitor is usually connected to the generator's terminal bus to provide reactive power in its excitation process.

Figure 1.2  Popular wind turbines. (A) Fixed-speed induction generator. (B) Doubly-fed induction generator. (C) Permanent magnet synchronous generator.

1.1.2.2.2. Doubly-fed induction generator

The mechanical part of a doubly-fed induction generator (DFIG) is essentially the same as that of an FSIG, but DFIG uses a wound rotor induction motor with a slip ring. The stator and rotor of the DFIG can feed power to the grid; Fig. 1.2B shows a typical structure. The stator of the doubly-fed wind turbine is directly connected to the grid and can only output power. In contrast, the rotor is connected to the grid through an AC/DC/AC power converter, with power flow determined by the generator's operating mode. If the rotor speed of the DFIG is higher than the synchronous speed, DFIG is in a supersynchronous operational state, and the rotor outputs power to the grid. When the rotor speed is lower than the synchronous speed, DFIG must absorb power from the grid. The rotor speed of the DFIG can run at a maximum of 1.3 times synchronous speed, which can output a large amount of power to the grid with high economy. DFIG also has the characteristics of variable-speed operation and a wide range of operations, so DFIG is the main type of wind turbine today. Nevertheless, there are so many imperfections. Using brushes and slip rings reduces operational reliability and increases maintenance costs. The actual operation of wind farms also shows that the gearbox is also prone to damage, which has become a bottleneck restricting the application of DFIG.

1.1.2.2.3. Permanent magnet synchronous generator

The impeller of the permanent magnet synchronous generator (PMSG) is directly connected to the rotor of the generator. By using a multipole PMSG, the gearbox is avoided and operational reliability is improved. PMSG does not require external excitation, and the stator is directly connected to the power grid through a full-power converter to realize variable-speed operation and greatly improve power generation efficiency. The typical structure of the PMSG is shown in Fig. 1.2C. The advantages of the PMSG are as follows: (1) The damage probability of mechanical components caused by wind energy fluctuations is greatly reduced without a gearbox. (2) No external excitation is required, the system structure is simpler, and the power generation efficiency is significantly improved. (3) The full power converter weakens the connection between the electrical system and the mechanical system of the turbine, and the mutual interference is weakened. The disadvantages are mainly the following: (1) The permanent magnet generator is directly connected to the impeller, which places higher requirements on the mechanical strength of the shafting. (2) The temperature greatly influences the permanent magnet, and a reliable cooling system is required. (3) The price of permanent magnet materials is relatively high, and PMSG costs more than the other two types.

In addition, in 2007, the International Council on Large Electric Systems released a report on the dynamic characteristics of wind power generation. The report proposed classifying the dynamic models of wind turbines into four general dynamic models according to their physical characteristics: Constant-speed asynchronous (type 1), variable rotor resistance induction generator (type 2), doubly-fed induction (type 3), and fully rectified (type 4). In this book, the traditional names are used for convenience in the descriptions and discussions of customary methods.

1.2. Interaction between grid-connected wind power and power grid

1.2.1. Overview of machine–grid interaction problems

The potential interaction between large-scale wind farms and the power grid has been a topic of concern in recent years. Studies have found that this interaction consists mostly of active power oscillation, and the corresponding oscillation frequency is lower than the system power frequency. The machine–grid vibration that first attracted people's attention originated from the subsynchronous resonance (SSR) problem of the steam turbine. When steam turbine SSR occurs, the electrical and mechanical state quantities of the turbine produce continuous or even increased oscillations. In severe cases, the rotor shafting of the steam turbine is seriously damaged. In the 1960s, when the Northwest and Southwest Combined Systems in the United States were interconnected, low-frequency oscillation (LFO) was observed for the first time. In the early 1970s, the Mohave Power Plant in the western United States suffered two events of serious damage to the shaft system of the unit within a year. Both accidents were caused by self-excited torsional vibration caused by coupling between the generator shafting and the series compensation. The fault recording shows that the line current contains an obvious 30 Hz component. Although this is lower than the system frequency, it is not within the category of LFO. Since this oscillation phenomenon is caused by inappropriate series compensation capacitors on the transmission line, such electromechanically coupled oscillations are defined as SSR. From 1977 to 1980, the Navajo and San Juan Power Plants within the Western Power Grid in the United States also experienced SSR problems; at the same time, the Square Butte Power Plant in the United States experienced a subsynchronous oscillation (SSO) phenomenon when it was connected to high-voltage direct current (HVDC) transmission lines. HVDC projects such as Fenno-Skan in Sweden and Rihand-Delhi in India have also demonstrated the possibility of SSOs. This series of events triggered a wave of academic research on SSR/SSO phenomena.

With the large-scale integration of wind power, photovoltaic, and other renewable energy generation into the grid through power electronic converters, some new SSR/SSO problems have been raised. In 2009, a power grid in southern Texas in the United States caused a group of doubly-fed wind turbines to be radially connected to the series compensation grid due to a line fault, causing severe SSR that was widely known as a subsynchronous control interaction (SSCI). In 1991, the third IEEE Literature Supplement mentioned that extremely long and high parallel capacitance compensation lines might also cause low-order torsional vibration (modal) interactions and proposed the HVDC-induced torsional vibration (torsional interaction, or TI), defined the concept of synchronous torsional interaction (SSTI). Table 1.1 presents the main accidents, as well as their types, that have occurred since the 1960s from the interaction of wind farms and grids.

1.2.2. Classification of machine–grid interactions

1.2.2.1. Institute of Electrical and Electronics Engineers definition and classification of subsynchronous resonance for conventional turbogenerators

In 1992, an Institute of Electrical and Electronics Engineers (IEEE) working group proposed standard terminology to define and classify the SSR problem of conventional turbogenerators. SSR is divided into self-excitation (SE), induction generator effect (IGE), torsional interaction (TI), and torsional amplification (TA), as shown in Fig. 1.3. The IEEE defines SSO as the general term for oscillations caused by any phenomenon that results in oscillations in the subsynchronous frequency range and negligible or apparent complementary supersynchronous frequencies. Therefore, device-dependent SSO (DDSSO), IGE, TI, and TA are considered phenomena, while SSO is the oscillation caused by these phenomena.

Figure 1.3  Conventional classification of the subsynchronous resonance phenomenon and Institute of Electrical and Electronics Engineers terms.

Table 1.1

HVDC, high-voltage direct current; LFO, low-frequency oscillation; SSCI, subsynchronous control interaction; SSO, subsynchronous oscillation; SSTI, synchronous torsional interaction.

1.2.2.1.1. Subsynchronous resonance

As defined by IEEE terminology, SSR is a power system state where the grid exchanges energy with a turbogenerator at one or more natural frequencies below the system’s synchronous frequency. SSR is further divided into SE (also known as steady-state SSR) and transient SSR (including TA). Steady-state SSR contains SSRs caused by IGE and TI.

1.2.2.1.1.1. Induction generator effect

The SE of an induction generator by series compensation is caused by IGE, as the rotor circuit turns faster than the rotating magnetic field produced by the subsynchronous armature current. In this case, the resistance of the rotor to the subsynchronous current becomes negative as viewed from the armature terminals. IGE occurs when the negative resistance is greater than the sum of the armature and grid resistances at some subsynchronous frequency.

1.2.2.1.1.2. Torsional interaction

TI is the interaction between the mechanical system (turbine generator) and the grid with series compensation. The shaft of the turbogenerator responds to system disturbances at its natural frequency and produces a corresponding subsynchronous voltage at the generator terminals. If this subsynchronization frequency matches the electrical resonant frequency of the grid, the corresponding stator current will generate torque and excite torsional vibration. The magnitude of the torque will continue to increase, resulting in increased oscillations.

1.2.2.1.1.3. Torque amplification

TA occurs after large disturbances in the series capacitor compensation system. System disturbances cause electromagnetic torque oscillations at frequencies complementary to the grid’s natural frequency. If this frequency coincides with one of the natural frequencies of the shaft, resonance occurs between the electrical frequency of the network and the mechanical frequency of the shaft.

1.2.2.1.2. Device-dependent subsynchronous oscillation

DDSSO is defined as oscillations caused by the interaction between the turbogenerator and various fast-acting controllers of power system components (such as HVDC converters, static var compensators, high-speed governors, and controllers).

1.2.2.2. Definition and classification of subsynchronous oscillation related to wind power systems in some studies

The oscillation mechanism and characteristics associated with wind turbines are quite different from traditional SSR events associated with steam turbine generators, so some scholars have redefined terms, definitions, and classifications to better understand the SSCI mechanism of wind turbines. According to the various SSO interaction objects and mechanisms, oscillations are classified as torsional vibration interaction, electrical network resonance, and control interaction, as shown in Fig. 1.4. This classification is valid for the SSOs of both traditional power generation grid-connected systems and renewable energy generation grid-connected systems.

1.2.2.2.1. Torsional vibration interaction

Torsional vibration interaction refers to the interaction between the mechanical part of the generator shaft and the converter controller of the power electronic device (such as HVDC, FACTS, etc.). Torsional vibration interactions may be caused by conventional steam turbines, hydroturbines with low generator-to-turbine ratios, type 1–3 wind turbines, the mechanical parts of large motors with fixed series compensation, HVDC converters, FACTS converters, power system stabilization, governor controllers, and circuit breakers. This type of interaction covers all oscillation problems involving traditional turbine generator shafting and the shafting of wind turbines. It covers IEEE-related shafting terms such as TI and TA. The oscillation frequency caused by torsional vibration interaction is within the subsynchronous frequency range (f r < f 0), where f r is the oscillation frequency, and f 0 is the fundamental frequency of the system.

Figure 1.4  Oscillation classification based on interaction mechanism.

1.2.2.2.2. Electrical network resonance

Electrical network resonance refers to the state in which the series-compensated grid exchanges energy with induction generators at one or more natural frequencies below the synchronous frequency. Electrical network resonance occurs between the generation and transmission of electricity in a power system where inductive and capacitive elements are installed. Electrical network resonance is also known as LC resonance. Electrical network resonance may be caused by the interaction of some equipment and the converter. These devices include fixed series compensation, controllable series capacitors, blocking filters, DC filters, parallel compensation, etc., while converters include synchronous machines, asynchronous machines, type 1–3 wind turbines, and type 3–4 wind turbines. LC resonance includes an oscillation phenomenon defined as IGE in the IEEE classification. The oscillation frequency caused by the resonance of the electrical network is in the subsynchronous frequency range.

1.2.2.2.3. Control interaction

Control interaction occurs between the power electronic converter (PV or wind turbine converter) control and series compensation or a weak AC network. The converter control in this interaction plays a key role in analyzing the mechanism and characteristics of the oscillations. The basic principle of this interaction is similar to that of electrical network resonance, except that the interaction is a virtual capacitance/inductance interaction provided by the power electronic converter control rather than a physical capacitance and inductance element interaction. Control interactions may be made by converters for type 3–4 wind turbines, HVDC based on voltage/current source converters, FACTS devices and weak AC grids, converters for type 3–4 wind turbines, VSC-HVDC, and VSC-based FACTS controllers. Such oscillations cannot be explained by existing IEEE terminology. The frequency of oscillations induced by the control interaction is in the sub- or supersynchronous frequency range (f r < f 0 or f 0 < f r <2f 0). In practical power systems, electrical network resonance, torsional vibration interaction, and control interaction can exist simultaneously. This coexistence has been observed in the recent SSO events in China's Guyuan and Hami wind power systems. In the Guyuan event, the electrical network resonance and control interaction coexist, and SSO is induced by electrical network resonance and maintained by control interactions. In the Hami wind power generation system, the control interaction and the torsional vibration interaction coexist. The oscillation is caused by the control interaction and propagates through the power grid, causing the torsional vibration interaction of the nearby turbine generators.

1.2.2.3. Relationships among various machine–grid interactions

Based on the definition and classification of oscillations by IEEE and existing research, the relationship between various machine–grid interactions can be described according to definition and function, as shown in Fig. 1.5. The complex oscillation of a multipower connected grid can be divided into two categories, namely subsynchronous interaction (SSI) and LFO. The traditional theory holds that LFO is caused by the negative damping effect of the rapid excitation of the generator with a general frequency between 0.1 and 2.5Hz, which generally manifests as the relative swing between the rotors of each power supply. SSI usually manifests as the power fluctuation between the motor and the grid at a lower-than-synchronous speed—that is, the power fluctuates at a frequency lower than 50 Hz. SSI includes SSTI and SSCI. SSTI is related to the mechanical dynamics of the shafting and will eventually act on the shafting as a mechanical torsional moment, which may cause damage to the mechanical structure of the wind turbine shafting. SSR, as mentioned, is caused by series capacitance in the grid, while SSO is now considered a stability problem for control systems with high-speed electronic switches due to inappropriate phasing around the oscillation frequency in the control algorithm relationship, resulting in the formation of positive feedback. SSO includes SSCI and SSTI, and SSTI includes SSR.

Figure 1.5  Relationships of various interactions between machines and grid.

1.2.2.3.1. Synchronous torsional interaction

SSTI mainly refers to the resonance of the mechanical system of generators and power electronic devices or electrical components in the power system below the synchronous frequency. Controllers of power electronic devices such as HVDC and FACTS quickly control or respond to power, current, and other factors in the subsynchronous frequency range that affect the phase difference between the electromagnetic torque and rotational speed of the generator. If electromagnetic torque and rotational speed are out of phase by more than 90 degrees, these devices introduce negative damping into the generator, causing subsynchronously amplified oscillations in the generator shafting.

1.2.2.3.2. Subsynchronous control interaction

SSCI is the resonance generated by the interaction between the power electronic control system and the power system equipped with series compensation capacitors, a new type of oscillation that appears in wind power development that is different from SSO thermal power units. SSCI is caused by the interaction between the wind turbine controller and fixed series compensation. It is mainly determined by the parameters of the wind turbine controller and the transmission system. It has nothing to do with the natural modal frequency of the shafting—the resonant frequency is not fixed and varies with the operating state of the wind power system and the control algorithm adopted by the converter. SSCI occurs because the fast direct current control of the wind turbine leads to negative damping within the system, and the resonant current generated by disturbance of the system induces a corresponding subsynchronous current on the generator rotor, thereby causing the rotor current to change. After sensing this change, the converter adjusts the converter output voltage, causing the actual current in the rotor to change. If the output voltage boosts the rotor current, resonant current oscillation intensifies, destroying system stability.

1.2.2.3.3. Low-frequency oscillation

LFO often occurs in power systems and is mainly due to the negative damping effect of power system, which frequently occurs on weak-connection, long-distance, heavy-load transmission lines and is more likely under the conditions of fast and high-amplification excitation systems. When the generators in the system are running in parallel through the transmission line, an unavoidable disturbance will cause the rotors of each generator to sway relative to each other. If system damping is insufficient or the system is negatively damped, continuous oscillation will occur at a fluctuation frequency generally between 0.1 and 2.5Hz, which is an LFO (also known as power oscillation or electromechanical oscillation). The LFO problem belongs to the category of small disturbance stability analysis, which studies the problem of power angle oscillation between generator rotors and even out of synchronization. According to the scope of the oscillation and the value of the oscillation frequency, power system LFO is divided into two modes: interarea and local.

The interarea mode is the oscillation of one part of the generator cluster relative to another. In an interconnected system with weak connections, this kind of oscillation often occurs between two or more coupled generator clusters. Due to the large electrical distance and relatively large equal inertial time constant of the generator, its oscillation frequency is relatively low, generally between 0.1 and 0.7Hz. This kind of oscillation is more harmful, and once it occurs, it is transmitted to the whole system through the tie line.

The local mode is the oscillation between units in the plant or between units in the plant within a short electrical distance. The oscillation frequency is generally between 0.7 and 2.5Hz. This oscillation is limited to the area. Compared with the former, its influence range is relatively small and easy to remove.

1.3. Overview of research methods for the machine–grid interaction mechanism

The purpose of analyzing the interaction between the grid-connected wind power generation system and the power grid is to determine the main oscillation modes in the wind power generation system, judge its stability, find the system variables that play a leading role in different oscillation modes, study the possible mutual transformation relationship between different oscillation modes, and provide a theoretical basis for formulating corresponding oscillation suppression strategies. According to engineering practicability and analysis accuracy, the main analysis methods can be divided into two categories. One is the screening method, which determines the units that will interact with the power grid. The commonly used methods include frequency sweeping methods and the unit coefficient method. The other type can accurately and quantitatively analyze the interaction characteristics after fine modeling of the wind turbine, primarily including the complex torque coefficient, time domain simulation, Prony algorithm, and small signal analysis methods.

Figure 1.6  Traditional research methods of stability mechanism.

Research on the stabilization mechanism can be started from the two aspects shown in Fig. 1.6. One is to use PSCAD, EMTDC, and other electromagnetic transient research software to establish the electromagnetic transient model of the power grid. This model has nonlinearity characteristics, multiple time scales, and randomness, and the time domain simulation method is used to study the oscillation mode. After the voltage and current waveforms of the running buses are obtained by simulation, the frequency-impedance characteristics of the oscillation mode can also be studied using the frequency sweep method. The damping torque coefficient of the oscillation mode is studied by the test signal method. The frequency, damping, amplitude, and phase of each oscillation mode are studied by the Prony algorithm.

The other is to establish the mechanism model of the large power grid system and use MATLAB/SIMULINK to solve and analyze the model. There are mainly small signal models based on the principle of small disturbance linearization, and the eigenvalue analysis method is used to analyze each oscillation mode. The complex torque coefficient method based on the state space model can calculate the damping torque coefficient to be analyzed and studied. Mechanism modeling and simulation modeling can confirm each other and conclude modal stability.

1.3.1. Mechanism model analysis method

1.3.1.1. Complex torque coefficient method

The complex torque coefficient method was proposed by I.M. Canay in 1982 and has become one of the basic methods for analyzing system dynamics problems. This method is based on the linearization model of the system to be studied. First, the generator set is made to oscillate with equal amplitude near the natural frequency of the shafting. The response curves of the mechanical torque and electromagnetic torque of the wind turbine to the oscillation are then obtained by calculation. Whether the oscillation converges is judged by the positive and negative values of the corresponding mechanical damping and electrical damping, and the convergence speed of the oscillation is judged by the magnitude of the corresponding mechanical damping and electrical damping to determine whether the system will interact accordingly.

The complex torque coefficient method can be used to analyze the interaction of large-scale power systems. It not only fully displays the trend of the electrical damping coefficient changing with frequency but also studies the influence of system parameter changes on electrical damping, which helps formulate an effective suppression strategy. In addition, the method also accounts for the dynamic process of various control systems and the influence of unit operating conditions on the interaction, which has high engineering practical value. However, the applicability of this method is still controversial. Although many researchers have used the complex torque coefficient method to analyze various interactions in multimachine power systems, if the multimachine system is analyzed, the rest of the generators outside the research unit must be equivalent to infinite power sources, so the complex torque coefficient method is only applicable to single-machine-to-infinite systems.

1.3.1.2. Impedance analysis method

The basic principle of the impedance analysis method is to divide the system into two subsystems: power supply and load. The power supply subsystem is usually represented by its Thevenin equivalent circuit—that is, it consists of an ideal voltage source U S and output impedance Z S in series; the load subsystem can be represented by a load input impedance, Z 1. Fig. 1.7 shows the equivalent circuit model of the voltage source system.

Figure 1.7  Equivalent circuit model of voltage source system.

The current flowing from the source to the load is

(1.3)

It is assumed that the power supply voltage is stable at no-load, and the load current is stable when the ideal power supply is supplied. In this case, U s (s) and 1/Z l(s) are stable, and load current stability depends on the second item on the right in (1.3):

(1.4)

Therefore, the stability of the interactive system depends on H(s). Note that H(s) is similar to a closed-loop transfer function of a system with negative feedback control. The forward channel gain of the negative feedback is 1, while the feedback channel gain is Z S (s)/Z 1(s), that is, the ratio of the output impedance of the power supply to the input impedance of the load. According to the linear control theory, H(s) is stable only when Z S (s)/Z 1(s) satisfy the Nyquist stability criterion. After deriving the Z S (s)/Z 1(s) of the wind power generation system, we can substitute the actual values of the corresponding parameters to analyze the root locus of the open-loop system Z S (s)/Z 1(s). When the range of values satisfies the Nyquist stability criterion, the system is stable. When the system is unstable, the closed-loop transfer function H(s)/Z S (s) is used to apply a current signal to its input to obtain the output voltage signal. By using the Prony algorithm, FFT, or HHT algorithm to analyze the output waveform, the mode and type of oscillation can be identified.

1.3.1.3. Small signal analysis method

Small-signal analysis, also known as eigenvalue analysis, is an accurate analysis method based on linear system theory that can provide a large amount of characteristic information about the object under study. When using the small-signal analysis method, the object under study is first linearized at the steady-state operating point to obtain its small disturbance model. The eigenvalues and eigenvectors of the state matrix of the system state equation are then solved. Finally, through modal analysis and sensitivity analysis, system variables strongly correlated with specific torsional vibration modes are found to monitor and formulate corresponding suppression strategies.

The biggest advantage of the small signal analysis method is that the model used is very accurate, all the modal information of the system under study, and the system variables that play a leading role can be obtained, and the analysis accuracy is high. Through the changing trend of the eigenvalues before and after the adjustment of control parameters, a control strategy to effectively suppress various interactions is formulated. Due to fine modeling of the system when the small-signal analysis method is used, the order of the state matrix will be very high when analyzing large-scale wind farms, and the dimension disaster problem may occur, but establishing the equivalent value of wind farms to simplify the model can effectively avoid this problem.

1.3.2. Analysis method of electromagnetic transient simulation model

The time-domain simulation uses numerical integration to gradually solve differential equations of the entire power system, which can be used to analyze various interaction problems. The time domain simulation method is suitable for both linear and nonlinear mathematical models. The model used by this method can be very fine. In addition, the network elements can use the centralized parameter model and the distributed parameter model, the mass block model of the shaft system of the unit can be made more detailed, and even the distributed parameter model can be used. Therefore, the time domain simulation method can provide detailed simulations of various network operations such as generators, system controllers, system faults, and switching actions. The typical electromagnetic transient simulation software used in this method includes EMTP, PSCAD/EMTDC, SIMPOW, and NETOMAC.

The time domain simulation method can obtain the curve of each variable in the system over time, which is intuitive, realistic, and suitable for transient analysis after various large disturbances. The disadvantage of the time-domain simulation method is that it cannot reveal the generation mechanism and influencing factors of the interaction and cannot identify and analyze the oscillation frequency and damping characteristics of each mode.

1.3.2.1. Frequency sweep method

When the frequency sweep method is used for analysis, the target system to be studied establishes its positive sequence network model. Other generators in the system use the equivalent circuit model of the secondary transient reactance. The equivalent impedance viewed from the rotor of the generator under study to the system side at a specific frequency is then calculated. Finally, the interaction is estimated according to the equivalent impedance-frequency curve.

Equivalent reactance crossing the zero point or the equivalent resistance at the corresponding frequency when it is close to zero or negative indicates an IGE. When the resonant frequency obtained from the equivalent impedance-frequency curve is complementary to a certain natural frequency of the wind turbine, SSTI will occur at this modal frequency. If the damping of the shafting of the generator set is weak in this mode, further SSO occurs. When the frequency corresponding to the minimum reactance value of the equivalent reactance-frequency curve is equal to or close to the complementary frequency of a certain natural frequency of the unit, the shafting torque amplification phenomenon may occur.

The frequency sweep method is simple and easy to calculate, does not require a fine model of the unit, and has a low economic cost. However, because its analysis method is overly simple and has great limitations, it cannot analyze systems containing nonlinear components such as power electronic devices and does not consider the influence of unit operating conditions and controllers. The method can only qualitatively analyze the interaction situation, and other methods must be used to check the results.

1.3.2.2. Test signal method

The test signal method adopts time domain simulation to realize the complex torque coefficient method. The disturbance is applied to the current reference link of the rectifier side, and the DC closed-loop control can directly and quickly respond to the disturbance. Since the complex torque coefficient method was introduced above, it will not be explained here.

1.3.2.3. Fast Fourier transform and Hilbert–Huang transform

Fast Fourier transform (FFT) and Hilbert–Huang transform (HHT) are signal processing algorithms that can be based on measured and time-domain simulation data to perform further modal analysis on measured or time-domain simulated output voltage and current waveforms.

FFT is one of the most commonly used signal processing methods and can transform a signal from the time domain to the frequency domain. Through FFT, the spectrogram of the power signal can be obtained, and the amplitude and phase angle information of each frequency component of the signal can be directly read on the spectrogram.

In 1996, N.E. Huang proposed an algorithm to decompose a signal into a series of intrinsic mode functions (IMFs)—empirical mode decomposition (EMD). Based on this, in 1998, a relatively complete HHT algorithm was proposed consisting of two parts. The first part is EMD. After decomposition of the EMD algorithm, the signal is decomposed into a series of IMF signals. The basic principle is that for nonstationary signals, the inherent amplitude and frequency are transformed into a modal function that changes with time, and the nonstationarity of the signal can be well expressed. The second part is to perform a Hilbert transform on each IMF signal to obtain the Hilbert spectrum of the signal. The Hilbert spectrum represents the time-frequency distribution of the signal, from which the instantaneous frequency and instantaneous amplitude of the signal at any time can be obtained. Therefore, the HHT algorithm can easily observe the local dynamic behavior and characteristics of the signal. The decomposed signal is unique and has good local properties in both time and frequency domains.

1.3.2.4. Prony algorithm

The Prony algorithm was proposed by Baron de Prony in 1975. This method fits equally spaced sampling data through a linear combination of exponential functions. It can then analyze the frequency, attenuation factor, amplitude, and phase of the signal. Unlike the small-signal analysis method for frequency-domain analysis, the Prony algorithm is a time-domain method for identifying the relevant modal parameters of the interaction without establishing a detailed model of the system to be studied and solving the eigenvalues of the large-scale power system state matrix. The order of the system model can be determined according to the identification purpose and needs. At the same time, when the system model is completely unknown, the reduced-order transfer function can be obtained, which is of great significance to the design of the controller parameters in the system.

The Prony algorithm can analyze both simulation results and real-time measurement data in the field, giving it high engineering practicability. Although this method does not require fine modeling, when fitting the collected signals, system order, sampling frequency, and sampling time greatly influence the data fitting accuracy. Improper selection of parameters will affect the accuracy of analysis results and even lead to erroneous analytical conclusions.

1.4. Overview of control methods for machine–grid