DEGREE PROJECT, IN ELECTRIC POWER SYSTEMS , SECOND LEVEL STOCKHOLM, SWEDEN 2015
Impact of Large Amounts of Wind Power on Primary Frequency Control
A TECHNICAL AND ECONOMIC STUDY
NAKISA FARROKHSERESHT
KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING
Impact of Large Amounts of Wind Power on Primary Frequency Control: a
Technical and Economic Study
Author:
Nakisa Farrokhseresht
Supervisor:
Prof. Mohammad Reza Hesamzadeh Prof. Hector Chavez
Examiner:
Prof. Mohammad Reza Hesamzadeh
A thesis submitted in fulfilment of the requirements for the degree of Master of Science
in the
Electricity Market Research Group Electric Power Systems Department
School of Electrical Engineering KTH Royal Institute of Technology
Abstract
Renewable energy sources help reaching the environmental, social and economic goals of producing electrical energy in a clean and sustainable matter. Among the various renewable resources, wind power is assumed to have the most favorable technical and economic prospects and offers significant potential for reducing greenhouse gas (GHG) emissions. As wind power installations are more and more common in power systems, additional research is needed in order to guarantee the quality and the stability of the power system operation.
Maintaining the frequency as close as possible to its rated level is one of the most im- portant tasks for grid operators in order to maintain a stable electricity grid. However, the significant penetration of wind generation in power grids has raised new challenges in the operational and planning decisions of power systems. Wind turbine units almost always include power converters decoupling the frequency dynamics of the wind power generators from those of the grid. This decoupling causes a reduction in the total system inertia, affecting the system’s ability to overcome frequency disturbances.
To study the impact of wind power on the system inertia, first the Nordic 32-A System, representing a scaled version of the Swedish grid, is implemented in PSS/E. A system identification of model parameters with actual data follows. This ad-hoc identification method determines the dynamic parameters of the governors and prime movers in the model. The two metrics of primary frequency control; the instantaneous minimum fre- quency and the rate of change of frequency (ROCOF) are simulated using the identified power system, and via an extrapolation, the maximum wind power penetration in Swe- den is found, considering that the system has to comply with the instantaneous minimum frequency requirements and also that the tripping of the generators’ ROCOF relays is prevented.
The second part of the work focuses on an economic study of the cost to guarantee an adequate frequency response, particulary the Primary Reserve (PR). The Primary Reserves is the capacity of the generators that is reserved for the governors to use for Pri- mary Frequency Control (PFC). Primary Reserves also include the ramping capability requirement of power plants for regulating power imbalances caused by contingencies.
Recent studies have shown that having more renewable resources, such as wind with no PFC capability as well as an electricity market design with no incentive for PFC, are important drivers for a decline in the frequency response in the system. One so- lution is the careful design of a PFC ancillary service market by introducing suitable constraints to ensure the adequacy of Primary Frequency Control. However, applying these constraints will increase the generation cost especially when more and more wind power is integrated. This work proposes the use of an adequacy constraint to evaluate
the economic impact of wind integration with respect to its influence on guaranteeing an adequate PFC. To analyze the cost increment for maintaining an adequate frequency response in the presence of wind power, an optimal power flow (OPF) problem is de- signed with an objective function of the generation cost minimization and considering a PFC adequacy constraint. The results show that the inclusion of the new constraints in the optimal dispatch OPF leads to a higher dispatch cost.
Keywords: Inertial response, primary frequency control, power system simulation, sys- tem identification, wind power integration, power system optimization optimal power flow
Acknowledgements
There are several people I would like to thank for helping me not only to complete this master thesis project but generally, in my life in Sweden and Belgium.
I would like to begin by thanking Associate Professor Mohammad Reza Hesamzadeh for creating the thesis project, and giving me the opportunity to work on it. Professor Hesamzadeh has been my main supervisor, and has given much appreciated and con- tinuous support, encouragement and positive interaction. Also I would like to express my gratitude to my other supervisor, Assistant Professor Hector Chavez, for his support and guidance. His valuable comments, insight and encouragement were always of the greatest assistance to me.
I would like to give a special acknowledgement to my master program coordinator Pro- fessor Johan Driesen for his guidance and kind help. In addition, a special thanks goes to EIT/KIC-InnoEnergy for funding my two years master program: Energy in Smart Cities. I owe Bert Willems a lot of thanks. You were not only my financial coordinator but more importantly you became one of my best friends. I sincerely want to thank Hossein Shahrokni, my course instructor. Thank you for your kind help and guidance.
I would like to thank my colleagues of the Electricity Market Research Group of KTH, especially Mahir Sarfati, the people in the Electric Power Systems department of KTH, particulary Dr. Ebrahim Shayesteh, and my friends in the ELECTA group of the depart- ment of Electrical Engineering of KULeuven, in particular Dr. Priyanko Guha Thakurta.
I am also grateful to my boss, Mr. Hassan Khamseh of the BIDEC company, where I have been working for almost four years as a mechanical engineer and never forget his support and his warm encouragement. Many thanks go to my lovely friends in Iran for cheering me up when I needed it; Mina Safari, Zohreh Kashi, Shahrzad Mohammadpour, Pegah Tiba and Farzad Farkhondehkalam.
I will never forget all the kindness from the Jacqmaer family; Frans, Hilde and Pieter.
Thanks for everything, for your kind wishes, your prays and for all the candles you lighted for my success. During these years, you were with me either in times of joy or difficulties and you help me sincerely and I thank you from the bottom of my heart.
Last, but not least, I would like to express my gratitude to my lovely family and my uncle Ali Farrokhseresht for their financial and emotional support. Thank you Babaee to stimulate the love for nature in me and teach me to dare to dream and hold on to my dreams. Thanks to Giti, my tree of life, I learned that the goal is not of the greatest importance, but that the path leading to the goal is more valuable! Finally my little sister, my cute classmate! Thank you for sharing this fascinating journey with me!
Contents
Abstract i
Acknowledgments iii
Contents iv
List of Figures vii
List of Tables ix
Abbreviations x
Symbols xi
1 Introduction 1
1.1 Background . . . 1
1.1.1 Wind Power Integration . . . 1
1.1.2 Power Systems Stability . . . 3
1.1.3 Generation Scheduling . . . 4
1.2 Problem Definition . . . 5
1.3 Thesis objectives . . . 6
1.4 Resources/Tools Used for that Purpose . . . 7
1.5 Published papers . . . 8
1.6 Outline of this work . . . 8
2 Frequency Control for Power Systems 10 2.1 Introduction. . . 10
2.2 Frequency Control Systems . . . 11
2.3 Inertial Response . . . 12
2.3.1 Swing Equation. . . 12
2.3.2 Center of Inertia . . . 14
2.4 Primary Frequency Control (PFC) . . . 16
2.5 Metrics for Primary Frequency Control (PFC) Adequacy. . . 18
2.5.1 ROCOF . . . 18
2.5.2 Frequency Nadir . . . 19
2.6 PFC Requirements . . . 20
2.6.1 UK. . . 20
2.6.2 Ireland. . . 20
2.6.3 Sweden . . . 21
2.7 Simulation tool PSS/E . . . 21
2.7.1 Network Representation in PSS/E . . . 22
2.7.2 Power Flow Calculation . . . 22
2.7.3 Dynamic Simulation . . . 23
2.7.4 Program Automation . . . 23
3 Wind Power 24 3.1 Introduction. . . 24
3.2 Power Extraction From The Air Stream . . . 24
3.3 Wind Turbine . . . 26
3.3.1 Fixed-Speed Wind Turbine . . . 27
3.3.2 Variable-Speed Wind Turbine . . . 27
3.4 Doubly Fed Induction Generator (DFIG) . . . 28
3.5 Wind Turbine Model in PSS/E . . . 29
3.5.1 Running a Static Power Flow . . . 29
3.5.2 Running a Dynamic Power Flow . . . 30
4 Optimal Power Flow (OPF) with PFC Adequacy Constraints 31 4.1 Introduction. . . 31
4.2 DC Power Flow . . . 32
4.3 Economic Dispatch (ED) . . . 34
4.4 Optimal Power Flow (OPF) . . . 34
4.5 Introducing PFC Constraints . . . 35
5 Case Study 41 5.1 Introduction. . . 41
5.2 Nordic 32-A Test System . . . 41
5.3 Modification of the Nordic 32-A Test System . . . 44
6 Method and Simulation Results 46 6.1 Introduction. . . 46
6.2 Impact of Wind Integration on PFC Adequacy . . . 46
6.2.1 Center-of-Inertia (COI) frequency . . . 47
6.2.2 Identification of model parameters using actual data . . . 52
6.2.3 Wind Integration . . . 53
6.2.4 Simulation Results . . . 57
6.2.4.1 Impact of Wind Integration on the ROCOF . . . 57
6.2.4.2 Impact of Wind Integration on the Nadir . . . 59
6.2.5 Summary . . . 59
6.3 Economic Impact of Wind Integration on Primary Frequency Control . . 60
6.3.1 Adding Governors with a Ramp Rate Capability . . . 60
6.3.2 Stress Test . . . 61
6.3.3 Wind Integration . . . 63
6.3.4 Optimal Power Flow formulation With PFC adequacy Constraints 63 6.3.4.1 Validation of the DC Power Flow equations. . . 64
6.3.4.2 Calculating the Total Cost Difference . . . 65
6.3.5 Simulation Results . . . 69
6.3.6 Summary . . . 71
7 Conclusions and Future Work 72
7.1 Conclusions . . . 72
7.2 Future Work . . . 75
A Implementing the Nordic 32-A Test System in PSS/E 76 A.1 Developing Nordic 32-A test System . . . 76
A.2 Power Flow . . . 77
A.3 Dynamic Simulation . . . 77
A.4 Wind Integration . . . 82
B Wind Model Parameters 85 C Matlab and Python Code for Identification of Section 6.3 89 D Matlab code and GAMS Implementation of the PFC-OPF of Section 6.3 94 D.1 Matlab File . . . 94
D.2 PFC-OPF GAMS File . . . 96
Bibliography 98
List of Figures
1.1 World cumulative installed capacity of wind power . . . 2
1.2 Regional distribution of the globally installed wind power capacity (MW) for the end of 2012 and 2013 . . . 3
1.3 Electricity production by wind power in Sweden . . . 3
1.4 Classification of power systems stability . . . 4
1.5 Problem when great amounts of wind power are integrated in a power grid 6 2.1 Ideal steady-state characteristics of a governor with speed droop . . . 17
2.2 Common dead-band configurations . . . 18
3.1 Airflow over wind tunnel . . . 25
3.2 Fixed-speed wind turbine . . . 27
3.3 Variable-speed wind turbine with a synchronous/induction generator . . . 28
3.4 DFIG with a Power Converter connected to the rotor terminals . . . 28
3.5 Control block diagram of DFIG wind turbine . . . 29
3.6 Overall wind turbine model of DFIG . . . 30
4.1 Governor operation and frequency behavior after a power plant outage . . 37
4.2 Generator ramping capability . . . 39
5.1 The single-line diagram of Nordic 32-A test system . . . 42
5.2 The block diagram of GENSAL generator . . . 43
5.3 Block diagram of GENROU generator . . . 43
5.4 The control diagram for the Simplified Excitation System . . . 43
5.5 The dynamic control model for STAB2A . . . 44
5.6 The block diagram for the HYGOV governor . . . 44
6.1 Measured frequency in the Nordic system (NORDEL) after a sudden trip- ping of 530, 800 and 1100 MW generation . . . 47
6.2 Procedure for calculating the COI frequency. . . 51
6.3 Frequency response of the original Nordic 32-A grid and the measured frequency response after a actual contingency . . . 52
6.4 Algorithm for the ad-hoc model identification method . . . 54
6.5 Algorithm for calculating the ROCOF and frequency Nadir after wind is integrated . . . 57
6.6 Frequency response after contingency of 550 MW for different amounts of integrated wind power production . . . 58 6.7 Linear extrapolation of the predicted ROCOF and frequency Nadir behavior 58
6.8 Result of identification: comparison of real frequency data and the simu-
lated center-of-inertia frequency . . . 61
6.9 Calculating the ramp rate cias the slope of the mechanical power over time 62 6.10 Method to determine the change in generation cost when the PFC ade- quacy constraints are imposed. . . 66
6.11 Inertia and cost difference when wind is integrated in the system . . . 70
A.1 Loadflow solutions . . . 77
A.2 Convert/Reconstruct Loads and Generators . . . 78
A.3 An example of a dyr-file for a hydro and thermal power plant . . . 79
A.4 The dynamic data spreadsheet . . . 80
A.5 Assign Channels for Machine Quantities . . . 81
A.6 Initialization of the dynamic simulation . . . 81
A.7 Channel plot . . . 82
A.8 Speed versus time for machine 1012, after tripping machine 1014 . . . 83
A.9 The electrical system configuration for AC/AC wind farm . . . 83
A.10 Dynamic data file for GEWTG2 . . . 84
List of Tables
2.1 Different frequency controls levels . . . 11
3.1 Power flow parameters of GE 1.5MW. . . 30
6.1 Original and identified dynamic parameters of the Nordic 32-A model . . 55
6.2 Effect of wind integration on ROCOF and frequency Nadir . . . 59
6.3 Generator data including power generation P Gen, machine base M base, ramp rate ci and plant type . . . 62
6.4 Effect of wind integration on the system inertia and the frequency Nadir . 70 6.5 Effect of wind integration on the number of responsive units . . . 70
6.6 Effect of wind integration on the dispatch cost . . . 71
A.1 Load conversion. . . 78
A.2 Power flow data for GE 1.5MW and a wind farm . . . 84
B.1 GE Wind Turbine Electrical Control GEWTE2 . . . 85
B.1 GE Wind Turbine Electrical Control GEWTE2 . . . 86
B.1 GE Wind Turbine Electrical Control GEWTE2 . . . 87
B.2 GE Wind Turbine Generator/Converter GEWTG2 . . . 87
B.3 Two Mass Shaft GEWTT1 . . . 87
B.4 GE Pitch Control GEWTP2. . . 88
B.5 GE Wind Turbine Aerodynamics GEWTA2 . . . 88
Abbreviations
COI Center Of Inertia
CIGRE Conseil International des Grands R´eseaux ´Electriques
DAM Day-Ahead Market
DC Direct Current
DFIG Doubly Fed Induction Generator
ED Economic Dispatch
ENTSO-E European Network of Transmission System Operators for Electricity
GHG GreenHouse Gas
GWEC Global Wind Energy Council LTC Load Tap Changer
NLP Non-Linear Programming OPF Optimal Power Flow
PF Power Flow
PFC Primary Frequency Control
PR Primary Reserve
PSS/E Power System Simulator for Engineering PTDF Power Transfer Distribution Factors RES Renewable Energy Sources
ROCOF Rate Of Change Of Frequency RTM Real Time Market
TSO Transmission System Operator UFLS Under Frequency Load Shedding
Symbols
A area [m2]
δ angle [rad]
E power [W]
f frequency [Hz]
F force [N]
H per unit inertia constant [s]
I current [A]
J moment of inertia [kg − m2]
M system inertia [MWs/Hz]
P power [W (Js−1)]
ρ density [kg/m3]
Q reactive power [var]
R resistance [Ω]
S base power [MVA]
t time [s]
θ angle [rad]
T torque [Nm]
U voltage [V]
V speed [m/s]
ω angular velocity [rads−1]
W kinetic energy [J]
X reactance [Ω]
Y admittance [Ω−1]
Z impedance [Ω]
Chapter 1
Introduction
1.1 Background
1.1.1 Wind Power Integration
Every society needs energy and related services to meet the social and economic devel- opment and to improve the human welfare and health. However, greenhouse gas (GHG) emissions resulting from the provision of energy services cause an historic increase in atmospheric GHG concentrations [1]. Recent data shows that the consumption of fossil fuel is the major source of GHG emissions [1]. The deployment of Renewable Energy Sources (RES) is one of the possible options to mitigate climate change.
RES which have the potential to provide energy services with zero or almost zero emis- sions of both air pollutants and greenhouse gases, supply almost 14 percent of the total world energy demand [2]. The global financial crisis did not pose problems for the rapid growth of the capacity of renewables in 2009; wind power a 32% increase, hydropower a 3% increase, grid-connected photovoltaics a 53% increase, geothermal power a 4% in- crease, and solar hot water/heating a 21% increase [1].
Among the various renewable resources, wind power is assumed to have the most fa- vorable technical and economic prospects and offers significant potential for reducing greenhouse gas emissions. Roughly 1.8 % of the worldwide electricity demand has been met by wind power energy by the end of 2009, but it is predicted that the share of world- wide wind power will grow up to 20 % by 2050 [1]. Wind power is a major new energy resource in both Europe and the U.S in 2009: approximately 39 % of all the capacity
1.1 Background Chapter 1
installed in these two parts of the world came from wind power [1]. From 2000 till 2009, new wind power plants accounted for almost 11% of the new electricity generating instal- lations. The Global Wind Energy Council (GWEC) predicts that the installed capacity of wind power will continue to increase and their forecasts are presented in Figure 1.1 [3]. Figure 1.1 shows the steadily increasing trend of the global installed wind power capacity. By the end of 2012, there were 24 countries with an installed wind capacity of more than 1000 MW. The cumulative installed capacities of wind power in different regions of the world for the years 2012 and 2013 are shown in Figure 1.2[3].
This trend is also seen in Sweden where the share of the electricity production coming
39 48
59 74
94 121
159 198
238 283
318 367
418 474
536 596
0 50 100 150 200 250 300 350 400 450 500 550 600 650 2003
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Global)cumulative)installed)wind)capacity)(GW)
Market forecasts Historical data
Figure 1.1: World cumulative installed capacity of wind power [3]
from wind power has increased significantly from 0.5 % in 2003 to 4.4 % in 2012 [4].
Over the period 2003 - 2012, the production of electricity from wind power has been increased more than tenfold (Figure 1.3). Sweden also has a planning framework for wind power, projecting a production of 17 GW (6 GW onshore, 11 GW offshore) by 2030 [5].
As wind power installations are more and more common in power systems, additional research is needed in order to guarantee the quality and the security of the power system operation in view of the increased presence of this new energy source which has different characteristics from traditional sources.
1.1 Background Chapter 1
0 20,000 40,000 60,000 80,000 100,000120,000 Europe
Asia NorthlAmerica LatinlAmerica PacificlRegion AfricalandlMiddlelEast
Series1
0 50,000 100,000 150,000 200,000 250,000 Europe
Asia NorthlAmerica LatinlAmerica PacificlRegion AfricalandlMiddlelEast
Europe Asia North
America
Latin America
Pacific Region
Africaland MiddlelEast Endl2012 109,817 97,715 67,748 3,530 3,219 1,165 Endl2013 121,474 115,927 70,811 4,764 3,874 1,255
Global wind power capacity (MW)
Figure 1.2: Regional distribution of the globally installed wind power capacity (MW) for the end of 2012 and 2013 [3]
0 1 2 3 4 5 6 7 8
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Wind production (TWh)
Figure 1.3: Electricity production by wind power in Sweden [4]
1.1.2 Power Systems Stability
Power systems stability has been recognized as an important issue for a secure system operation [6]. Power system stability is the ability of a power system to regain an equi- librium state after being subjected to a physical disturbance [7]. The study of power systems stability can be divided into the following topics: the study of rotor angle sta- bility, of frequency stability and of voltage stability [7]. This classification of power systems stability is shown in Figure1.4. This work focuses on the frequency stability.
1.1 Background Chapter 1
power system stability
frequency stability
small distrubance angle stability
rotor angle stability
voltage stability
transient stability
large disturbance voltage stability
small disturbance voltage stability Figure 1.4: Classification of power systems stability [7]
Maintaining the frequency as close as possible to its rated level is one of the most im- portant tasks for grid operators in order to maintain a stable electricity grid [8]. If the frequency deviates significantly from its scheduled value, Under Frequency Load Shed- ding (UFLS) is more likely to occur. Also the possibility of tripping of the over-frequency generator protection relays increases which can lead to a blackout [8].
The definition of frequency stability given by CIGRE and IEEE is the following: “Fre- quency stability refers to the ability of a power system to maintain a steady frequency following a severe system disturbance, resulting in a significant imbalance between gen- eration and load” [9]. Primary Frequency Control (PFC) is the leading mechanism of the frequency control system to ensure reliable operation [10]. The PFC is defined by ENTSO-E as “the power delivered by the rotating masses of the synchronous machines in response to frequency drops” and also as “the governor response that acts to arrest frequency decays” [11].
1.1.3 Generation Scheduling
In order to have the secure and the stable power system, the socioeconomic cost should be minimized. This can be done by scheduling the generation well. The generation scheduling normally consists of three time frames: the day-ahead market (DAM), the intraday market and the real-time market (RTM). The day-ahead market (DAM) usually opens in the morning, on the day before the actual dispatch of the generation units [12].
It is also called the planning period and in this period market participants submit their bids and offers to the market based on forecasts of the loads. Then, the market operator sets the forecast price and the forecast dispatch level. The next phase is the intraday
1.2 Problem Definition Chapter 1
market which takes place one hour before the actual day (in the case of NORDEL).
Additional information such as updated forecasts and units’ availability help the market participants to make adjustments in their trading [13]. Finally, in the real time market which is also known as the operating period, the market operator defines the real price and the real dispatch for all the participants. The operation of the real-time markets varies from bidding zone to bidding zone, and can be done over a time period of 5 min- utes, up till periods of one hour before the actual dispatch [12].
However, the load forecast in the planning period may not always be correct. There- fore in the real-time market, generators may have to change their production instantly.
Hence, the frequency control system is required to control the generator outputs. But this frequency control system needs “reserve capacity” in order to operate adequately.
One of the important parts of these reserves is the primary reserve (PR). The “primary reserve” is the capacity that is required by the primary frequency control system and it is employed to stabilize the frequency deviation in the entire interconnected grid [14].
1.2 Problem Definition
There are two main types of wind turbine generators: fixed-speed and variable-speed.
In the fixed-speed wind turbine, the generator is coupled via a transformer immediately to the grid. But a more common turbine generator is the variable-speed wind turbine due to its advantages; it generates an almost constant torque, it can absorb wind fluc- tuations, and it can improve the power quality of the grid. However, this type of wind turbine has negative effects on the PFC [15]. Since in modern variable-speed wind tur- bines power electronic converters are employed to decouple the generator from the grid, the moving parts of the wind turbines are not synchronized with the system frequency.
Also, a large penetration of wind power implicates a reduction of the power supplied by conventional synchronous generators, so the contribution of wind machines to the total system inertia is low to zero [15] [16].
In addition, recent studies have shown that having more renewable resources, such as wind with no PFC capability as well as an electricity market design with no incentive for providing PFC, are important drivers for a decline in the frequency response in the system [8] [17]. Moreover, a classical optimal power flow problem without additional
1.3 Thesis objectives Chapter 1
system constraints including the provision of a reserve capacity can not guarantee an adequate operation of the grid in the presence of a large amount of wind power. Fi- gure1.5summarizes the problem definition. This thesis seeks to investigate the problem and provide solutions.
Large penetration of wind
Reduce the power supplied by conventional generators
- Less overall inertia in the grid - Less PFC capability - Less reserve capacity
Insufficient frequency stability
Figure 1.5: Problem when great amounts of wind power are integrated in a power grid
1.3 Thesis objectives
This thesis aims to perform a technical and economic analysis of the effect on the primary frequency control of the Swedish grid, when a high amount of wind power is integrated in the system. In the technical part of the thesis, the penetration level of wind generation is determined that leads to insufficient PFC for the case of the Swedish grid. The following items are discussed in this part:
• Review of the NORDEL grid code requirements for primary frequency control,
• Implementing the Nordic 32-A test system as the representation of the Swedish grid in PSS/E,
• Identification of the grid’s model parameters with actual data,
• Including wind turbines into the model,
• Evaluating the impact of wind penetration on a few important primary frequency control metrics,
• Determining the amount of wind generation that leads to an inadequate primary frequency control.
1.5 Published papers Chapter 1
The second part of the work is economic study of the influence of large amount of wind on PFC. The economic part has the aim to carefully design an OPF for the economic operation of the system so that an adequate primary frequency control is guaranteed.
However, introducing additional constraints will increase the generation cost, especially if more and more wind power is integrated. The following items are considered in this part:
• Applying governors with ramp rate capability,
• Performing “stress test” to calculate ramp rate capability of each generator in the gird,
• Including wind turbines into the identified model,
• Formulating an optimal power flow including constraints to guarantee an adequate PFC operation,
• Evaluating the economic impact of wind integration when the developed mini- mal requirements to ensure primary frequency adequacy are added to the control system.
1.4 Resources/Tools Used for that Purpose
In this work the Nordic 32-A test system representing the real Swedish grid is im- plemented in the power system analysis software PSS/E. The procedure for running power flows, performing dynamic simulations and integrating wind turbines in the grid in PSS/E are explained in the Appendix A. An ad-hoc system identification method is applied in this work which requires PSS/E to be automated. In order to automate PSS/E, calculations are performed in Matlab, which calls Python to execute PSS/E. All the Matlab and Python codes for the PSS/E automation are provided in Appendix C.
Moreover, the optimization problem in the second part of the thesis is solved by the KNITRO solver in the General Algebraic Modeling System (GAMS) platform [18]. The GAMS codes are provided in Appendix D.
1.6 Outline of this work Chapter 1
1.5 Published papers
• N. Farrokhseresht, H. Chavez, M. R. Hesamzadeh, Determination of Acceptable Inertia Limit for Ensuring Adequacy Under High Levels of Wind Integration, In- ternational Conference on European Energy Market, Krakow, Poland, 28-30 May 2014.
• N. Farrokhseresht, H. Chavez, M. R. Hesamzadeh, Economic Impact of Wind Inte- gration on Primary Frequency Response, IEEE PowerTech Conference, Eindhoven, the Netherlands, 29 June-2 July 2015.
1.6 Outline of this work
The report is written in 7 chapters with the following descriptions:
• Chapter1has been specified to describe the thesis. This includes the background of the thesis and a description of problem definitions and different thesis steps.
• Chapter2focuses on frequency control for power systems and the concepts of pri- mary, secondary and tertiary control are briefly explained. Two important metrics for primary frequency control are introduced. In the next part, the requirements for primary frequency control in the UK, Ireland and Sweden are presented. This Chapter ends with a brief explanation about the power system analysis software PSS/E.
• Chapter3 concentrates on wind power and two main wind turbine technologies:
the fixed-speed and variable-speed wind turbine are presented. Also in this Chap- ter, the doubly-fed induction generator (DFIG), as one kind of the variable-speed wind turbines which is commonly used, is explained.
• Chapter4discuses DC Power flow, Economic Dispatch (ED) and Optimal Power Flow (OPF). The last Section of this Chapter presents the new adequacy con- straints in a classical OPF for ensuring PFC adequacy.
1.6 Outline of this work Chapter 1
• Chapter5illustrates first, a case study consisting of the Nordic 32-A test system, representing a scaled version of the Swedish grid. Then the modification on the original Nordic 32-A test system which are needed in order to have capability of dynamic simulation will be explained.
• Chapter 6 explains the method for studying the impact of wind integration on the adequacy of primary frequency control , and also the economic impact of the wind integration on the generation cost, where as a test grid the CIGRE Nordic 32-A system was taken. This Chapter includes an ad-hoc identification method which required that PSS/E was automated. It discusses wind integration and presents an OPF with PFC adequacy constraints. In the next part of this chapter, two different scenarios are studied; the first scenario considers the PFC adequacy constraint in the OPF, while in the second scenario, the PFC constraint is not included. This way, the economic cost of this constraint can be found. At the end of each Section, the simulation results and a summary are given in detail.
• Chapter7summarizes the main conclusions and provides some recommendations for future research.
Chapter 2
Frequency Control for Power Systems
2.1 Introduction
Nowadays, the demands on the quality and security of supply of the voltage and fre- quency are higher and automatic controllers and regulators were introduced in order to meet these requirements [19]. Therefore there is a need for an ancillary service1 to supply these control actions. The task of the control systems of a power system is to keep the system within acceptable operating limits in such a way that the security of supply is maintained and the quality of the power, such as the voltage magnitude and the frequency, is within specified limits.
In this chapter, first the basics of frequency control including the concepts of primary, secondary and tertiary control are briefly explained. After describing the inertial re- sponse and primary frequency control in detail, some important metrics to describe the primary frequency control adequacy are provided. The primary frequency control re- quirement for UK, Ireland and Sweden are discussed in the next part. The chapter ends with a brief explanation about the power system analysis software PSS/E which is used in this work to model a power system and analyze the frequency control.
1Ancillary services are defined as all services required by the transmission or distribution system operator to enable them to maintain the integrity and stability of the transmission or distribution system as well as the power quality [20]
2.3 Frequency Control Systems Chapter 2
2.2 Frequency Control Systems
The response of the power system and its generators to a frequency change can be divided into four phases (Table2.1) [10] [21].
Table 2.1: Different frequency controls levels
No. Control Name Time frame Control objectives
1 Inertial response 0-2 s Transient frequency dip minimization 2 Primary control 2-20 s Arrest frequency decays 3 Secondary control 20 s - 2 min Steady-state frequency 4 Tertiary control 15 min Economic-dispatch
In the first phase, which takes place during the first seconds after the frequency changes, the rotor of the generators releases or absorbs part of its kinetic energy. This action is mathematically described by the swing equation and is called “Inertial Response”. The inertial response is inherently provided by conventional generators in power systems and no control is activated within this phase.
If the frequency signal deviates from the set value, a signal is produced that will influ- ence the valves, gates, servos, etc, in order to bring the frequency back to an acceptable value. That is the purpose of “Primary Control”. All the generators are participating in the primary control irrespective of the location of the disturbance. A typical time response for this primary control is in the order of a few seconds (2-20 s).
In the “Secondary Control” phase, the remaining frequency error which is still present after the primary frequency response phase is compensated by adjusting the power set- points of the generators. The secondary control acts in a time response period of a few seconds to minutes, typically 20 s-2 min.
Finally the “Tertiary Control” level occurs in a time frame of minutes (typically 15 minutes) and modifies the set-points of the active power in the generators to achieve a desired economically optimal global power system operation strategy. Not only fre- quency and active power controls are considered, but also voltage and reactive power are controlled in this stage.
This work focuses on first two levels which will be explained in detail in the next parts.
2.3 Frequency Control Systems Chapter 2
2.3 Inertial Response
When there is a large contingency in the grid, the frequency begins to decline imme- diately and the rate of this initial decline is mainly determined by the inertia of the system. As the inertia is connected with the motion of synchronous devices, the swing equation describes the inertia response well, thus it will be explained below.
2.3.1 Swing Equation
The net torque causing acceleration (or deceleration) when there is an unbalance between the torques acting on the rotor is [22]:
Ta= Tm− Te (2.1)
Where
Tm the mechanical or shaft torque supplied by the prime mover less retarding torque due to rotational losses, in N-m;
Te the net electrical or electromagnetic torque, in N-m;
Ta the net accelerating torque, in N-m.
The differential equation describing the rotor dynamics based on law’s of rotation is:
Jd2θm
dt2 = Tm− Te (2.2)
Where J is the total moment of inertia of synchronous machine (kg.m2), θmis the angu- lar displacement of the rotor with respect to the stationary reference axis on the stator (rad). It is more convenient to chose the angular reference relative to a synchronously rotating reference frame moving with constant angular velocity ωsm, thus:
θm = ωsmt + δm (2.3)
Where δm is the rotor position before disturbance at time t = 0. First derivative of equation (2.3) gives the rotor angular velocity ωm as:
ωm= dθm
dt = ωsm+dδm
dt (2.4)
2.3 Frequency Control Systems Chapter 2
And the second derivative of equation (2.3) gives the rotor acceleration as:
d2θm
dt2 = d2δm
dt2 (2.5)
Substituting equation (2.5) in (2.2):
Jd2δm
dt2 = Tm− Te (2.6)
Multiplied equation (2.6) by ωm:
J ωmd2δm
dt2 = ωmTm− ωmTe (2.7)
Power is equal angular velocity times torque, thus;
J ωm
d2δm
dt2 = Pm− Pe (2.8)
The quantity J ωm is known as the inertia constant and is denoted by the M . The M is related to kinetic energy Wk by:
Wk= 1
2J ωm2 = 1
2M ωm (2.9)
or
M = 2Wk
ωm (2.10)
Since ωm does not change by a large amount before stability is lost, ωm ' ωsmM . Thus,
M = 2Wk ωsm
(2.11)
The swing equation (2.8) in terms of M :
Md2δm
dt2 = Pm− Pe (2.12)
If p is the number of poles of a synchronous generator, the electrical power angle δ is related to the mechanical power angle δm by:
δ = p
2δm (2.13)
2.3 Frequency Control Systems Chapter 2
Also,
ω = p
2ωm (2.14)
Thus, swing equation (2.12) in terms of δ:
2 pMd2δ
dt2 = Pm− Pe (2.15)
Equation (2.15) is divided by the base power Sbase in order to be normalized:
2 p
2Wk
ωsmSbase d2δ
dt2 = Pm
Sbase − Pe
Sbase (2.16)
The quantity of per unit inertia constant H can be defined as:
H = Wk
Sbase (2.17)
The unit of H is in seconds and it has value in the ranges from 1 to 10 seconds, depending on the size and the type of machine. Substituting equation (2.17) in (2.16):
2 p
2H ωsm
d2δ
dt2 = Pm(pu)− Pe(pu) (2.18)
According to (2.14), the swing equation can be written as:
2H ωs
d2δ
dt2 = Pm(pu)− Pe(pu) (2.19)
2.3.2 Center of Inertia
If a load suddenly increases by ∆PL at time t = 0 at bus k for a grid with multiple machines , at t = 0+, each machine i will react according to its proximity to the change.
Each generator will then increase its generation according to the synchronizing power coefficients PSiK. Generators that are closer to bus k, will contribute more, and genera- tors that are farther away, will contribute less. PSiK is bigger if bus i is closer to bus k, and smaller if bus i is farther from bus k, so the contribution from generator i is [21] :
∆Pei= (−PSik) (−∆PL)
n
P
j=1
PSkj
= PSik
n
P
j=1
PSkj
∆PL (2.20)
2.3 Frequency Control Systems Chapter 2
where PSik = ∂Pik
∂δik|δik0 (2.21)
According to equation (2.19), the linearized swing equation for machine i is:
2Hi
ω0 d2∆δi
dt2 = −∆Pei (2.22)
Where δi is the rotor angle of generator i and ω0 is the nominal speed. The inertia constant Hi has the dimension of time (s) and indicates the time that the system can provide nominal power by using only the energy stored in its rotating masses. Substi- tution equation (2.20) in (2.22):
2Hi ω0
d2∆δi dt2 = −
PSik
n
P
j=1
PSkj
∆PL (2.23)
Taking Hi to the right hand side of equation (2.23), we have:
2 ω0
d2∆δi
dt2 = − PSik Hi
∆PL n
P
j=1
PSkj
. (2.24)
In order to eliminate the term PSiK, first we use ∆ωi instead of ∆δi for all generators i = 1, 2, . . . , n, then sum up the equations for each i:
2 ω0
dH1∆ω1
dt = − PS1k n
P
j=1
PSkj
∆PL
. . . + 2
ω0
dHn∆ωn
dt = − PSnk n
P
j=1
PSkj
∆PL
⇒ 2 ω0
n
X
i=1
dHi∆ωi
dt = −
n
P
i=1
PSik
n
P
j=1
PSkj
∆PL= −∆PL
(2.25)
In steady state, the speed will be the synchronous speed but during transients, the speeds of the generators and hence the bus frequencies, differ. Now the ”Center Of
2.4 Frequency Control Systems Chapter 2
Inertia (COI)” of the system can be defined as:
ω ≡
n
P
i=1
Hiωi
n
P
i=1
Hi
or ∆ω ≡
n
P
i=1
Hi∆ωi
n
P
i=1
Hi
. (2.26)
Differentiating ∆ω with respect to time:
d∆ω
dt ≡
n
P
i=1
d(Hi∆ωi) dt n
P
i=1
Hi
, (2.27)
or
n
X
i=1
d (Hi∆ωi)
dt =
" n X
i=1
Hi
# d∆ω dt
. (2.28)
Now substitute equation (2.28) into (2.25):
2 ω0
" n X
i=1
Hi
# d∆ω dt
= −∆PL, (2.29)
Thus:
d∆ω
dt = −∆PLω0 2
n
P
i=1
Hi
, (2.30)
And finally:
d∆f
dt = −∆PLf0 2
n
P
i=1
Hi
≡ mf, (2.31)
Where mf can be evaluated at time instant 0, immediately after the contingency and is then called the initial rate-of-change-of-frequency (ROCOF) [15].
2.4 Primary Frequency Control (PFC)
A power system needs a closed loop control system to regulate the frequency of the system. If the system frequency decreases (increases), the primary frequency control system sends instructions to the generators to increase (decrease) the power output.
Primary frequency control is mainly provided by generators’ governors. A governor is the feedback controller that senses the system frequency and acts on generator’s prime
2.4 Frequency Control Systems Chapter 2
Figure 2.1: Ideal steady-state characteristics of a governor with speed droop [23]
movers (such as steam or water turbines) to regulate frequency deviations. Governors with a speed-droop characteristic have several settings:
• Droop R
The governor droop R is defined as the variation in power output in steady state with respect to the variation in system frequency (Figure 2.1). R is calculated as the ratio of the speed deviation ∆ω or the frequency deviation ∆f to a change in the valve/gate position or the power output ∆P . It is normally expressed in percent:
percent R = percent speed or frequency change percent power output change × 100
= ωN L− ωF L ω0
× 100
(2.32)
where
ωN L steady-state speed at no load;
ωF L steady-state speed at full load.
For example, a 5% droop means that generator output will increase by 100% if there is a frequency deviation of 5%. Looking at Figure 2.1, it can be seen that governors for primary control are proportional controllers, with the droop R as the controlling gain.
• Dead-band db
The dead-band is defined as “the total magnitude of the change in steady-state
2.5 Metrics for Primary Frequency Control Chapter 2
Figure 2.2: Common dead-band configurations [25]
speed within which there is no resulting change in the position of the governor- controlled valves or gates” [24] and it is expressed in percent of the rated speed.
The most common types of the dead-band are shown in Figure2.2[25]. The droop characteristic can show a discontinuous step at the borders of the dead-band, or can be continuous. For instance, a maximum dead-band of 0.06% (0.036 Hz for nominal frequency of 60 Hz) for a large steam turbine and 0.02% for hydraulic turbines is specified by IEEE standard [24]. If there is a small frequency deviation which lies entirely within the dead-band, the governor will be inactive.
2.5 Metrics for Primary Frequency Control (PFC) Ade- quacy
There are two important metrics for PFC adequacy: ROCOF and frequency Nadir.
2.5.1 ROCOF
The initial slope of the frequency deviation versus time after a contingency is called the rate-of-change-of-frequency (ROCOF). The frequency dynamics are governed by the swing equation [23]:
df (t) dt = 1
MH
(Pm(t) − Pe(t)) (2.33)
where
2.5 Metrics for Primary Frequency Control Chapter 2 f (t) system frequency (Hz);
MH system inertia (MWs/Hz);
Pm(t) system mechanical power (MW);
Pe system electrical load (MW).
After the loss of a power plant of size Pl at time t = 0, the swing equation becomes as follows at the moment of the contingency:
ROCOF = df
dt(0) = 1 MH
(−Pl) (2.34)
The system inertia MH is calculated as:
MH = Pl
|ROCOF | (2.35)
It can be seen from equation (2.34) that the ROCOF depends mainly on the kinetic energy stored in the rotational parts of the generators and loads. The more inertia in the system, the smaller the ROCOF magnitude, and a slower and hence less severe frequency drop will take place. The ROCOF magnitude should not be too large, otherwise the islanding detection relay will be tripped and the generator will be disconnected from the grid.
2.5.2 Frequency Nadir
The frequency Nadir is the lowest frequency reached after a contingency and it is the main metric which determines Under Frequency Load-Shedding (UFLS). The UFLS leads to disconnecting large groups of costumers at predetermined frequency set-points and it is a drastic form of emergency frequency control. Loads that are disconnected through UFLS must be reconnected via special procedures. Therefore UFLS is an emer- gency operating measure and it should be avoided in normal situations [10].
The magnitude of the frequency Nadir is governed mainly by the size of the contingency, the kinetic energy of the rotating machines, the number of generators participating in the primary frequency control, the reserves and their distribution over the generators, and the dynamic characteristics of the loads and machines such as ramp rate capability [26]. Each of these characteristics should economically be stimulated to provide an ade- quate Nadir and hence avoiding UFLS. The general condition for having PFC adequacy
2.6 PFC Requirements Chapter 2
is [27]:
fN adir≥ fmin (2.36)
Where fmin is the minimum acceptable frequency and fN adir is the frequency Nadir.
2.6 PFC Requirements
The high penetration of wind power has an impact on the stability of the power sys- tem. Some countries, such as UK and Ireland, have prepared specific grid codes for the ROCOF relay to maintain continuity and security of the electric supply. This section presents the requirements for primary frequency control in the UK and Ireland. Also the requirements for two metrics of PFC adequacy (ROCOF and frequency Nadir) for Sweden will be specified.
2.6.1 UK
The electric power system in the UK is operated by National Grid, and has a maximum demand of about 60 GW and an installed capacity of 80 GW. The demand is met by nuclear, coal fired and gas fired power plants and the annual electricity consumption is around 360 TWh. National Grid is responsible for providing a sufficient frequency responsive reserve by defining a “Mandatory Frequency Response”. All the generators connected to the UK transmission grid should fulfil the requirement to have the capacity of providing this “Mandatory Frequency Response”. Generators must have a 3-5%
governor droop characteristic and be capable to provide continuous modulation power response through their governing systems. The National Grid ROCOF relays are set at 0.125 Hz/s but [28] shows that the integration of wind power may lead to ROCOFs close to 1 Hz/s.
2.6.2 Ireland
The Irish power system consists of two different TSOs: EIRGRID for southern Ireland and SONI for northern Ireland. The maximum magnitude of the ROCOF relays settings recommended in the Irish grid is 0.5 Hz/s. As the republic of Ireland has set an electric- ity target of 40% from renewable resources by 2020 [29], wind capacity will continue to
2.7 Simulation tool PSS/E Chapter 2
grow significantly in this period. The technical and operational implications associated with this high share of renewable energy in the power system of Ireland were studied in [29]. The results of this study show that two issues are limiting the acceptable level of wind integration: frequency stability after loss of generation and transient stability after severe network faults. Some additional recommendations for system operation were de- rived based on this study. For instance, the ROCOF relays in distribution networks are to be replaced by alternative protection schemes or the threshold of the ROCOF relays is to be increased.
2.6.3 Sweden
Sweden is part of the NORDEL system. NORDEL was established in 1963 and is a body for co-operation between the transmission system operators in Denmark, Finland, Iceland, Norway and Sweden. The aim of the NORDEL is to establish a Nordic electricity market. The installed capacity of NORDEL is about 100.8 GW, of which about 8.9 GW is wind power [30].
As the Nadir adequacy point of view, an automatic load shedding for Sweden is specified at 49.4 Hz@0.15 s [31]. But in the case of ROFOC, there is no requirement on the maximum value for the magnitude of the ROCOF in the Nordic Grid Code. However, a report by Elforsk defines 0.5 Hz/s as the maximum acceptable ROCOF magnitude [32].
Thus, the primary frequency control is adequate for Sweden when:
• The magnitude of the ROCOF is be less than 0.5 Hz/s,
• The frequency Nadir is larger than 49.4 Hz.
2.7 Simulation tool PSS/E
All the calculations in this work are performed with the professional software pack- age PSS/E (Power System Simulator for Engineering). The PSS/E is used by many power system utilities for stability studies [33]. It has an extensive library of power systems components including generators, exciters, governor, stabilizer and protection
2.7 Simulation tool PSS/E Chapter 2
models [34]. The PSS/E consists of a complete set of programs for the study of the power system with both steady-state and dynamic simulations.
2.7.1 Network Representation in PSS/E
The power system network is modeled in PSS/E using a description with the bus ad- mittance matrix:
I = Y.U (2.37)
where I is vector of positive-sequence currents flowing into the network at its buses, U is vector of positive-sequence voltages at the network buses and Y is the network admittance matrix [34].
2.7.2 Power Flow Calculation
The following are the basic input data for power flow calculation in the PSS/E:
• Transmission line impedance and charging admittance,
• Transformer impedance and tap ratios,
• Admittance of shunt-connected devices such as static capacitors and reactors,
• Load-power consumption at each bus of the system,
• Real power output of each generator or generating plant,
• Either voltage magnitude at each generator bus or reactive power output of each generating plant,
• Maximum and minimum reactive power output capability of each generating plant.
And the outputs of power flow calculation are:
• The magnitude of the voltage at every bus where this is not specified in the input data,
• The phase of the voltage at every bus,
2.7 Simulation tool PSS/E Chapter 2
• The reactive power output of each plant for which it is not specified,
• The real power, reactive power, and current flow in each transmission line and transformer.
2.7.3 Dynamic Simulation
After solving the steady state power flow, a dynamic simulation can be performed in the PSS/E. It consists of all the functionality for transient, dynamic and long term stability analysis. System disturbances such as faults, generator tripping, motor starting and loss of field can be incorporated in this dynamic simulation. The program consists of an extensive library of generator, exciter, governor and stabilizer models as well as relay model including under-frequency, distance and over-current relays.
2.7.4 Program Automation
The PSS/E provides a mechanism to control the PSS/E execution other than via direct user interaction [35]. There is the ability to specify a set of operations for the PSS/E to perform in a file and to tell the PSS/E to use the instructions in that file as commands.
This controlling of the execution is done by the API (Application Program Interface).
There are two automation processes in the PSS/E based on the API; the Python in- terpreter (Python programs) and the IPLAN simulator (IPLAN programs). This work uses Python which is an interpreter, interactive, object-oriented programming language.
This issue will be explained in Chapter 6and Appendix A.
Chapter 3
Wind Power
3.1 Introduction
Among the various renewable energy resources, wind power is assumed to have the most favorable technical and economic prospects [1]. People have utilized wind energy from the very early recorded history. The first accepted establishment of the use of windmills was in the tenth century in Sistan, in the eastern part of Iran. The wind drives mills and raises water from the streams in order to irrigate gardens [36].
First, this chapter introduces the physical laws describing the conversion from wind energy to electrical energy [37], and then discusses two main wind turbine technologies:
the fixed-speed and variable-speed wind turbine. In the next section, the Doubly-Fed Induction Generator (DFIG) is explained in detail as it is one kind of variable-speed wind turbine which is commonly used [15]. The chapter ends with explaining the modeling of wind turbines in PSS/E.
3.2 Power Extraction From The Air Stream
The kinetic energy in a flow of air with a density of ρ [kg/m3] and speed of V [m/s]
through a unit area perpendicular to the wind direction is expressed as 12ρV2 per unit volume. The mass flow rate of an air stream flowing through an area A is ρAV , and thus
W = (ρAV )1/2V2= 1/2ρAV3 (3.1)
3.2 Power Extraction From The Air Stream Chapter 3
Figure 3.1: Airflow over wind tunnel [37]
The air density ρ depends on the air pressure and the air temperature:
ρ = ρ0(288B
760T) (3.2)
Where ρ0 is the density of dry air at standard temperature and pressure (1.226 kg/m3 at 288 K,760 mm HG),T is the air temperature (K) and B is the barometric pressure in mm Hg. As the pressure and the temperature are both function of the height above sea level, taking an air density of 1.2 kg/m3, thus:
W = 0.6V3 per unit area (3.3)
Only a proportion of the power W can be converted to useful energy by a wind turbine.
An ideal air flow through a wind turbine is shown in Figure 3.1. The mass flow rate is the same at position 0, 1 and 2: upstream, at the rotor and downstream:
Mass flow rate, ˙m = ρA0V0= ρA1V1= ρA2V2 (3.4)
The force of F on the blade is calculated as:
F = ˙m(V0− V2) (3.5)
The power W is given by the rate of change of kinetic energy:
W = ˙m(1/2V02− 1/2V22) (3.6)
3.3 Wind Turbine Chapter 3
From equations above, it can be found that:
V1 = 1/2(V0+ V2) (3.7)
The downstream velocity factor b is defined as the ratio of the upstream and downstream wind speeds:
b = V2
V0 (3.8)
Then,
F A1
= 1/2ρV02(1 − b2) (3.9)
Then by using equation (3.6) and (3.9):
W
A1 = 1/2ρV03× 1/2(1 − b2)(1 + b) (3.10) The fraction of energy extracted by the wind turbine is called the coefficient of perfor- mance Cp:
Cp = W
W1 (3.11)
Because,
W1 = 1/2ρA1V03 (3.12)
Then,
Cp= 1/2(1 − b2)(1 + b) (3.13)
The maximum value of the coefficient Cp is found for b equal to 1/3:
Cp,max = 16
27 or about 59% (3.14)
Cp,maxis called Belts’ limit and it used for all types of wind turbines. Another coefficient is the “Capacity Factor” which is defined as effective number of operating hours (kWh) per installed capacity (kW) and it is typical in the range of 35-40% [37].
3.3 Wind Turbine
There are two main types of wind turbines: fixed-speed and variable-speed. In this section, these two types of wind turbines will be discussed.
3.4 Doubly Fed Induction Generator Chapter 3
Figure 3.2: Fixed-speed wind turbine [40]
3.3.1 Fixed-Speed Wind Turbine
A fixed-speed wind turbine is shown in Figure 3.2. The induction generator is directly connected to the grid. In this type, a capacitor bank is necessary for providing reactive power which is absorbed by the induction generator. The gear box is present in order to couple the low speed of the turbine to the high speed of the generator. Fixed-speed turbines are simple, robust and cost-efficient and they were used by many manufacturers in the 1980s and 1990s [38]. The main problem of this type is however that the fluctuation in the wind speeds cannot be controlled [39]. Another disadvantages of this type are the risk of loss of synchronism because of over-speed in case of voltage dips and increasing of reactive power consumption, especially after fault clearance.
3.3.2 Variable-Speed Wind Turbine
The variable-speed wind turbine consists of a converter connected to the stator of the induction or synchronous generator as shown in Figure 3.3. This type of wind turbine can generate an almost constant generator torque. The wind fluctuations are absorbed by changes in the generator speed [41]. An increased capture of energy, an improved power quality and a reduced mechanical stress on the turbine are advantages of variable- speed wind turbines. However, the drawback is the use of more components and the complicated electrical system leads to a higher cost.
Variable-speed turbines with “partial scale converters” are known as doubly-fed induc- tion generators (DFIGs). This work uses the DFIG in the simulations as this type is widely used in wind farms [38].
3.5 Wind Turbine Model in PSS/E Chapter 3
Figure 3.3: Variable-speed wind turbine with a synchronous/induction generator [42]
Figure 3.4: DFIG with a Power Converter connected to the rotor terminals [43]
3.4 Doubly Fed Induction Generator (DFIG)
The schematic of a Doubly-Fed Induction Generator (DFIG) wind turbine is shown in Figure 3.4. The main part of the DFIG consists of an induction generator with power supply on the rotor as it can be seen in Figure3.4. The stator is directly connected to the grid, while the rotor circuit is connected via a power converter to the grid. The power converter regulates the rotor current and hence controls the electromagnetic torque, field and the stator output voltage. Figure 3.5illustrates the general block diagram for controlling a DFIG. The main parts are the generator and drive train, the turbine rotor, the grid-side converter with DC-link capacitor, the pitch controller and the rotor-side controller. The rotor-side converter controls the active and reactive power which the rotor consumes or produces. The grid-side converter controls the voltage of the DC-link capacitor [44].
3.5 Wind Turbine Model in PSS/E Chapter 3
Figure 3.5: Control block diagram of DFIG wind turbine [44]
3.5 Wind Turbine Model in PSS/E
The PSS/E provides dynamic simulation models for DFIG units and the models were developed by GE Energy. For instance, there exist the GE 1.5, 3.6 and 2.5 MW models [45].
Integrating a wind turbine of the GE 1.5 MW model which is used in this work in PSS/E consists of two steps: doing a static power flow and next a dynamic power flow. The two steps are discussed briefly below. The procedure of wind integration in PSS/E is provided in AppendixA.
3.5.1 Running a Static Power Flow
The first step of integrating a wind machine in power flow models, is running a static power flow. There, a wind turbine is treated as a conventional machine. The important parameters of a typical GE 1.5 MW machine are found in [43] and presented in Table3.1.
3.5 Wind Turbine Model in PSS/E Chapter 3
Table 3.1: Power flow parameters of GE 1.5MW [43]
Data GE 1.5
Generator Rating 1.67 MVA
Pmax 1.5MW
Pmin 0.07MW
Qmax 0.726 MVAr
Qmin -0.726 MVAr
Terminal voltage 690 V Unit Transformer Rating 1.75 MVA
Unit Transformer Z 5.75 % Unit Transformer X/R 7.5
Figure 3.6: Overall wind turbine model of DFIG [45]
3.5.2 Running a Dynamic Power Flow
The dynamic models of a GE 1.5 MW wind turbine consist of an aerodynamics model (GEWTA1), an electrical control model (GEWTE2), a model for the generator and power converter (GEWTG2), a pitch control model (GEWTP1) and a 2-mass model for the turbine shaft (GEWTT1). The connectivity between these models are shown in Figure 3.6. The wind model parameters used in this work are given in AppendixB.
