Thesis
Stability Related Issues for
High Wind Power Penetration
Exploring possibilities to enhance grid stability from synthetic inertia in a future scenario
Authors: Christian Ekstrand, Farsad Mansori
Supervisor: Magnus Perninge Examiner: Sven-Erik Sandström Date: 11-06-2020
Course code: 5ED05E, 15 hp Level: Advanced Level
Abstract
The future global energy transition favour renewables such as wind power, which is predicted to be one of the predominant sources harvesting abundant amounts of energy onwards. Consequently, causing several conventional synchronous generators to be decommissioned in a near future to achieve an overall reduction in greenhouse gases related to electricity generation.
However, this evolution comes with new challenges regarding power system stability that could jeopardize the reliability of the grid as we today know it.
Therefore, this thesis will examine how high penetrations of wind power are impacting each fundamental criterion regarding power system stability. For this purpose, are two different scenarios being carried out in Siemens PSS/E, representing a futuristic case as well as a present one. The simulation results themselves are being compared with analogies drawn from previous studies conducted within the field to determine if it can be improved.
Keywords: PMSG, Power system stability, PSS/E, Synthetic inertia.
Preface
This thesis has been conducted after concluding our one-year M.Sc. program on behalf of the Department of Physics and Electrical Engineering at Linnaeus University in Växjö, Sweden. The idea for the thesis originated from our lively interest in upcoming challenges regarding power system stability related to the approaching energy evolution. So, we would therefore like to express our gratitude to our supervisor Magnus Perninge that has helped us tremendously with creative ideas and guidance along the way.
Christian Ekstrand Farsad Mansori
Table of Contents
Abstract ______________________________________________________ I Preface ______________________________________________________ II Table of Contents _____________________________________________ III Abbreviations _________________________________________________ V Chapter 1 ____________________________________________________ 1
1. Introduction ... 1
1.1. Background ... 1
1.2. Problem definition ... 2
1.3. Purpose and objectives ... 3
1.4. Limitations ... 3
1.5 Published papers for literature review in this thesis ... 4
1.6 Outline of this work ... 4
Chapter 2 ____________________________________________________ 6 2. Power system stability ... 6
2.1 Voltage stability ... 7
2.2 Frequency stability ... 7
2.2.1 Inertial response _________________________________________ 8 2.2.2 Slow primary response or primary control _____________________ 9 2.2.3 Secondary control and tertiary control _______________________ 10 2.3 Rotor angular stability ... 11
2.3.1 Swing equation for a synchronous generator __________________ 11 2.3.2 Analysis of equilibria for non-linear systems __________________ 13 Chapter 3 ___________________________________________________ 15 3. HVDC ... 15
3.1 Line-commuted converter (LCC) HVDC technology ... 15
3.2 Voltage source converter (VSC) HVDC technology ... 16
3.2.1 Structure of the VSC _____________________________________ 17 3.2.2 Modelling of the VSC HVDC ______________________________ 18 Chapter 4 ___________________________________________________ 20 4. Wind power ... 20
4.1 Energy generated from the wind ... 20
4.2 DFIG ... 21
4.2.1 Modelling of the DFIG ___________________________________ 22 4.3 PMSG ... 23
4.3.1 Synthetic inertia control ... 24 Chapter 5 ___________________________________________________ 25
5. Case study ... 25
5.1 Scandinavian blackout in 2003 ... 25
5.2 Simplified test systems used for simulation ... 26
5.2.1 Case A and B __________________________________________ 26 5.2.2 Scenario 1 and 2 ________________________________________ 27 5.3 Previous studies ... 28
5.3.1 Frequency response from inertial control: [9] _________________ 28 5.3.2 Enhancements for further development: [6]-[8] ________________ 29 Chapter 6 ___________________________________________________ 31 6. Method and implementation ... 31
6.1 Method ... 31
6.1.1 Siemens PSS/E _________________________________________ 31 6.1.2 Synchronous generator model in PSS/E ______________________ 32 6.1.3 Generic wind turbine (Type 4) model used for Scenario 2 ________ 34 6.2 Implementation ... 37
6.2.1 Load flow and dynamic simulation in PSS/E __________________ 38 Chapter 7 ___________________________________________________ 40 7. Result and discussion ... 40
7.1 Voltage ... 40
7.2 Active and reactive power ... 42
7.3 Frequency deviation ... 47
7.4 Rotor angle ... 51
Chapter 8 ___________________________________________________ 55 8. Conclusion and recommendations for future work ... 55
8.1 Conclusion ... 55
8.2 Recommendations for future work ... 56 9. References ________________________________________________ 57 10. Appendices _______________________________________________ 61
Abbreviations
CIGRE Conseil International des Grands Réseaux Électriques / International Council on Large Electric Systems DFIG Doubly-Fed Induction Generator
IEEE Institute of Electrical and Electronics Engineers GSC Grid Side Converter
HVDC-LCC High Voltage Direct Current-Line Commuted Converter HVDC-VSC High Voltage Direct Current-Voltage Source Converter IGBT Insulated Gate Bipolar Transistors
PWM Pulse Width Modulation
PMSG Permanent Magnet Synchronous Generator PSS/E Power System Simulator for Engineering RSC Rotor Side Converter
ROCOF Rate Of Change Of Frequency TSO Transmission System Operators WTG Wind Turbine Generator
Chapter 1
1. Introduction
1.1. Background
Nowadays the demand of harvesting abundant amounts of energy resources from the wind in forms of electricity generation have increased rapidly. With ambitious predictions of an ever-increasing energy market from renewables to reduce carbon emissions related to electricity generation onwards. As of the year 2050, the International Renewable Energy Agency predict that wind power will lead the way in the energy transition globally and be the prominent source, as stated in [1]. Furthermore, along with the growth of wind installations, a vast majority of conventional power plants generating electric power from synchronous generators are simultaneously being phased out.
Furthermore, the marginal production cost related to renewable energy sources are decreasing, partly driven by technology improvements and legislative treaties to achieve an overall reduction in greenhouse gases [2].
Therefore, the aforementioned installations are more favourable over constructing or renewing conventional power plants such as nuclear or hydroelectric to match the interest from an economic, social or environmental standpoint currently [3]. According to the Transmission System Operator (TSO) in Sweden that are managing the national grid, the amounts of wind power integrated into the network will keep on growing over the years [4], as seen in (Fig. 1.1). At the same time, the decommission of nuclear power takes off after the year 2030 and the power needs are being compensated by rapid growth of wind power. But at the expense of less rotating synchronous machines.
Fig. 1.1. The energy net balance from different sources in the Swedish network according to the Swedish TSO in a future scenario between the years 2020-2040 [4].
1.2. Problem definition
Along with the reimbursement by means of generating electrical power to the existing grid in alternative ways. Some key essentials factors regarding the stability of the power system could come at risk. As more distributed generation replaces the previous mentioned synchronous machines that rotates synchronized with the grid frequency, less kinetic rotational energy is stored as a buffer in the system.
The Swedish TSO predict that a future scenario of less grid inertia and short- circuit power could jeopardize the fundamental importance of system stability [5]. Below in (Fig. 1.2) a future comparison of less rotating energy over the years are shown. As a result of decommissioned nuclear power being replaced by wind installations as reasoned from (Fig. 1.1), meaning that as we drastically change our way to generate power in the near future, so will the stability requirements to maintain stable operation as usual.
Fig. 1.2. Estimated mean values of rotating energy providing inertia into the Nordic synchronous interconnected grid over the years 2040 and 2020 [4].
In addition, during fluctuating wind conditions, concerns regarding reliable power generation could occur when it is needed the most. According to recent studies [6]-[9] the concerns of low system inertia could be partly compensated by providing the system with synthetic inertia in order to extract more power from wind turbines during unstable grid scenarios.
Since the various variable speed wind turbines do not inherently provide inertial characteristics intended for primary frequency response originally [10], making different control modelling applications vital to necessitate stability onwards. The aforementioned supplementary control applications could enhance variable speed wind turbines to perform similar to synchronous generators by releasing stored kinetic energy from the rotating masses.
To illustrate the problematics, (Fig. 1.3) highlights the methodology to summarize the problem definition. Consequently, introducing the issues which forms the objectives of this thesis.
Fig. 1.3. Illustrative summation of the stability related issues when great amounts of wind power are integrated into the power system.
1.3. Purpose and objectives
The purpose of this thesis is to point out the importance of the stability related issues for future scenarios. By developing a present scenario, as well as a futuristic one. In the futuristic scenario a wind farm with variable speed wind turbines replaces a conventional nuclear power plant with the same generation capacity, without synthetic inertia control.
By performing numerical analysis in Siemens PSS/E (Power System Simulator for Engineering) different case scenarios with loss of generation.
Different simulation results will be compared to define the impact of the decommissioned synchronous generator. Based on that, will alternative connection configurations from a literature review perspective be conducted based on previous studies. With the intent to deduce the objectives for which application is more suitable to emulate synthetic inertia response in a Nordic grid perspective.
1.4. Limitations
As previous stated, this work will be focusing on developing test scenarios for stability analysis. Due to student license constraints in the system analysis program used for this study, synthetic inertia applications will therefore be derived from previous studies. Thus, the focus being directed towards modelling the wind turbines without any frequency response support. Thereby the outcome of the strategies is referred to recent works conducted, which regardless enables adaptability for the simulation results produced.
1.5 Published papers for literature review in this thesis
• Q. Gao, and R. Preece, “Improving Frequency Stability in Low Inertia Power Systems Using Synthetic Inertia from Wind Turbines”, IEEE Manchester PowerTech, 18-22 June. 2017.
• M. Edrah, K. L. Lo, O. Anaya-Lara and A. Elansari, "Impact of DFIG Based Offshore Wind Farms Connected Through VSC-HVDC Link on Power System Stability," 11th IET International Conference on AC and DC Power Transmission, Birmingham, 2015, pp. 1-7.
• M. Yu, A. Dyśko, C. D. Booth, A. J. Roscoe and J. Zhu, "A review of control methods for providing frequency response in VSC-HVDC transmission systems," 2014 49th International Universities Power Engineering Conference (UPEC), Cluj-Napoca, 2014, pp. 1-6.
• R. Leelaruji, and M. Bollen, “Synthetic inertia to provide frequency stability and how often it is needen”, Energiforsk report 2015:224, Stockholm, September 2015.
1.6 Outline of this work
Chapter 1 has been specified to describe the underlying objectives, as well as an introduction to the topic. This includes a background description, problem definition, the purpose of the thesis along with delimitations within this paper.
Chapter 2 concentrates on power system stability for each subcategory.
Giving a brief introduction to voltage stability, follow up by a more comprehensive description of frequency stability, where the sequence of events is explained after being subjected to a fault. This eventually leads to the fundamental concept of rotor angular stability for synchronous machines from a power system perspective.
Chapter 3 focuses on theory related to HVDC configurations and applications, with the intent to present strategies for controlling power flow by using the VSC technology. The modulation technique for the technology itself emulating synthetic inertia will further be linked with the next two upcoming chapters.
Chapter 4 continues where the introduction section left off with further technical descriptions of wind power. Starting from a general perspective, which leads to a more meticulous description of two different turbine configurations. The theory of the first of the two turbine configurations are connected to previous studies brought up in the upcoming chapter. Whereas the other one is directly connected to the simulations performed within this study.
Chapter 5 introduces the study itself with the test system used to resemble realistic unforeseen events occurring in the grid. Here the objectives of the thesis are put into perspective for different case scenarios. As well as reviewing the aforementioned published papers. Which will be referred to when analyzing the simulation results for the incomplete dynamic model used without frequency support.
Chapter 6 presents the quantitative simulation part for the thesis in PSS/E along with the implementation itself. Where the parameters for each and every equipment are put into context, leading to the process for the simulation.
Chapter 7 finally feature the simulation results categorized by quantity at each node of interest for the different case scenarios. Analogies are drawn from previous studies that have been reviewed to compare the various outcomes.
Chapter 8 concludes the aforementioned chapters that are linked to each other along with conclusions drawn from the results presented. Furthermore, will the different solutions be described related to how the results could be enhanced further with the different applications brought up. Ending with recommendations for further development from reflections made during this thesis.
Chapter 2
2. Power system stability
This chapter introduces some fundamental aspects of power system stability related to (Fig. 1.3) by describing each essential category respectively to get an introduction to their specific role. Firstly, a more general approach will be presented as stated below, then elaborated further. According to IEEE/CIGRE, power system stability is defined as [11]:
“The ability of an electric power system, for a given initial operating condition, to regain a state operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact”.
Since the power system itself mainly consists of prime movers generating power connected to various loads consuming the power transmitted under constant changing conditions, it is considered a non-linear system operating under constantly varying conditions. Thereby, instabilities within the system corresponds to imbalances as a result of continuous non-equilibria between the balancing of opposing forces. Meaning that initial operating conditions and the nature of the disturbances occurring are crucial for the stability as a stable power system are able to reach a new state of equilibrium after being subjected to it [12]. As continually changing loads and generation are categorised as small disturbances, more severe ones such as loss of large production and breakers tripping could jeopardize the system to maintain synchronism as a whole [13]. To make sure the entire grid remains intact for any given circumstance, each subcategory shown in (Fig. 2.1) has to be met when analysing the power system instead of being treated as a single problem.
Fig. 2.1. Classification of power system stability [14].
2.1 Voltage stability
Voltage stability refers to the ability of a power system to sustain voltage levels within an acceptable range at all busses after being subjected to a disturbance [13]. When a sudden event occurs in forms of changing load demand, loss of generation or faults arising, instabilities within the system can have cascading effects. An unstable situation like this restrains the flow of reactive power, which could limit the controllability beyond stable limits.
Since transmission networks in the power system are considered predominantly inductive, the control of active and reactive power determines the characteristics for voltage drops, hence the term voltage stability [11].
Disturbances that progresses during short terms could be classified as transients from fast responsive machines operating as generators or motors following a stressed operating condition. Post fault transients could therefore reappear several seconds after the system has been restored due to high and aggressive currents surging in attempt to reaccelerate the motors. The grid could therefore still be recovering and be considered weak, causing the machines to stall and demand high currents [13]. On the other hand, if the system actually is considered stable, short term disturbances dies out and steady state operation resumes.
Whereas stability long term is characterised by the layout of the power system, in terms of topologies in relation to power transmitted from generation to load.
This phenomenon could last for several minutes if bottlenecks occurs, preventing flow of reactive power from heavily loaded transmission lines that causes congestion until power reserves kicks in [14]. Which leads to voltage instabilities over longer periods. The course of events following a disturbance impacts the continuous balance of power system frequency, which introduces the next problem.
2.2 Frequency stability
Normally, the power system is designed to tolerate and withstand different types of disturbances. A sudden variation or disturbance in either load- demand or generation could lead to an unmanageable and progressive voltage and frequency drop in the system [15]. In order to maintain stability between generation and load, demand forecast facilitates the predictions for which the TSO have to preserve within specified operation limits.
Thereby, frequency stability is referred to the ability of a power system to maintain steady frequency within a nominal range following a severe system upset, which could result in a significant imbalance between overall system generation and load [16]. Smaller disturbances causing the frequency to deviate are usually directly related to mismatches in load forecasting and actual system dispatch. Which could be correlated by some control systems [12]. Whereas, larger ones caused from generators tripping or faults occurring
in the interconnected systems could be far more devastating. Numerous preventive tactics to recover the system after a sever event are then used to remain in synchronism [17]. Where the frequency controls are covered over multiple time frames as shown in (Fig. 2.2) below. The preventive tactics for the different time frames will be further explained within these subchapters in chronological order, listed as [18]:
1. Inertial response, also referred to fast primary response.
2. Slow primary response control.
3. Secondary and tertiary control.
Fig. 2.2. General Frequency System Response and Controller involved [17].
2.2.1 Inertial response
A negative frequency deviation following a disturbance in a power system result in a release of stored kinetic energy from the rotating generator masses.
That means the inertial response of a generator releases available torque in direct proportion to the Rate Of Change Of Frequency (ROCOF) it experiences [16]. Whereas the system’s ability to oppose changes in frequency response are correlated to an inertia constant 𝐻. This constant is interpreted as the time in seconds the generator is able to proceed supplying the loads in relation to the rated apparent power 𝑆!"# as described in Eq. (2.1) below. The behavior of this non-linear dynamic balance will be described further in Section 2.3.
𝐻 = $.& (* ! )"#$%
&'$ [,-.] (2.1)
Consequently, lower levels of grid inertia expose the power grids inertial response when being subjected to a sudden change out of ordinary operation since it responds more rapidly. The ROCOF is a measure how the frequency dynamics deviate from a contingency power imbalance. According to [19], fast responding ROCOF also possesses drawbacks from a too fast response, causing adjacent generators to trip and malfunction post- disturbance. That is due to uneven distribution of lost power since the response on each machine is determined by its proportion of synchronizing power, as well as the location of the power plants.
2.2.2 Slow primary response or primary control
The generated power fed into the system which is governed by the demanding system frequency are in conventional generators regulated from its prime movers. If the system frequency decreases, the primary controllers inform the generator to increase its production, vice-versa the other way around if possible. In this way, deviating frequencies could be compensated locally from its governors [18]. As illustrated in the lumped closed loop in (Fig. 2.3) below where the control dynamics represents the primary response acting on the system.
Fig. 2.3. Simplified closed control loop.
Additionally, the frequency nadir has to be considered as well, which is the lowest frequency reached as illustrated in (Fig. 2.2). To prevent load-shedding as a result of exceeding the lowest acceptable frequency limit, additional primary control has to be implemented to rebound the frequency back towards stable operation [16]. Even though it has been investigated in a previous study [20], that additional fast acting primary response in forms of synthetic inertia could in fact diminish the frequency nadir.
During normal operation, the frequency stays within adequate limits which is considered an equilibrium. As soon as the load demand increases or the generation decreases, the surplus generation at disposal counteract the frequency incline to bring it towards a new equilibrium point as seen in (Fig 2. 4).
Fig. 2.4. Equilibrium points for an increase in the power demand [18].
The new equilibrium point is then denoted as the new frequency setpoint where the generation characteristics intersect each other for the new operation state [18]. That is why generators are equipped with appropriate governing and excitation systems to adapt to fluctuating frequencies arising. But these rapid responses have finite resources and are capable of maintaining additional supply of active power for a limited time period [16]. That brings us to prospective responses intended to act slower over longer time periods.
2.2.3 Secondary control and tertiary control
Following a large disturbance, the secondary control response is committed to rebound the frequency back the its initial nominal value. By controlling central automatic generation control, the TSO is obliged to recover the frequency as well as replenish the reserves through legislative grid codes [16].
The secondary response is therefore referred to the restoration of rated frequency by supplying the excess power that is needed and consequently being prepared for further disturbances. That is why each interconnected area within the power system is equipped with a central regulator to maintain stable operation with adjacent subsystems [18].
Further in the process, the tertiary control sets the operating points of each power plant out on the basis of optimal power flow, as well as economic dispatch to minimize the overall cost of operation following a disturbance.
The essential task of this reserve overlaps the secondary frequency control and are ready to take over and compensate the deviation long term, as seen in (Fig. 2.5). The tertiary control is basically an optimized control strategy over secondary reserve generators that could be connected within minutes [21].
Either in individual units or by cooperation, the generator could counteract disturbances that otherwise could jeopardize the stability of the system as a whole.
Fig. 2.5. Idealized primary, secondary, and tertiary frequency response for a 60 Hz system [21].
2.3 Rotor angular stability
The constant balance of electrical power fed into the power system from various generators cannot at all times maintain equal harmony in the relation to power consumed, including losses along the way. That is due to a variety of different dynamic phenomenon’s that could be initiated by a disturbance in the network. Thus, compromising the ability of a power system to remain stable and regain a state of operation equilibrium as prior to the contingency.
When investigating the ability for prime movers generating electric power to the grid with synchronizing torque to remain in synchronism after a disturbance [22], rotor angular stability is the term that it is referred to.
2.3.1 Swing equation for a synchronous generator
To investigate the behavior of electromechanical power oscillations that could impact the electrical system further, the swing equation will be derived. A synchronous machine connected to an infinite bus according to (Fig. 2.6) will be used as a simplified example. The indexes denoted with E represents the
electrical quantity, same goes for the mechanical quantity denoted with M to distinguish the two.
Fig. 2.6. Simplified generator system connected to an infinite bus.
Firstly, considering the synchronous generator to rotate with angular velocity equal to 𝜔, in steady state, supplying constant power 𝑃, = 𝑃0 over a transmission line with equivalent reactance 𝑋01. This equivalent reactance is the summation of the generator transient reactance, as well as the contribution from the transmission line, amongst other components. Consequently, resulting in power 𝑃0 being transmitted from the sending generator at an angle 𝛿 to the receiving ideal voltage source, representing a strong grid.
𝑃0 =-2( -)
*+ sin 𝛿 (2.2)
Now assume that following a disturbance until a new steady state is reached, the mechanical power and electrical power differs due to deviation in torque from a slight change in synchronous speed. As a result of applying the angular accelerating torque at the combined system inertia 𝐽,, which corresponds to the description of Eq. (2.3), assuming there is some damping 𝐷 acting on the rotating mass [23]. Along with some manipulations from the expression of the inertia constant 𝐻 from Eq. (2.1), as well as assuming the synchronous speed is approximately equal to the net-frequency. Consequently, getting the swing equation which is describing the oscillatory imbalance between 𝑃0 and 𝑃, according to Eq. (2.4).
𝜔, 𝐽, 335%4% = 𝑃,− 𝑃0− 𝐷3435 (2.3)
67
8"#$ 335%4% = 𝑃,− 𝑃0− 𝐷3435 (2.4)
The analysis of the power system’s dynamic performance from Eq. (2.4) can be interpreted as two first order differential equations expressed in angular acceleration and deviation in angular velocity. Which represents the state vectors, describing a dynamic non-linear system. By introducing two state variables [𝑥9 𝑥6]:= 2𝛿 𝛿̇4:, the stability of the equilibrium points can be investigated further in a state-space representation for a sufficient small continuous interval [18].
𝛿̇ = 𝜔,− 𝜔;<# (2.5)
𝛿̈ =)67"#$6𝑃,− 𝑃0− 𝐷𝛿̇7 (2.6)
𝑥̇ = 8 𝑥̇₁ 𝑥̇₂; = <
𝑥6
)"#$
67 =𝑃,− -2( -)
*+ sin 𝑥9− 𝐷𝑥6>? (2.7) 2.3.2 Analysis of equilibria for non-linear systems
The equilibrium points of the non-linear dynamic system are at the points in state space where the time derivatives vanish, thus resulting in reposing state of the system. One method to analyze the stability properties of the existing equilibrium points 𝑥".= in the dynamic system 𝑥̇ = 𝑓(𝑥) is Lyapunov’s theorem, when being subjected to a small disturbance [24].
The theorem states that within a region of attraction, the system will asymptotically converge close to a stable equilibrium point 2𝑥9".= 𝑥6".=4: = [𝛿$ 0]: provided by counteracting damping acting on the oscillations. To achieve that, the synchronous machine must be able to deaccelerate, so the angular velocity reaches zero before exceeding a critical point within the region [22]. At worst, the synchronized machine will otherwise fall out of step beyond control. To illustrate how the mechanical and electrical power in a synchronous generator operates according to the swing equation, a diagram with varying rotor angle is shown in (Fig. 2.7) along with its equilibrium points.
Depending on the state of operation there are different equilibrium points that can be obtained. If the mechanical power is less than the electrical power, there exist two equilibrium points denoted as 𝛿$ as well as 𝜋 − 𝛿$ [18]. By linearizing the non-linear system from Eq. (2.7) during a small perturbation denoted as ∆, a sufficient approximation of the dynamics around the equilibrium points can be obtained. Whereas the eigenvalues 𝜆 representing the poles of the linear system are obtained by taking the determinant of the state matrix according to Eq. (2.9), where 𝐼 denotes the identity matrix [24].
Where all equilibrium points must satisfy 𝑥6".= = 0 and 𝑥9".== sin>9 ??!
* .
∆𝑥̇ = 8∆𝑥̇₁
∆𝑥̇₂; = H
0 1
−)67"#$-2(-)
*+ cos 𝑥9".= −)67"#$𝐷L M∆𝑥9
∆𝑥6N (2.7)
0 = det|𝐼𝜆 − 𝐴| (2.8)
𝜆9,6 = −A6)67"#$± jVWA6)67"#$X6− )67"#$-2(-)
*+ cos 𝑥9".= (2.9)
Lastly, the solution generates two eigenvalues of the stable linearized system.
If the rotor has been accelerated so that 𝛿 > 𝛿$, the right-hand side of Eq.
(2.4) deaccelerates and shrinks back to the stable equilibrium point 𝑥9".= = 𝛿$ since 𝑃, < 𝑃0. Given that deviating 𝛿̇ is sufficient small [13]. Same reasoning can be made when 𝛿 < 𝛿$ and the right-hand side of the swing equation accelerates back to the asymptotic stable equilibrium point [18]. But if the rotor angle exceeds the proven unstable pole when still accelerating, the system has surpassed the unstable region and won’t be able return to stable operation. Same thing can be said if the mechanical power would exceed the maximum electrical power according to [25].
Fig. 2.7. Varying electrical power with respect to rotor angle, assuming the mechanical power is constant.
2.3.2.1 Region of attraction for small-signal stability
The estimated region of attraction around the stable equilibrium point are bounded by the transient energy in forms of kinetic and potential energy, as described in Eq. (2.11). Given that the candidate for the Lyapunov function 𝑉 is positive definite [5]. By applying Lyapunov’s stability theorem according to [26], the value of 𝑉̇ corresponds to the counteracting damping applied as an opposing force to decay the trajectory towards a stable point. That remains negative as time goes to infinity [24], as seen in Eq. (2.12).
𝑉6𝛿̇, 𝛿7 = 𝑉B+ 𝑉?
= )7
"#$𝛿6̇ + M𝑃,(𝛿$− 𝛿) +-2( -)
*+ (cos 𝛿$− cos 𝛿)N (2.11)
𝑉̇6𝛿̇, 𝛿7 = −𝐷𝛿6̇ ≤ 0 (2.12)
Concluding that as long as there exists sufficient damping in the system, provided by the stiffness and inertia constant in the system. The equilibrium points that has strictly negative real part are an asymptotically stable solution for small disturbances.
Chapter 3 3. HVDC
This chapter will address some possible solutions derived from previously stated problems regarding low system inertia and concerns regarding instabilities in case of a sudden fault. By instead interconnecting system control through High Voltage Direct Current (HVDC) technology, these concerns could further be enhanced. Recent studies, [27] have suggested that certain enforcements could in fact provide inertial response to frequency deviations, as well as counteract oscillating transients.
HVDC technologies is therefore a preferred technology for certain transmission applications due to some favorable solutions. It is generally advantageous over High Voltage Alternating Current (HVAC) when it comes to large scale power transmission over long distances, where HVAC has limitations in forms of losses and controllability. That is due to the characteristics of inductive and capacitive elements in cables or overhead lines, causing high charging currents. Furthermore, the technology also enables interconnection of two asynchronous systems with different frequencies [28]. Whereas there are two different topologies regarding the configuration of HVDC technology by using different types of power electronics to govern the flow of power transmitted [29]. Which will be introduced briefly within this chapter to contemplate why one of them are more favorable over the other when evaluating system control. As well as introducing the control strategies itself specified for the literature review part of this study.
3.1 Line-commuted converter (LCC) HVDC technology
The earliest developed configuration of the two where an LCC current source converter technology, consisting of thyristor-based semiconductors, as seen in (Fig. 3.1) which requires a synchronous voltage source in order to operate.
The commutation is conducted by connecting these components through bridges in pairs and transferring pulses of current in different valve topologies [29]. Various numbers of pulse configurations are used to interact with lagging current of reactive characteristics. However, each commutating pulse operation consumes reactive power when transmitting the converted power.
Fig. 3.1. Thyristor-based representation used in LCC HVDC.
The reactive power consumption is therefore inconvenient for the grid since it also causes harmonic oscillations which needs filtering to prevent resonance interference with residual equipment, as well as power losses in the AC network [30]. By instead making use of Pulse Width Modulation (PWM) through power electronic devices that are able to switch on and off, instead of a current blocking approach. Therefore, the flow of reactive power is able to be sustain locally instead of demanding on an auxiliary source to commutate, which enhances controllability in a wider range of operation.
3.2 Voltage source converter (VSC) HVDC technology
By instead taking advantage of a self-commutated approach through modulating pulses at the gate of Insulated gate bipolar transistors (IGBT), acting as voltage source converters (VSC). Thereby, each set of VSC’s are able to control reactive and active power instantaneously and independently with high switching frequency [31]. Similarly, to the LCC technology the topology of the converters itself are structured in a resembling fashion as illustrated in (Fig. 3.2) where many IGBT’s are connected in series that represents a semiconductor. The number of layers is related to the blocking voltage capability for the converter, which increases the DC bus voltage.
Therefore, the blocking diode are placed in parallel in order to ensure the four- quadrant operation for each individual converter. Also, the DC bus capacitors shown furnish stored static energy for controllability of power flow, as well as filtering for the harmonics associated with the switching frequency from each converter [29]. As soon as the output voltage amplitude is reduced below the supplied AC voltage, the VSC converter generates reactive power to compensate. Whereas, if the converter output leads, active power is instead supplied by each phase.
Fig. 3.2. Conventional three-phase two-level VSC topology.
3.2.1 Structure of the VSC
As mentioned earlier, conventional HVDC systems are dependent on reactive power supplied from the AC grid throughout large switchyards with extensive filters and other various equipment. Unlike the dynamic voltage control from the VSC configuration that are able to commutate themselves locally which also enables black-start capability, in case of a severe disturbance [29]. That means that the transient behaviours of sudden faults on one side of the decoupled grid, will not impinge the system on the other side of HVDC link of this configuration. As was shown in a recent study for an offshore wind farm connected through VSC’s [7], where it was proven that the onshore grid fault did not influence the active power across the other side. The configuration along with its fundamental components are shown in (Fig. 3.3) to illustrate a simplified overview to get acquainted with the roles of each part.
Fig. 3.3. One-line scheme of the VSC-HVDC configuration.
3.2.1.1 Equipment and framework for VSC-HVDC transmission
Special converter transformers that can withstand harmonics and unusual stresses adjust the AC voltage to suitable level for the HVDC system. That is partly due to adaptions for offset currents and leakage impedances that could occur. Therefore, there are also filters equipped for harmonic resonance instead of supplying reactive power as in conventional systems [30].
However, there are instead phase reactors that adjust the reactive power flow, as well as limiting the short circuit current for good measure. Eventually between the conversion and receiving end, transmission cables convey the DC link over longer distances until it is inverted, and a similar procedure is repeated until flowing over to the other asynchronous decoupled grid area.
This aforementioned process has proven to be more advantageous for integration of renewables due to the share substantial size of the installation on site compared to classic LCC, as stated in [29]. Partly due to the extensive AC filtering needed for each phase along with reconsiderations for auxiliary sources for commutation and supply of reactive power. But the flexible controllability in unforeseen scenarios being the most expedient motive [31].
3.2.2 Modelling of the VSC HVDC
The power flow control strategy of the HVDC link with PWM are separated into two independent control loops along the axis at each converter valve.
Which is illustrated in (Fig. 3.4) and (Fig. 3.5) below from a modelling study of VSC HVDC [7]. Whereas the control scheme for the grid connected side mainly governs the terminal voltage by controlling the reactive power exchange in four-quadrant operation. Thereby, the active power balance can maintain stable within desired limits. Moreover, the error between the reference value and what is measured eventuate into a reference along the q- axis that determines the reactive power output. Acting as an excitation system, similar to those of conventional synchronous generators in case of a voltage drop during a disturbance, according to [32]. As a result, the excess reactive power helps the voltage to recover.
Fig. 3.4. Control scheme of the grid side connected converter [25].
Similarly, the generator side connection is configurated to control the flow of active power over the link during fluctuating generation. As well as supplying necessary amounts of reactive power to the generators in case of a wind farm conjunction [31]. As before, error signals generated from comparation between reference and measured values in case of active power and voltage are processed through a proportional integral controller for each axis respectively. Eventually forming two voltage signals from the inner control loop that are transformed into pulses that modulates the gate [7].
Fig. 3.5. Control scheme of the generation side converter [25].
3.2.2.1 Emulating inertia control strategies
The wide controllability of the VSC configuration enables variable control over various parameters that could mitigate the impact of sudden instabilities occurring in the grid. This facilitates reliable bulks of generated power being transmitted over longer transmission distances, as well as interconnecting grid areas. But most importantly supporting grids with low inertia, which is discussed in [27] where several control strategies are proposed to backup these problematics. Consequently, making use of the stored rotational energy from a variety of variable rotating machines into electrostatic energy stored in the capacitors contained in the HVDC link. Resembling the kinetic energy present in a conventional synchronous machine in forms of energy discharged and supplied to the mains. But instead being associated with the rated VSC power capability in relation disposable energy stored, with respect to three phase voltage magnitude and angle of the rectifier converters [33], which will be put into perspective in Section 5.3.2.
Chapter 4
4. Wind power
The rapid increase in energy demand from renewable sources as previously reasoned results in a thriving wind power industry that utilizes natural resources to harvest abundant amounts of energy in forms of electricity. By making use of the kinetic energy in the mass flow of air over a sweeping area, turbine blades can exploit the free energy of nature into mechanical power.
4.1 Energy generated from the wind
Given that a fraction of the wind for the taking is limited by the Betz limit 𝐶?, which is referred to the maximum theoretical percentage that could be extracted to approximately 59% of the total energy available [2]. Given as a function of the tip speed ratio 𝜆 and pitching angle of the wind blades Θ. The power produced by the wind turbine depends on the interaction between aerodynamic forces from the wind being applied to the rotor. As seen in Eq.
(4.1) the power generated from the blowing wind are an extension of the kinetic energy relation and the equivalent efficiency 𝜂01, that depend on the overall performance of the wind turbine.
𝑃8C#3 =96 𝜌 𝐴 𝑣D 𝜂01𝐶?(𝜆, Θ) (4.1)
Whereas, the distribution of forces applied to the rotating shaft connected to the generator acquires angular momentum from the rotating masses with a moment of inertia that drives the turbine [34]. Most wind turbine shafts are coupled through a gear box, where different ratios between the rigid masses are more flexible to adapt to fluctuating wind speeds as seen in (Fig. 4.1).
When it comes to the rotational output flexibility of the generator, there are either fixed speed or variable speed configurations. Fixed speed configurations are directly connected from an asynchronous squirrel cage induction generator to the local grid transformer at constant speed. This robust, yet simple configuration generates electric power regardless of speed controllability and demand of power [35]. Fluctuations wind are directly converted into mechanical fluctuations and consequently into electric power.
Fig. 4.1. Illustration of a distribution of stiffness and inertia in a geared mechanical system [34].
For more compatibility with varying grid scenarios and more interactive with reactive power balance, variable speed configurations are more suitable.
Counteracting a too rigid of a coupling for mechanical and electrical torque translated into produced power. Variable speed dynamics are more favorable by using different configurations of power electronics to offer a variety of flexibility, see (Fig. 4.2) below. The flexibilities regard capability to regulate the reactive power flow as well as making use of the existing inertia and stiffness from the rotating machine. It acts as an energy buffer smoothing out wind turbulence and transient torques acting on the drivetrain [36]. When considering generators using power electronics to variable govern the power generated by different techniques, some are more favorable than others for different applications [35]. Thereby, two configurations will be described of briefly to convey their ability to contribute with variable speed. That is the Doubly-Fed Induction Generator (DFIG) using a wound-rotor induction generator with variable slip. As well as the Permanent Magnet Synchronous Generator (PMSG), that uses full scale frequency converters.
Fig. 4.2. Power conversion stages in a typical wind turbine system [36].
4.2 DFIG
The asynchronous turbine configuration consists of a direct connection via the stator to the AC mains, as well as a closed accession through the rotor which enables variable speed control during incoherent wind speeds. The majority of the generated power by the wind turbine are delivered directly to the grid through the stator windings, and up to ± 30% slip of the rated power can go via the rotor connection [16]. The DFIG configuration as seen in (Fig. 4.3) has the capability to decouple active and reactive power independently by the rotor excitation current bidirectionally through the slip rings in a back-to-back configuration [34]. This feedback enables a variable speed operation by compensating the difference in mechanical and electrical power by injecting a rotor current with variable frequency through the power electronic converts, consisting of IGBT’s acting as a VSC. Both during normal operation, as well as during faults the behavior of the wound rotor induction generator is thus governed by the converters on each side. In an over-synchronous situation, the power flows from the rotor via the converters, whereas in the opposite direction the other way around much like the VSC-HVDC [16].
Fig. 4.3. Doubly Fed Induction Generator configuration.
4.2.1 Modelling of the DFIG
The Rotor Side Converter (RSC) are capable of four-quadrant operation to control reactive power flow in either direction to maintain stability of the system during fluctuating scenarios of electricity generation. The benefits of locally regulating the reactive power is to maintain a stable terminal voltage.
Given that the amplitude of the stator flux linkage and the rotor current is proportional to the air gap torque developed by the generator.
Thus, the relation between desired torque and rotational speed can be controlled with PWM to regulate the signal at the gate of the IGBT [7].
Whereas the Grid Side Converter (GSC) are able to keep the DC link voltage within an appropriate limit to govern the reactive power exchange between the grid and the injected power. An imbalance during a transient may cause variations of the frequency and voltage supplied to the AC grid and could therefore damping the power oscillations by modulating the reactive power flow [36].
Fig. 4.4. Overall vector control scheme of the VSC’s for the DFIG model [7].
The vector modelling approach for the aforementioned quantities, such as reactive power, active power and terminal voltage of the two VSC’s are thoroughly explained in [7]. Thereby, the scheme of the control loops is illustrated in (Fig. 4.4) for consistency. By measuring the signals and compare it to the reference signals, reference currents are generated through the proportional integral controllers from the resulting error signals. Furthermore, these signals are once again compared to the reference values through another inner controller that form voltage signals indented to modulate the pulses connected to the gate of the IGBT’s [7], [18].
4.3 PMSG
Instead of using an asynchronous wound-rotor induction generator with partial variable slip, the permanent magnet configuration could be more favorable since it is decoupled from the mains with full variable speed control.
Consequently, the electrical behavior on the machine side of the converter in (Fig. 4.5) are unaffected by the grid behavior [37]. Whereas complications following a fault at the grid correlates directly to the operation of an asynchronous generator. Thereby could a full scale conversion in a larger scale have a larger impact following a disturbance, which was demonstrated in [7] with constant active power supplied regardless of the condition of the power grid. Since the control of the frequency converter allows the rotor speed to be completely decoupled from the grid frequency.
Fig. 4.5. Full converter PMSG configuration [37].
Whereas the turbine control strategy itself for the PMSG are theoretically similar to the modelling of the DFIG as earlier resonated in Section 4.2.1. The main difference is full controllability directly connected to the stator [35].
Further in Section 6.1.3, the incorporated equivalent simulation model will be presented along with the overall block diagram representing multiple wind turbines as one. There, each dynamic control model will be described respectively according to (Fig. 4.6) shown below.
Fig. 4.6. Overview of the dynamic model conductivity [37].
4.3.1 Synthetic inertia control
In order to be able to provide the grid with frequency support from wind turbines with variable speed, the earlier mentioned modelling strategies could be useful to emulate synchronous generators in some sense. By manipulating the response acting on the controllers, some contribution of inertial response from the angular momentum from the Wind Turbine Generator (WTG). Since, during the first few seconds of a sudden disturbance, the interaction between mechanical and electrical power can be considered fixed. Same goes for the nominal frequency, meaning that the initial ROCOF are proportional to the combined system inertia [18].
Fig. 4.7. Synthetic inertia controller for the system.
Resulting in a dynamic inertial system response depending on the synthetic inertia constant 𝐻;<#5E"5CF provided by the controller. As shown in (Fig. 4.7) above, a simplified block diagram for the additional power generated ∆𝑃 are visualized according to [6]. The static gain block is depending on the compensation of active power in relation to the ROCOF to govern the eventual imbalance before the primary frequency control reacts. A practical example from a case study are described in Section 5.3.1.
Chapter 5 5. Case study
An overview of the test model implemented in this work will be introduced in this chapter, along with the case scenarios occurring which represents our current situation, as well as a futuristic one. Firstly, a devastating incident that occurred in southern Sweden 2003 will be retold to be aware of the severity.
Since a heavy loss of generation from a nuclear power plant eventually sparked a cascading event, which eventually resulted in a blackout. From a Nordic European grid perspective, these simplified test systems are put into context to examine these issues within this thesis. As well as introducing an alternative approach when generating power from the wind, which decouples two synchronous networks via VSC HVDC.
5.1 Scandinavian blackout in 2003
Cascading events that eventually lead to system collapse beyond controllability was the case back in 2003 when one of the nuclear blocks in Oskarshamn power station tripped due to a sudden emergency shutdown. That resulted in a drop in system frequency as illustrated in the first dip in (Fig.
5.1) which later caused a double busbar to trip at a substation located adjacent to Ringhals nuclear power plant at the west coast. The combination of heavy loss of generation from these large synchronous generators, as well as congestion in remaining transmission lines caused bottlenecks in the remaining grid. Consequently, overloading affected the system stability since the residual generators were not able to keep up, leading to further grid areas to fall out of synchronism until it escalated beyond stable operation, resulting in a complete blackout [18], [38].
Fig. 5.1. Illustration of the sequence of events happening back in 2003. The solid line is the voltage magnitude and the dashed on represents the grid frequency [18].
5.2 Simplified test systems used for simulation
By investigating the severity of system instability, a simplified test system is studied to clarify the outcome in case a fault jeopardizes the nominal grid operation. Representing a national grid operating at steady state. Suddenly after 1.5 seconds of normal operation, a three-phase fault disconnects bus 3018 as seen at the blue encirclement in (Fig. 5.2), preventing generated power to be supplied to the grid. Two different cases occur, one where the fault is cleared after a short time period as well as being out of service indefinitely. These two cases will be compared in two different scenarios which represents our present situation as well as a futuristic one, that is highlighted by the green encirclement seen below.
Fig. 5.2. Illustration of the fault occurring at bus 3018, as well as the generator being replaced by wind turbines.
5.2.1 Case A and B
Much like the cascading blackout that happened back in 2003, it all started with an unforeseen loss of production. In this event a significantly smaller thermal power plant with production capacity of 100 MW suddenly disconnects from bus 3018 following a fault. As clarified in (Fig. 5.3), Case A reconnects the generator towards the grid once the fault is cleared 150 ms later. Whereas in Case B the generator stays disconnected due to some internal
malfunction following the disturbance. This means that there suddenly is a capacity shortage for the remaining simulation. Since the objectives of this thesis partly is directed towards investigate the existence of fast acting inertial frequency response, the simulation proceeds for 4.5 additional seconds, meaning that auxiliary power reserves will not be able to support external frequency control.
Thereby, the primary and secondary frequency response are not considered in any of the two scenarios. So, the main purpose of case B is therefore to analyze and compare the system behavior to prevent cascading effects. Since the focus are towards generation every load is regarded fixed without any dynamic modulation considered for consistency. These two cases are then repeated over different circumstances, which brings us to the aforementioned scenarios occurring.
Fig. 5.3. Illustration of the two cases happening. The generation unit is reconnected after the fault is cleared in Case A but remains disconnected in Case B.
5.2.2 Scenario 1 and 2
Since the topical bus where the fault occurs in are interconnected with a quite central junction connecting two grid areas as well as supplying loads locally.
The resulting impact of the disturbance will therefore be evaluated for two different scenarios. To put it into context, the decommissioning of conventional synchronous generators as previously resonated are illustrated in (Fig. 5.4). Whereas in Scenario 1, two conventional nuclear power plants with rated generation capacity of 750 MW respectively are connected to nodes
denoted as 101 and 102. The generators are in turn interconnected to the transmission grid throughout step up transformers. When it comes to Scenario 2, one of the nuclear power plants have been replaced by a wind power farm situated at the same grid area, consisting of several Type 4 PMSG. An equivalent lump of wind turbines combines for an equal generation capacity of 750 MW, reproducing the replaced nuclear power plant. Consequently, reducing the amounts of rotating kinetic energy stored in the large synchronous machine essential for system stability. That is why the study is repeated to investigate their ability to supply the weakened grid with active as well a reactive power, in order to sustain stable operation and avoid cascading effects onwards.
Fig. 5.4. Clarified illustration of the two scenarios occurring.
5.3 Previous studies
To analyze and compare the results produced within this work, some analogies regarding system stability from previous works are being brought up to investigate how the model needs to be developed further. Based on that, case studies regarding synthetic inertia support from DFIG will be raised to emphasize the relation between Chapter 3 and Chapter 4. With parallels drawn towards Chapter 7.
5.3.1 Frequency response from inertial control: [9]
Investigations regarding the impact of inertial control for different wind scenarios are analyzed in an Energiforsk report [9]. There is a notable difference between the outcome of frequency response within the system. In a scenario where conventional power generation representing 13.3% of the
total generation capacity are replaced by wind power, and a sudden loss of generation occurs accounting for 5.2%. The frequency nadir reaches a lower limit of 48.98 Hz without inertial control, compared to 49.05 Hz with the conventional power plant operating. Whereas the system frequency with inertia support reacts slower due to additional active power supplied, which compensates the loss of 5.2% power generation post fault. Resulting in a frequency nadir at approximately 49.1 Hz, which also recovers slower since the wind turbine speed has declined. Thereby the generated power decreases, whereas the aerodynamic power increases to restore its initial operation gradually.
5.3.2 Enhancements for further development: [6]-[8]
As mentioned in Section 3.2.2, different control techniques could be implemented to supply active power, as well as being able to control the flow of reactive power. Consequently, enhancing the recovery rate of the gradual decreased rotational speed from the wind turbines whilst the frequency rebounds back to normal operation. In a published paper [7] that partly focuses on strategies to counteracts low frequency nadirs. Suggests that variable speed wind turbines such as DFIG in a larger scale should be interconnected with VSC HVDC, much like (Fig. 5.5). Claiming that the fast acting control of both active and reactive power can improve the performance. Making up for the weaknesses that the DFIG has, when forming a too rigid of a coupling directly towards the grid asynchronous. Moreover, it was shown that the system became more stable when supporting the system voltage with reactive power at the grid converter. When comparing it to a case without reactive power exchange, similar to a case without HVDC. Same goes for the eigenvalue analysis, proving that oscillations were dampen out faster and resumed stable operation more rapidly.
Fig. 5.5. Overview of synthetic inertia achieved by interconnecting a DFIG wind farm offshore via VSC HVDC.
The other papers that are essential to analyze for this particular study are directly connected to the implementation of control systems for high penetration of wind power. It was shown in [8] that the rotor angular stability in fact was improved at every synchronous generator in the grid after being subjected to a fault during 500 ms. Proving that the scenario with VSC HVDC actually recovers faster compared to when all synchronous machines are interconnected. The reason being that the oscillatory behavior of the machines inherently requires controllers for adjusting the realignment of synchronizing torque with the synchronous grid frequency. But the authors emphasize that their results represent a somewhat small penetration which they consider an idealized situation.
Bringing us to a paper [6], that highlights the role of synthetic inertia for a power system as a whole. Here the authors develop a complete DFIG based wind farm to analyze the impact of different synthetic inertia constants when dynamic loads are considered during the disturbance. Concluding that a larger synthetic inertia constant compensates active power imbalances which slows down the ROCOF, leading to a higher frequency nadir and a more stable system. However, when the authors apply the same model with varying inertia in proportion different amounts of wind penetration. When a larger share of the generation capacity originates from wind, regardless of additional control systems. The frequency nadir seems to decrease, making the system more responsive and fragile to disturbances. Concluding that there is a tradeoff between system inertia and ROCOF regarding system stability for high wind penetration.
Chapter 6
6. Method and implementation
The system model used in this work is the PSS/E program application guide example. The model shown in (Fig. 5.2), including three grid areas and consists of 23 buses in total as well as 6 power plants, where 5 of them are thermal generation units and the other one hydroelectric. A total of 11 two- winding transformers interconnect nodes with different voltage levels, transferring flow of power to 5 fixed shunt, and 8 non-dynamic loads. As a whole, the system has 23 AC lines, where 7 of them are tie lines that connect two different network areas.
6.1 Method
The quantitative simulation part in this work is performed in Siemens PSS/E 34.2 University edition. This chapter presents a brief description of each component used in the program and the models that are used for dynamic simulation implemented for each case scenario.
6.1.1 Siemens PSS/E
PSS/E is a package of programs for numerical studies in power system generation performance and transmission networks, in both steady state and dynamic conditions. This high-performance transmission planning and analysis software is developed by Siemens. So, the software itself is an integrated set of computer programs that handle power flow and related network analysis functions. Furthermore including balanced and unbalanced fault analysis, which is essential when analysing a loss of generation. Along with circuit equivalent calculation from the parameters used [39].
PSS/E has well developed models for static as well as dynamic simulations of power networks, to analyse power system stability. The dynamic simulation of a physical process in PSS/E is performed in three general steps.
• Construction of a set of differential equations describing the behaviour of the physical system in general.
• Determination of a set of values of constant and variable parameters describing, in detail, the condition of the physical system at some instant.
• Integration of the differential equations with the values determined above as initial conditions.
For numerical computations in PSS/E, a specific model must be chosen for every piece of equipment from the library in the program. The data has to be implemented for each component and the power flow, as well as the dynamic simulations, are done by taking IEEE recommendations into consideration, internally. The dynamic models of the test system used in PSS/E for this work will thereby be brought up in the coming sections [40].
6.1.2 Synchronous generator model in PSS/E
The synchronous generator models used by the program are represented as a synchronous machine. They present the electrical transmission network with a positive sequence with known instantaneous amplitude and phase, but the current has to be determined.
Fig. 6.1. Generator model equivalent current source and Norton equivalent circuit [40].
Generally, the generator is represented as a voltage source behind the step-up transformer and a dynamic impedance. But in PSS/E the generator itself is represented by their respective Norton equivalent, where the voltage source is replaced by an equivalent source current ISORCE, illustrated in (Fig. 6.1).
The dynamical control system structure is therefore divided into different models, which is illustrated in (Fig. 6.2). The implementation of parameters determines the dynamic behaviour of these generator that is described below.
Fig. 6.2. General description of the topology used for synchronous generators.
