Frequency control concepts through decentralized energy resources

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FREQUENCY CONTROL CONCEPTS THROUGH DECENTRALIZED ENERGY RESOURCES

Lappeenranta–Lahti University of Technology LUT Energy Technology Triple Degree; Master’s thesis 2021

Florian Hölscher

Examiner(s): Prof. Jamshid Aghaei

Prof. Dr. Ing. habil. Lutz Hofmann (LUH) Prof. Dr. Ing. Peter Werle (LUH)

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ABSTRACT

Lappeenranta–Lahti University of Technology LUT LUT School of Energy Systems

Energy Technology

Florian Hölscher

FREQUENCY CONTROL CONCEPTS THROUGH DECENTRALIZED ENERGY RESOURCES

Master’s thesis 2021

84 pages, 39 figures, 22 tables and 1 appendix

Examiner(s): Prof. Jamshid Aghaei, Prof. Dr. Ing. habil. Lutz Hofmann (LUH), Prof. Dr.

Ing. Peter Werle (LUH)

Keywords: frequency control, decentralized energy resources, wind turbine, grid inertia, power system stability, hidden inertia emulation, deloading, overspeed, overspeeding, fast frequency response

With the transition of the electrical energy market towards renewable energy sources, new challenges in the field of power system stability arise. As inverter-based resources, such as wind, solar and accumulators, are integrated into power systems, directly grid connected synchronous generators are displaced and system inertia deteriorates. This leads to a requirement for new methods of frequency control.

Fast frequency response is a recently introduced term to describe a variety of control schemes that aim to include modern power sources in the provision of inertia and control energy. This work investigates the feasibility of different approaches, with a focus on wind, but also including photovoltaic power. Deloading as well as inertia extracting strategies are investigated, all in a 12 GW, non-aggregated, 12-bus power system. After observing the influence of reduced system inertia, the control scheme’s effectiveness is tested in a number of comparative studies, comparing results for different wind power penetration depths and wind speeds, as well as testing the inclusion of photovoltaic power.

It has been found that, due to the fast response of inverter-based resources in comparison to mechanically actuated primary response in thermal power plants, faster changes in grid frequency can be compensated and even over-compensated, if fast frequency response methods are implemented. In wind power plants, deloading strategies were more successful than inertia extraction when operating at medium and high wind speeds. For high renewable power penetration depths, over-speeding showed the most promising results out of the

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compared control schemes. It was further found that due to the reduced reserve power for deloading at low wind speeds, inertia extracting methods are more effective in these cases than pitch-controlled deloading. Photovoltaic power was found to be especially suitable for the reduction of the short-term rate of change of frequency, due to its very fast, purely electronic response.

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Declaration page I

Declaration:

I declare that this thesis has been composed solely by myself and that it has not been submitted, in whole or in part, in any previous application for a degree. Except where states otherwise by reference or acknowledgment, the work presented is entirely my own.

Hannover, 04.10.2021 Florian Hölscher

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Contents page VII

List of Figures

2.1 Classification of power system stability problems. [16] . . . 4

2.2 Effect of inertia during a frequency disturbance, without frequency response. 5 2.3 Frequency response stages by the European Network of Transmission System Operators for Electricity (ENTSO-E). Based on data from [54]. . 7

2.4 Share of electricity production by source in Europe, 1990 to 2019. [58], data from [57], [59] . . . 9

2.5 Inertia constants estimated in EU-28. Change between 1996 and 2016. [18] 9 2.6 Schematic view of droop control. . . 11

3.1 Scheme of a direct drive PMSG wind turbine. . . 13

3.2 Angle of attack α as a function of wind speed, blade speed and pitch angleβ. . . 15

3.3 Comparison of power lines of stall and pitch controlled turbines. . . 16

3.4 abc- and dq-reference systems in a PMSG. . . 20

4.1 Schematic view of hidden inertia emulation (HIE). Based on [31] . . . 22

4.2 Deloading techniques for wind power plants. (a) Pitch control. (b) Over-speed control. [35] . . . 23

4.3 Deloading process in photovoltaic power plants. Based on [36]. . . 24

5.1 Explicit Euler method and its error. . . 26

6.1 Overview of the implemented wind power plant model with implemented VHIE and pitch control. . . 28

6.2 Plan of the used bench mark grid including two aggregated wind farms. Based on [48]. . . 30

6.3 Calculated P_a (green) compared to measured P_a (blue) of two manufac- turers. Based on [39] . . . 32

6.4 Converter control loop. . . 38

6.5 Control diagram of the variable hidden inertia emulation (VHIE) subsystem. Left: Frequency support phase, right: Speed recovery phase. . . 43

6.6 States of the implemented VHIE control and their transition conditions. 44 6.7 Power coefficient in dependence of pitch angle for different tip-speed ratios. 46 6.8 Control diagram of the pitch-controlled deloading subsystem. . . 46

6.9 Control diagram of the over-speeding-controlled deloading subsystem. . . 47

6.10 Schematic power gradients of the implemented over-speed control. . . 48

7.1 Comparison of frequency gradients before and after introduction of wind power. . . 52

7.2 Comparison of frequency gradients for different frequency control strategies. 54 7.3 Power gradients of a wind turbine under VHIE control. . . 55

7.4 Power gradient of a wind turbine under pitch control. . . 56

7.5 Power gradients of a wind turbine under combined VHIE and pitch control. 57 7.6 Frequency comparison under VHIE control with and without controlled rotor speed recovery phase (SR). . . 58

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page X List of Figures 7.7 Comparison of power gradients under VHIE control: Left: With imple-

mentation of SR. Right: With uncontrolled SR. . . 59 7.8 Comparison of frequency gradients for different wind power penetration

scenarios without implementation of fast frequency response (FFR). . . . 60 7.9 Comparison of frequency gradients for different wind power penetration

scenarios under combined pitch and VHIE control. . . 61 7.10 Comparison of frequency gradients for different wind power penetration

scenarios under over-speeding control. . . 61 7.11 Frequency gradients at different wind speeds. . . 65 7.12 Comparison of rotor speeds for different wind speeds. Values relative toω_r0. 66 7.13 Low wind speed power output: Left: Under pitch control. Right: Under

VHIE control. . . 68 7.14 Low wind speed RoCoF. Left: Under pitch control. Right: Under VHIE

control. . . 68 7.15 Frequency comparison for different penetration depths of IBR. . . 70

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List of Tables page XI

List of Tables

2.1 Categorisation of control energy levels. [4] . . . 8

6.1 Input and output parameters of the wind power plant model. . . 28

6.2 Relevant grid parameters before introduction of inverter-based resourcess (IBRs). . . 31

7.1 Comparison of results obtained before and after introduction of wind power. 53 7.2 Comparison of results obtained by different frequency control strategies. . 54

7.3 Comparison of results obtained with controlled and uncontrolled speed recovery. . . 59

7.4 Scenarios of wind power penetration of the grid. . . 60

7.5 Comparison of frequency nadir obtained at different wind energy penetration depths. . . 62

7.6 Comparison of RoCoF obtained at different wind energy penetration depths. 62 7.7 Comparison of recovery time obtained at different wind energy penetration depths. . . 63

7.8 Wind speed scenarios. . . 64

7.9 Comparison of results obtained at different wind speeds. . . 64

7.10 Comparison of initial rotor speed and rotor speed low point and recovery time for different wind speeds. . . 66

7.11 Results obtained with different control schemes atν_w = 6^m_s. . . 69

7.12 Photovoltaic scenarios. . . 69

7.13 Comparison of frequency nadir obtained at different IBR penetration depths. . . 70

7.14 Comparison of Rate of Change of Frequency (RoCoF) obtained at different IBR penetration depths. . . 71

7.15 Comparison of recovery time obtained at different IBR penetration depths. 71 9.1 Converter specifications. . . 83

9.2 Generator specifications. . . 83

9.3 Turbine specifications. . . 83

9.4 VHIE control specifications. . . 84

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Acronyms page XIII

Acronyms

DFIG doubly-fed induction generator

EESG electrically excited synchronous generator

ENTSO-E European Network of Transmission System Operators for Electricity

FFR fast frequency response FS frequency support phase HIE hidden inertia emulation IBR inverter-based resources LFC load frequency control MPP maximum power point

MPPT maximum power point tracking PCR primary control reserve

PM permanent magnet

PMSG permanent magnet synchronous generator

PV photovoltaic

PV-PP photovoltaic power plant RES renewable energy sources RoCoF Rate of Change of Frequency SCR secondary control reserve SG synchronous generator

SgCE Synchronous grid of Continental Europe SI Synthetic Inertia

SR rotor speed recovery phase SSM state-space model

TCR tertiary control reserve TSO transmission system operator

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page XIV Acronyms

VHIE variable hidden inertia emulation

WT wind turbine

WTG wind turbine generator

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List of Latin Symbols page XV

List of Latin Symbols

F force

H_max maximum synthetic inertia coefficient H_syn synthetic inertia coefficient

H inertia coefficient

J moment of inertia

K_RoCoF RoCoF gain for over-speeding K_SR speed recovery coefficient K_dq dq-transformation matrix

K_i integrating term

K_p proportional term

L_D0 zero squence inductance L_Dq q-axis inductance

L_aa, L_bb, L_cc stator coils’ self inductances L_ab, L_ac, L_ba... stator coils’ mutual inductances L_d d-axis inductance

L_f fluctuating component of stator inductance L_m average stator smutual inductance

L_s average stator self-inductance

P_FS power during frequency support phase P_L non-motor load active power

P_MPP power at maximum power point P_N nominal active power

P_OS activated over-speed control power P_SR power during rotor speed recovery phase P_T_,₀ nominal turbine power

P_VHIE activated variable hidden inertia emulation power

Pδ air gap power

P_a aerodynamic power

P_moto motor load power

P_pitch_,_set pitch deloading control power demand

P active power

Q_L non-motor load reactive power

Q reactive power

R_s stator resistance

RoCoF_act frequency support activation Rate of Change of Fre- quency

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page XVI List of Latin Symbols

RoCoF_deact frequency support deactivation Rate of Change of Frequency

R radius

S_D aggregated decentralised apparent power S_FS frequency support signal

S_SR rotor speed recovery signal S_gen generator apparent power S_r rated apparent power

S apparent power

T_el electrical torque

Tm mechanical torque

T torque

U_p synchronous internal voltage X_d synchronous reactance

A state matrix

B input matrix

C output matrix

D feedthrough matrix

u_D decentralised resources input vector x_D decentralised resources state vector KKT nodal-terminal-incidence-matrix Y_KK,A nodal-terminal-incidence-matrix Y_TT,a active component’s admittance matrix Y_TT,p passive component’s admittance matrix i_T,a active component’s terminal currents vector i_T,p passive component’s terminal currents vector u_T,a active component’s terminal voltage

u_T,p passive component’s terminal voltage

i_D,ref reference terminal current of decentralised resources i_D terminal current of decentralised resources

i_T terminal current

u_K Node voltage

a acceleration

c_p_,_set power coefficient set by primary control reserve c_p power coefficient

e control error

f_N nominal frequency

f frequency

h discretising time step i₀ zero sequence current

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List of Latin Symbols page XVII

i_d d-axis current

i_q q-axis current, source current

i current

j imaginary unit

k number of time steps

m mass

p pole pair number

t time

u_N node voltage

u₀ zero sequence voltage

u_d d-axis voltage

u_q q-axis voltage

u voltage

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List of Greek Symbols page XIX

List of Greek Symbols

Ψ magnetic flux linkage

ΨPM permanent magnet magnetic flux linkage Ψd d-axis magnetic flux linkage

Ψ_q q-axis magnetic flux linkage β pitch angle

β_set pitch angle set by primary control reserve λ tip-speed ratio

ν_w wind speed ω angular speed

ω₀ nominal angular speed ω_r0 nominal rotor angular speed ω_r rotor angular speed

ρ air density

σ droop

τ_D converter time constant of decentralised rescources τ_m mechanical time constant

θ_r rotor angle

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page 1

1 Introduction

In light of the ongoing climate crisis and the Paris Agreement, the international community is making increasing efforts to reduce carbon emissions to net zero. These necessitate the energy sector, currently responsible for 73 % of global emissions [50], to undergo rapid transformation.The energy sector’s transition towards renewable energies sets new challenges for the operation of electrical grids world wide.

Weather fluctuations causing volatility of renewable infeed in the power grid have made electric power generation less predictable, creating the need for new solutions for power system stability. This necessitates the requirement for long term storages and variable loads for longer periods of underproduction. Another problem system operators are facing however, is reduced system inertia. Where formerly grids were kept stable by high system inertia provided by directly grid connected synchronous generators (SGs), future grids are expected to show significantly lower inertia values.

This is due to the fact that most renewable sources are converter interfaced, and are therefore not inherently able to provide inertia. New ways to respond to sudden imbalances between electricity generation and consumption are hence investigated by researchers and grid operators throughout the world.

1.1 Current state of technology

Existing research has already elaborated a variety of control strategies aimed at the provision of frequency control reserves by converter-based power sources. Beyond the introduction of possible control schemes however, little research has been con- ducted on their effects on distributed (unaggregated) power networks. Especially the combination of different control schemes has seen little investigation so far. In practical application, Canadian Hydro-Québec TransÉnergie and Texas-based ER- COT are the only transmission system operators (TSOs) requiring synthetic inertia from converter-based energy sources today, due to their high penetration depths of renewable sources [51]. However in Europe, the ENTSO-E has published a guideline allowing and encouraging national TSOs to implement similar requirements in their grid codes [52].

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page 2 1 Introduction

1.2 Aim of this thesis

Within the field of power system stability, the contribution of this thesis is the investigation of frequency support by inverter-based generation units. An emphasis is laid on wind turbine generators (WTGs), as wind power makes up for the largest part of renewable production today. Furthermore, in contrast to photovoltaic systems, wind turbines possess real inertia in the rotation of their blades, which makes them the most promising renewable source for inertia provision. Additionally however, a deloading strategy for photovoltaic (PV) is modelled and compared to study the combination of wind and solar FFR.

To investigate the effects of reduced centrifugal mass and different options to counter them, a distributed benchmark network is applied. This network is complemented with two aggregated renewable generation units. These are equipped with additional control loops to provide frequency control response. The single system components are modelled to describe their physical properties. The permanent-magnet SG is represented as a system of linear equations and the converter is represented by a current source.

The main research questions investigated are: How can IBRs provide inertia and primary control energy in case of a frequency event? What effect does this have on important frequency parameters such as post-contingency recovery time and frequency nadir? How do the results change under different operating conditions? For the clarification of these questions, different test cases are elaborated and compared.

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page 3

2 Power System Stability

The IEEE/CIGRE Joint Task Force on Stability Terms and Definitions [13] defines power system stability as

"... the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact."

Furthermore, it categorises three fields of power system stability: Voltage stability, rotor angle stability and frequency stability. The first is defined as a power system’s ability to maintain stable voltages within the permitted voltage band at all nodes in nominal operation as well as after contingencies [13]. Due to voltage control being a local phenomenon, the TSO ensures adequate reactive power compensation in the proximity, to prevent voltage constraint violations. As a consequence of voltage instability, voltage may collapse entirely, potentially leading to large-scale blackouts. Some of the factors that may contribute to voltage instability are the limited capability of generators to deliver reactive power, reactive power demand of transmission lines and load characteristics [1]. An overview on the classification of power system stability problems is given in Figure 2.1.

Rotor angle stability is defined as the capability of directly grid-connected machines to remain in synchronous operation after the occurrence of a contingency [13]. It may be further divided in transient or small signal stability, according to the severity of the disturbance. It can also be categorised as oscillatory or non-oscillatory instability, where oscillatory instability may take one of four modes (local, inter-area, control and torsional mode), non-oscillatory instability can be traced back to a shortage of synchronising torque or damping [14], [2].

Frequency quality is judged by the steadiness of the frequency gradient. This steadiness is determined by the ability to maintain stable operation during large grid disturbances. Parallel to voltage stability depending on reactive power balance, frequency stability depends on the equalisation of supply and demand of active power.

Frequency instability may lead to the disconnection of loads and generating units, causing a cascading escalation of the frequency disturbance that leads to large-scale blackouts. It is commonly associated with the splitting of a larger power grid into smaller, desynchronised zones as a consequence of major disturbances [15].

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page 4 2 Power System Stability

Figure 2.1 Classification of power system stability problems. [16]

2.1 Inertia

In Isaac Newton’s Philosophiæ Naturalis Principia Mathematica of 1687, he describes inertia as follows [3]:

"The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line."

It is thereby the first of Newton’s Laws of Physics. It can just as easily be adopted to a rotating mass, which will not stop spinning until a counteracting force will bring it to halt. In today’s electrical power networks, Newton’s first law plays a crucial role in frequency control. As conventional power plants have synchronous generators directly connected to the grid, grid frequency is directly linked to the rotational speed of all connected rotating electrical machinery. This interconnected network of machines is constantly subjected to two forces: That of the production units trying to accelerate it, and that of the consumers trying to decelerate it. Whenever these powers are out of balance, we will see a change in grid frequency that must be controlled. The higher the total inertia of the system, the slower the change will be, giving TSOs more time to take appropriate measures. The physical dimension to describe the inertia of a rotating system is the moment of inertia J. In analogy to Newton’s second law, which postulates for force in translatory motion:

F =m·a (2.1)

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2.1 Inertia page 5 Where m is mass and a is acceleration, inertia is also referred to as angular mass, as torque T in rotational motion is described as:

T =J·θ˙ (2.2)

Where ˙θ is angular acceleration. We see that in rotational movement, moment of inertia (from now on referred to as inertia) takes the place of mass. Just like mass, it is an inherent property of a body and as such, can be calculated from its mass distribution. For complicated geometrical objects however, this becomes a time-consuming effort, necessitating CAD-modelling of the investigated body. A more viable approach is the monitoring of changes in angular speed. If the actuating power is known, inertia can be estimated based on eq. 2.3, with the measured frequencyf and the actuating power difference ∆P. This way, the aggregated inertia of wide-spread power systems can be determined. The procedure is explained in more detail by the UK’s TSO National Grid in [53] by the example of the UK power grid.

df

dt = ∆P

J (2.3)

Figure 2.2demonstrates the effect of reduced inertia during a frequency event.

Figure 2.2 Effect of inertia during a frequency disturbance, without frequency response.

In power system engineering, it is more common to use the inertia constantH rather than inertiaJ. This simplifies the comparison of inertias of different machines, as it

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page 6 2 Power System Stability relates the machine’s inertia to its rated power S_r and rotational speed ω:

H= ¹²J ω²

S_r (2.4)

Another way to describe the reaction of a power system to a step change is the mechanical time constantτm. It gives the time needed by the machine to accelerate from stand still to rated speedω₀ and is linearly proportional to inertia, quadratically proportional to rotational speed and anti-proportional to torque.

τ_m = J ω²₀

S_rp² (2.5)

Where p is the machine’s pole pair number. It can also be represented by the electromechanic machine constant k_m, which, according to [48], relates to τ_m as follows:

k_m = p J = 1

τ_m ω²₀

S_rp (2.6)

With the inertia known, the swing equation describes the acceleration of the system in dependence of the actuating torques. In a generator, mechanical torque T_m accelerates the rotor and the opposing electromagnetic torque T_e decelerates it.

df

dt = T_m−T_e

2H (2.7)

Although not actively controlled in conventional power systems, the system’s inertia is sometimes referred to as spinning reserve [17].

2.2 Control energy provision

Amongst the three kinds of system stability specified in the introduction to this chapter, the focus of this work lies on frequency control, for which control energy needs to be provided to keep active power production and consumption in balance.

Control energy provision is structured in three levels, according to reaction time and duration of the provision:

• Primary control reserve (PCR)

• Secondary control reserve (SCR)

• Tertiary control reserve (TCR)

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2.2 Control energy provision page 7

Figure 2.3 Frequency response stages by the ENTSO-E. Based on data from [54].

Figure 2.3 gives a schematic view of the sequence of frequency response actions.

PCR is activated via a control loop of the power plant as explained in section 2.4. The plant operator measures the grid frequency on-site and primary reserve is activated once the dead-band of 10 mHz is exceeded. This way, communication delays are avoided. PCR is then increased proportionally to frequency deviation (see chapter 2.4), with the maximum positive or negative reserve active at 49,8 Hz respectively 50,2 Hz. Owing to the equivalence of frequency throughout the grid, PCR is allocated grid wide. In the area of the Synchronous grid of Continental Europe (SgCE), a total of±3000 MW is deployed. It has to be fully available after 30 seconds and stay available for at least 15 minutes. [4]

SCR is activated within the load frequency control (LFC) area in which the disturbance occurred (polluter-pays principle). A LFC area is equivalent to the grid zone of each TSO, who’s responsible for balancing supply and demand within his zone.

The TSOs are cooperating , supplying each other with live data about the state of their grid, to avoid counter activation of reserve. SCR’s purpose is to supersede PCR, which will then be available again as control reserve, and return the frequency to its nominal operating point. Once PCR is displaced by SCR, line power between LFCs is restored to its pre-contingency condition. SCR needs to begin operation after 30 seconds and be fully available after 5 minutes. [55]

TCR, also called minute reserve, is requested manually by the TSOs. This may become necessary during long-lasting disturbances. It has to equal out supply and demand in each LFC area. TCR is scheduled on short notice in a resolution of 15 minute time blocks, supporting or replacing SCR. Just like SCR, its activation is based on a Merit Order List. The German TSOs use a common list while also coordinating with neighboring countries to avoid oppositional work of their control

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page 8 2 Power System Stability systems. [56]

Table 2.1summarises the control energy levels.

Table 2.1 Categorisation of control energy levels. [4]

Control energy level Demands Provision Primary reserve Fully available within 30

seconds and available for 15 minutes

Automatically activated on plant level based on frequency deviation.

Secondary reserve Fully available within 5 minutes

Automatically activated based on active power im- balance within the LFC area and the frequency deviation.

Tertiary reserve Fully available within 15 minutes

Manually called, depending on necessity and considering the schedule management.

2.3 Influence of RES on power system stability

Renewable energy sources (RES) have been promoted in Europe ever since the 1970s’

oil crisis [5]. Since the 1990s however, due to the EU’s attempts to combat the climate crisis, electricity production from RES has been steadily expanded to what is now a considerable share of overall electricity production (seeFigure 2.4). 15,4 % of European electricity production in 2019 has been sourced from wind and solar plants, with the largest part (11,6 %) from wind [57]. These, together with the increasing number of battery electric storages, form the group of inverter-based electricity sources, as their generation units are not directly grid-connected but rather depend on an inverter to generate AC. Therefore, they provide no inertia to the grid. In case of solar systems and batteries, this is due to unavailability of a rotating mass and in case of wind power plants, the mass inertia is decoupled from the grid.

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2.3 Influence of RES on power system stability page 9

Figure 2.4 Share of electricity production by source in Europe, 1990 to 2019. [58], data from [57], [59]

As directly grid connected generators are being replaced by these electronic power sources, the overall power system inertia is reduced. For some European countries, which are part of either the SgCE, Nordic Grid or British National Grid, the change is visualised in Figure 2.5. Reduced system inertia translates to a faster change in frequency df

dt, from now on referred to as RoCoF, as shown by the general swing equation (eq. 2.7). Conventional primary frequency control however, as remarked in chapter 2.4, relies on time consuming mechanical activation. The faster RoCoF leaves it less time to react, causing larger frequency deviations during disturbances.

Figure 2.5 Inertia constants estimated in EU-28. Change between 1996 and 2016.

[18]

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page 10 2 Power System Stability The effect of converter-based generators on voltage stability is more controversial in the literature. In general, the power factor of modern inverters can be controlled freely, giving the possibility to quickly set the reactive power output according to voltage levels [19]. However, most research indicates that voltage stability can be affected adversely when SGs are replaced by interfaced generation. In [20], investigations revealed increased reactive power demand for higher wind energy penetration levels.

In [21] it is pointed out that doubly-fed induction generators (DFIGs) reactive power output capability is lower than that of SGs and further remarks that during transient events, DFIGs consume reactive power similar to squirrel cage machines, further reducing voltage stability. Also according to [21], better voltage stability may be achieved when wind power in the grid is more dispersed, rather than centralised.

Similar findings were made by [22] for photovoltaic generators. Little research however can be found on interfaced SGs, as all of the mentioned sources for wind power examined DFIGs.

2.4 Droop Control

Droop control is a strategy applied by all power plants that engage in primary frequency response and voltage control. A linear function P(f) respectively Q(U) is applied to determine the primary control active power P and reactive power Q supply (seeFigure 2.6).

σ_f =−∆f

∆P; σ_U=−∆U

∆Q (2.8)

The droop σ represents how strong the reaction to frequency or voltage deviations is. While a base load power plant will have a steep droop, resulting in little power adjustments, a peak load plant will follow a more flat function [4]. In Germany, σ= 5 % is common for renewable sources [6]. In steam power plants, active power is set by controlling the steam valves and thereby steam pressure before the turbine [4].

Providing positive control power necessitates that before the frequency event, the power plant is operated with partly closed valves, which can then be opened to increase injection of steam. In the field of renewable energies, control strategies based on shifting the nominal operating point away from the maximum power point tracking (MPPT)-curve are referred to as deloading (see chapter 4.2). Other droop control functions than linear ones and dynamic deloading for increased frequency stability and power yield are discussed in the literature [23], [24], [25].

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2.4 Droop Control page 11

Figure 2.6 Schematic view of droop control.

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page 13

3 Wind Turbine Design

A wind turbine (WT) is an energy conversion system for electricity generation. Its mechanical part consists of a turbine, a shaft and, depending on the design type, a gearbox. The electrical part mainly consists of a generator, a power electronic converter (in case of a variable speed wind turbine) and a coupling transformer.

Further, it may be equipped with an active or passive filter to reduce the emission of harmonics into the grid, as well as converter and turbine control systems. Wind energy is captured by the rotor blades, propelling the generator via the shaft and the gearbox. The generator produces AC voltage at a variable, comparably low frequency that is determined by rotor speed and gearbox ratio. This voltage is fed to the converter, rectified, and then again inverted to grid frequency. Via the transformer, energy is then fed into the utility grid. The general layout is visualised inFigure 3.1.

Figure 3.1 Scheme of a direct drive PMSG wind turbine.

Developments in the field of WT technologies have contributed to different engineering designs and implementations. This chapter will summarise the different types of 3-blade horizontal axis turbines as only those are used in large-scale wind energy conversion systems today, and are therefore relevant for frequency support at the moment. WTs can for instance be categorised by:

• Speed control – Fixed speed – Variable speed

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page 14 3 Wind Turbine Design

• Power control – Stall control – Pitch control

• Generator concept – DFIG

– electrically excited synchronous generator (EESG) – permanent magnet synchronous generator (PMSG)

• Drive train concept – Direct drive – With gearbox

These will be described in the following.

3.1 Speed control concepts

Fixed speed WTs were turbines which were directly connected to the grid, their speed was therefore determined by the grid frequency, gearbox ratio and generator pole pair number. Their efficiency was severely limited as it was not possible to keep the tip-speed ratio at a constant optimum rather than changing with the wind speed.

The tip-speed ratio λ as presented in eq. 3.1, gives the ratio of rotor tip speed to incoming wind speed, with ω_r the rotor rotational speed, R the rotor radius and ν_w the wind speed. Today’s variable speed WTs are conceptualised for a large range of wind speeds, as their rotor speed can be actively adjusted, rather than being directly linked to wind speed or grid frequency. They are decoupled from the grid via a converter, allowing their speed to be adjusted by controlling the pitch angle and the converter power demand. [26]

λ= ω_rR

ν_w (3.1)

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3.2 Power control concepts page 15

3.2 Power control concepts

Two speed control concepts are commonly encountered in wind turbine design: Stall and pitch control. Stall controlled machines have been used through-out the last century due to their simplicity, as they need no active control. When the wind speed increases beyond the rated value, the angle of attack α increases so that the blade goes into stall, thereby eliminating propulsion. In modern megawatt-class wind turbines, they are no longer used due to their irregular distribution of mechanical stress and imprecise power limitation. [26]

Instead, pitch controlled systems are used which can adjust the rotor blade angle.

During partial-load operation, the blade pitch is controlled to maintain the aerody- namically optimal tip-speed ratio, achieving the highest possible power coefficient c_p [26]. This behaviour is referred to as MPPT. When reaching the rated turbine power, the pitch angle is increased to limit the power output to its rated value until the cut-out wind speed is reached and rotor blades are pitched in stall position, thereby stopping the power intake of the turbine. Figure 3.2shows the dependence of the angle of attack from wind speed, blade speed and pitch angleβ. Figure 3.3displays the behaviour of stall- vs pitch-controlled turbines over the applicable wind speed range.

Figure 3.2 Angle of attackα as a function of wind speed, blade speed and pitch angle β.

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Figure 3.3 Comparison of power lines of stall and pitch controlled turbines.

3.3 Generator concepts

After squirrel-cage induction generators have dominated the wind energy market in its early times of fixed speed, stall controlled WTs due to their robustness and simple technology, their lack of speed controllability and their permanent consumption of reactive power pushed them out of the market when systems became larger and demands in efficiency, controllability and power quality increased [27].

DFIGs haven taken hold in the market since the late 1990’s. Using a similar operation principle as the squirrel-cage machine, their three-phase wounded rotor enables them to offer the speed variability and controllability demanded by variable speed turbines.

Speed can be controlled via the active power flow, while the reactive power output is adjusted via the rotor current. Current and voltage are set by the newly introduced power converter, which decouples the generator from the grid and thereby allows for the turbine to rotate at variable speeds. Problematic are the brushes in the machine as well as the multiple-stage gearbox, which require a high level of maintenance and may cause machine failure. Further, the power electronic converter drives up the installation costs. [27]

Today, SGs are becoming increasingly popular, with new designs adapted for WT use, such as multi-phase SGs allowing easier conversion to DC, claw-pole machines using inductors instead of brushes, thereby reducing the need for maintenance, and synchronous reluctance rotors, promising simple construction and rapid response to load variations due to low inertia. [27], [28]

In SGs, the stator and rotor field are interlocked, thereby rotating synchronously.

As a result of this, the electrical frequency f is determined by the angular speed ωr

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3.3 Generator concepts page 17

and the pole pair number p.

f =p·ω_r (3.2)

In all rotating electrical machinery, the generated torqueT can be calculated based on the air gap power P_δ and rotational speed.

T = P_δ

ω_r (3.3)

Synchronous generators can be categorised as salient or non-salient pole machines.

Saliency describes the difference in magnetic permeability in the direct- and quadrature- axis of the rotor. With U being the stator voltage, U_P the synchronous internal voltage, θ_r the rotor angle, X_d the synchronous reactance, and the the number of phases 3, the air gap power is given by [2] to be

P_δ =−3UU_P

X_dsin(θ_r) (3.4)

Inserting the air gap power to eq. 3.3, torque is given by

T =− 3UU_P

X_dsin(θr)

ω_r (3.5)

The equation shows, that the synchronous machine’s torque production is due to the rotor angle, which represents the phase difference between the rotating magnetic field and the rotor. At higher loads, the angle will increase, resulting in higher torque. In generator operation, the angle will always be positive, in motor operation negative.

Beyond ±90°, operation becomes unstable.

In salient pole machines, this torque is supplemented by a reluctance torque. Re- luctance torque occurs due the difference of magnetic permeability in d- and q-axis of the rotor and the tendency of the rotor to align with the stator field in such a way, that the magnetic resistance in the circuit is minimised. However, salient pole machines are usually found in low speed applications such as hydro power plants and are therefore not described further in this work.

3.3.1 Direct drive permanent magnet synchronous generator

In today’s wind power systems, direct-drive systems are valued for their low maintenance and high reliability. This comes in effect even more when applied offshore, where maintenance is more difficult, while the system’s working conditions are rougher than on land. However, directly driven generators are operated at turbine speed,

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page 18 3 Wind Turbine Design necessitating higher torque in order to convert the same power at lower speed. This makes PMSGs the natural choice due to their high flux density, which results in high torque density. Compared to EESGs, they don’t only have an advantage in torque density and mass per kilowatt output power, but are also more reliable due to lower heat production in the rotor and a reduction of mechanical parts, especially slip rings.

Drawbacks of PMSGs include the risk of demagnetization at high temperatures, high material costs for the magnets, as well as environmental hazards connected to rare earth material mining. [27], [29]

In the following, a physical description of the PMSG according to [7] is given. The voltage in each stator winding is given by:







u_a u_b u_c







=







R_s 0 0 0 R_s 0 0 0 R_s













i_a i_b i_c







+







dΨa

dt dΨb

dt dΨc

dt







(3.6)

Where R_s is the stator resistance, i_a, i_b and i_c are the stator currents, u_a, u_b and u_c the stator voltages and Ψa, Ψb and Ψc are the magnetic flux linkages in each stator winding. The latter are defined by the mutual inductances between stator windings as well as the permanent magnets’ flux linkage with the stator windings.







Ψ_a Ψ_b Ψ_c







=







L_aa L_ab L_ac L_ba L_bb L_bc L_ca L_cb L_cc













i_a i_b i_c







+







Ψ_a,PM

Ψ_b,PM

Ψ_c,PM







(3.7)

WithL_aa,L_bbandL_ccbeing the stator coils’ self-inductances,L_ab,L_acetc. the stator’s mutual inductances and Ψ_a,PM, Ψ_b,PM and Ψ_c,PM the flux linkages between the rotor’s permanent magnets (PMs) and the stator coils. Self-inductances, mutual inductances and rotor-stator flux linkages are rotor angle variant [7]. Their dependence from the electrical rotor angleθ_e is given for the self-inductances by:







L_aa L_bb L_cc







=Ls+Lm







cos (2θ_e) cos2θ_e− 2π

3

cos2θ_e+2π 3







(3.8)

For the mutual inductances, it is given by:







L_ba L_cb L_ac







=







L_ab L_bc L_ca







=−L_m−L_f







cos2θ_e+π 6

cos2θ_e+ π 6 − 2π

3

cos2θ_e+π 6 + 2π

3







(3.9)

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3.3 Generator concepts page 19

And for the rotor-stator flux linkages it is given by:







Ψ_a,PM

Ψb,PM

Ψc,PM







= ΨP M







cos(θ_e) cosθ_e− 2π

3

cosθ_e+ 2π 3







(3.10)

Where L_s is the average self-inductance and L_m is the average mutual inductance.

L_f describes their fluctuating component. The electrical rotor angle θ_e is defined in the rotor reference frame to be 0 at the d-axis. It can then be expressed by the mechanical rotor angle θ_r and the pole pair number p:

θ_e=p·θ_r (3.11)

Generally in the description of rotating electrical machines, the dq-reference frame is preferred, which is fixed to the rotor. The direct-axis (d-axis) is fixed to the north pole of the rotor field, while the quadrature-axis (q-axis) stands perpendicular to it, as visualised in Figure 3.4. Describing the system variables in this coordinate system, the dependency from the rotor angle is eliminated. To account for unsymetries between phases, a zero sequence component is added. In order to transform the system of equations from abc- to dq-reference frame, the voltage and current vectors are multiplied with the dq-transformation matrixK_dq, given by [8]:

K_dq = 2 3







cos(θ_e) cosθ_e−2π 3

cosθ_e+2π 3

−sin(θ_e) −sinθ_e− 2π 3

−sinθ_e+ 2π 3

12 1

2 1

2







(3.12)







u_d u_q u₀







=K_dq







u_a u_b u_c







(3.13)







i_d i_q i₀







=K_dq







i_a i_b i_c







(3.14)

With the dq-transformation applied and eqs. 3.7 to 3.10 inserted in 3.6, the dq-voltage equations are obtained:

u_d=R_si_d−pω_r(i_qL_q)L_ddi_d

dt (3.15)

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Figure 3.4 abc- and dq-reference systems in a PMSG.

u_q=R_si_q−pω_r(i_dL_d+ ΨPM) +L_qdi_q

dt (3.16)

u₀ =R_si₀+L₀di₀

dt (3.17)

u₀ and i₀ represent the zero-sequence components. Given a symmetrically operated system, these can be omitted. Ld and Lq are the stator d- and q-axis inductances, given by:

L_d=L_s+L_m+3

2L_f (3.18)

L_q=L_s+L_m− 3

2L_f (3.19)

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page 21

4 Fast Frequency Response

FFR refers to a group of methods that aim at the provision of control energy by IBRs, rather than depending on mechanical systems for power adjustments as described in chapter 2.4 [60]. Sources that can provide FFR include rotating machinery such as WTGs, static power sources such as PV and accumulators or controllable loads.¹Due to their increased reaction speed, they are more suitable for low inertia grids than conventional PCR. Some of the options are discussed in this chapter.

4.1 Hidden inertia emulation

HIE aims at emulating the inertial response behaviour of synchronous machines. The goal is to reduce the RoCoF to keep it within permitted boundaries and thereby also reduce the frequency nadir. The frequency nadir marks the lowest point the frequency reaches after a contingency. For this, a control loop is applied that reacts to RoCoF deviations and some sources further apply a second control loop, which reacts to frequency deviations [30]. Both loops generate a reference torque additional to that of the MPP-tracker, thereby releasing the "hidden" inertia from the turbine and drive train. Figure 4.1 schematically describes the system trajectory. Starting from the MPPT operating point A, a negative RoCoF is detected and the converter increases the power output to point B. The power output might be limited by the maximum power of the converter, especially at high wind speeds, causing it to stay constant while the rotor speed decreases. However, with decreasing rotor speed, the available aerodynamic power P_a also decreases, causing the overall power output to decline starting from point B. [31] and [32] suggest point C, at which the additional power supply is turned off, to be set at the original power output. The total power output would then plunge to the MPPT-curve (point D’), if no additional measures are taken. This causes a severe secondary frequency drop, but also the quickest possible speed recovery, as a larger part of aerodynamic power is fed to the grid, leaving less for speed recovery. If the output power is adjusted to the arodynamic power curve (D”), no acceleration is possible, as the available wind power is completely fed to the grid. It is therefore the goal of HIE approaches to find the right trade off between the two trajectories (point D to E). When turbine speed is sufficiently recovered and no severe secondary frequency drop is to be expected, power output can be tracked back to the nominal point along the MPPT-curve (F to A).

1In its reaction time, FFR lies between traditional inertia, which occurs instantaneously, and PCR, which acts more slowly. Therefore it is referred to as synthetic inertia in some sources, even through it is not not necessarily sourced from a rotating mass. In this work, synthetic inertia is only used in the context of power extracted from interfaced rotating masses.

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page 22 4 Fast Frequency Response

Figure 4.1 Schematic view of HIE. Based on [31]

4.2 Dispatch of inverter-based resources

IBRs can provide PCR by withholding part of their generation capacity given at the instantaneous operating condition, thereby creating a headroom that can be activated in case of frequency events. This concept resembles that of PCR by conventional power sources. For wind as well as solar, choosing the appropriate headroom requires balancing the loss of power generation against the gain of control reserve. RES dispatch strategies for reduced power output are generally referred to as deloading.

4.2.1 Wind power deloading

In all wind power systems, mechanical power input is governed by the general wind power equation (6.14). The power coefficientcp in this equation is a function of pitch angle and tip-speed ratio. This gives two options for deloading: Pitch angle control or speed control.

Using pitch angle control, the blade angle is increased during nominal operation to decrease the turbine power. This gives a power reserve that can be activated during frequency events. Pitching the blades requires a mechanical system, potentially increasing reaction times. Categorisation as FFR however is justified, as response rates of up to 25^%/s[33] are significantly faster than those of thermal power plants.

Speed control creates the needed power reserve by reducing or increasing the rotor speed at a set wind power, as a sub-optimalλreduces the power output. It is always favourable to increase the rotor speed (over-speeding), rather than to decrease it

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4.2 Dispatch of inverter-based resources page 23 (under-speeding), as in case of a frequency drop, rotational energy can be released while moving the operating point towards its optimum, thereby increasing power.

With an under-speeding scheme, electrical power would first need to be decreased to increase rotor speed and shift the working point to the MPPT line. To trigger the system’s reaction, one or two additional control loops are needed which adapt the converter’s power output according to either frequency deviation, RoCoF or both. [34]

Irrespective of the control strategy, the power reserve can either be determined through delta control which creates a fixed proportion of available maximum power, balance control, which reserves a certain percentage of the rated power, or a fixed reserve [33].

Figure 4.2 Deloading techniques for wind power plants. (a) Pitch control. (b) Over-speed control. [35]

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page 24 4 Fast Frequency Response 4.2.2 Solar power deloading

Similarly to WTGs, photovoltaic power plants (PV-PPs) traditionally apply MPPT.

As the maximum power point of the P/V-curve depends on panel temperature and solar radiation, the converter sets the voltage so that maximum power P_{M P P} is harnessed. For deloaded operation, the operating point can be set either at a lower or higher voltage, thereby shifting operation to a sub-optimal point [36]. This creates a headroom, which can be activated in case of frequency contingiencies by resetting the voltage. Voltage can be set to any point between the deloading voltage U_del and the MPPT voltageU_MPP in case of negative frequency excursions, or below U_del in case of positive frequency excursions. A schematic view is given in Figure 4.3.

Figure 4.3 Deloading process in photovoltaic power plants. Based on [36].

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page 25

5 State-Space Modelling

State-space models (SSMs) describe dynamic systems by a set of first-order differential equations using state-variables. This is often easier than using a smaller number of n^th-order equations. The state-variables themselves need not to be measured during operation, rather it suffices to measure the input and output data as well as the state variable’s initial operating points. In opposite to transfer functions, SSMs are usually applied in the time domain, rather than in the Laplace domain. A special case is the single input – single output (SISO) system, which is a first order system as the dimensions of B, C and D correspond to the numbers of inputs and outputs.

All other cases are called multiple input – multiple output (MIMO) systems. They can further be written as continuous-time or discrete-time models. Their basic form in continuous-time is given in eq. 5.1 and 5.2. [61]

˙

x(t) =Ax(t) +Bu(t) (5.1)

y(t) =Cx(t) +Du(t) (5.2)

Where x(t) is the state vector of dimension n, u(t) is the input vector and y(t) is the output vector. Accordingly, the matricesA, B, C and D, are the state matrix, input matrix, output matrix and feedthrough matrix.

A variety of solving algorithms for initial value problems are described in the literature.

The most basic one is the explicit Euler method, depicted in Figure 5.1. In order to follow the real graph described by a differential function, it utilises the deviation of the graph in point A0 to calculate the tangent line. Going along this tangent line for a small enough time step, the resulting point A1 will be close enough to the original graph. The problem can be formulated according to [9] as:

˙

y=f(t, y), y(t₀) = y₀ (5.3)

Defining the discretising time steph, the function can be defined for any number of steps k:

t_k =t₀+kh (5.4)

For each step, the next step is then given by:

y_k+1 =y_k+hf(t_k, y_k) (5.5)

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page 26 5 State-Space Modelling

Figure 5.1 Explicit Euler method and its error.