UPTEC ES 17 003

Examensarbete 30 hpApril 2017

Future frequency control services in the Nordic power system

Helena Olsson

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Future frequency control services in the Nordic powersystem

Helena Olsson

An increased share of electricity production from variable energy sources, especially wind and solar power, and loss of inertia in the system, result in higher demands of frequency control. In the last decades, the quality of the grid frequency in the Nordic power system has gradually deteriorated. This thesis has examined if an introduction of a new frequency control service, called fast FCR N, can improve the frequency quality. Today, almost all of the frequency control in the Nordic countries is provided by hydropower units. Whether fast FCR-N can reduce wear and tear on the hydropower units was also studied. Numerical simulations of a one-area model representing primary frequency control and the Nordic electrical grid were carried out in Matlab Simulink. Two different designs of fast FCR-N, proportional and deadband design, were introduced in the system. The system performance regarding frequency quality and hydropower control work was evaluated.

The results show that both proportional and deadband fast FCR-N improve the system performance. Still, studies on a future scenario, assuming less inertia and frequency dependent load in the system, indicated that further actions need to be taken to get significantly better frequency quality in the future compared to today.

ISSN: 1650-8300, UPTEC ES 17 003Examinator: Petra JönssonÄmnesgranskare: Per NorrlundHandledare: Elin Dahlborg

Executive summary

This thesis has examined the performance of the current FCR-N in combination with a new

primary frequency control service that has an instant response to frequency deviations. The

results show that 60 MW of so called fast FCR-N improves the quality of the grid frequency

and reduces the control work of the hydropower units significantly. The number of minutes

the frequency exits the normal band (49.9 – 50.1 Hz) decreases by 15 %. In the hydropower

units, the travelled distance by the guide vanes decreases by 20 %.

Before introducing fast FCR-N, studies on how the service would affect other aspects of the

power system stability, e.g. inter-area oscillations, are needed. Furthermore, a market model

for fast FCR-N has to be developed.

Sammanfattning

För att hålla en stabil nätfrekvens i kraftsystemet måste det råda ständig balans mellan

konsumtion och produktion av el. På den nordiska elmarknaden handlas det med el på

timbasis. Varje drifttimme upphandlas en dag i förväg utifrån prognoser om hur stor

konsumtionen respektive produktionen kommer att bli. Eftersom prognoserna inte alltid

stämmer och för att konsumtion och produktion inom den upphandlade timmen kan variera,

krävs resurser som kompenserar för detta. I och med en allt större andel elproduktion från

variabla energikällor, främst vindkraft och solenergi, så ökar behovet av frekvensreglering,

d.v.s. resurser som kan hjälpa till att bibehålla den momentana balansen. Frekvensen i det

nordiska elnätet ska under normaldrift ligga inom ett frekvensband mellan 49,9 och 50,1 Hz,

men de senaste decennierna har det skett en gradvis försämring av frekvenskvaliteten. Tiden

frekvensen ligger utanför detta intervall har ökat och det har observerats att nätfrekvensen

oscillerar med en periodtid på mellan 40 och 90 sekunder, ett fenomen som ofta hänvisas till

som 60-sekunders-svävningen.

Idag står vattenkraften för nästan all frekvensreglering i Norden. Vattenkraft är ett flexibelt

kraftslag som snabbt kan reglera sin uteffekt och lämpar sig därmed bra för frekvensreglering.

Dock är 60-sekunders-svävningen ett tecken på att systemet inte lyckas kompensera för de

laststörningar, dvs. när producerad eller konsumerad effekt avviker från det planerade, som

har en dynamik med en periodtid på kring 60 sekunder. Det här arbetet undersöker därför om

en ny frekvensreglerande tjänst, som är snabbare än dagens, skulle kunna förbättra

frekvenskvaliteten och minska slitaget på turbinerna i vattenkraftverken. Denna snabbare

tjänst, som kommer att kallas snabb FCR-N, skulle kunna tillhandahållas av till exempel

batterier, svänghjul eller någon annan slags energilagringsteknik.

Två olika utformningar av snabb FCR-N undersöks. Den första är rent proportionell reglering

där uteffekten från energilagret svarar proportionellt mot frekvensavvikelsen på elnätet.

Eftersom det inte är möjligt att kräva obegränsad effektkapacitet av ett energilager, införs en

mättnadsgrad som innebär att uteffekten blir konstant när frekvensavvikelsen överskrider ett

visst värde. Den andra varianten är utformad med ett dödband kring den nominella

frekvensen. Det medför att energilagret endast bidrar med reglereffekt när

frekvensensavvikelsen överskrider ett visst värde. Den senare antas inte avlasta vattenkraften i

lika hög utsträckning som den proportionella designen, men kräver å andra sidan inte lika

mycket arbete av energilagret.

Resultaten visar att båda tjänsterna förbättrar frekvenskvaliteten i elnätet och bidrar till att

slitaget på vattenkraftturbinerna minskar. De olika tjänsterna har olika styrkor, men för att

reducera 60-sekunders-svävningen i så hög grad som möjligt är ren proportionell reglering att

föredra. Vidare visar resultaten att 60 MW snabb FCR-N, med en reglerstyrka på 600 MW/Hz

och en mättnadsgrad vid 0.1 Hz, är tillräckligt för att ge en relativt stor förbättring av

frekvenskvaliteten och en betydande reduktion av slitaget på vattenkraftturbinerna.

Problemet ligger inte bara i de snabbare förändringarna i elproduktion som följer av en ökad

mängd variabla källor. Allt fler enheter i kraftsystemet är kopplade till elnätet via omriktare.

Traditionellt har vattenkraft, kärnkraft och kraftverk med kol- eller bioenergi som energikällor

stått för kraftproduktionen i Norden. Dessa har synkront kopplade generatorer, vilka bidrar

med svängmassa till systemet. En stor mängd svängmassa bidrar till att systemet bättre kan

hantera snabba störningar och har därmed en stabiliserande effekt på nätfrekvensen. Det finns

även laster som är frekvensberoende och varierar sitt effektuttag beroende på nätfrekvensen.

Dessa har också en stabiliserande effekt på systemet.

I detta arbete undersöks även ett framtida scenario där det antas att det skett en kraftig

minskning av systemets svängmassa och elnätets frekvensberoende last. Resultaten visar att

frekvenskvaliteten och reglerarbetet som krävs av vattenkraften kommer att öka betydligt,

även för ett system där regleregenskaperna hos vattenkraftverken förbättras. Ett system med

60 MW snabb FCR-N gör bättre ifrån sig, men skillnaden mot dagens situation är inte så stor.

Det antyder att systemet är känsligt för stora variationer i mängd svängmassa och

frekvensberoende last. Därför behövs vidare studier kring hur tekniska lösningar i framtiden

kan ersätta förlusterna av svängmassa och frekvensberoende laster.

.

Preface

This master thesis project has been carried out at Vattenfall R&D, Solna, Sweden. It has been

the last part of my studies at the Master Program in Energy Systems Engineering at Uppsala

University and the Swedish University of Agricultural Sciences.

I would like to thank my supervisor Elin Dahlborg for all help and support throughout the

work. Thank you for introducing me to frequency control and for all time you have spent

explaining complicated things. So many x- and y-axes that have been drawn…

Thanks also to Per Norrlund for valuable discussions and good feedback on the report, and to

Anna Nilsson, my opponent, for your good inputs. Furthermore, I would like to thank all

colleagues at Vattenfall R&D for welcoming me with open arms to your office. Especially,

many thanks to Johan Bladh for introducing me to Elin in the first place, and later showing

such interest in my project, and thanks to Linn Saarinen for taking time answering my

questions.

My love and gratitude to Vide for your support and patience (and for correcting grammar and

spelling in the report). Last but not least, thank you Malin, Kristin, Markus and Daniel. These

5+ years of studies would not have been the same without you.

Helena Olsson

Uppsala, April 2017

Contents

Introduction ........................................................................................................................................ 1

1.1 Method and scope ........................................................................................................................ 2

1.2 Previous research ........................................................................................................................ 2

1.3 Outline of the thesis ...................................................................................................................... 3

Background and theory .................................................................................................................... 4

2.1 Swing equation ............................................................................................................................. 4

2.2 Inertia ............................................................................................................................................ 4

2.3 Static gain of a power plant (sv. reglerstyrka) .............................................................................. 5

2.4 Welch's power spectral density estimate ..................................................................................... 5

2.5 Challenges for the future power system ....................................................................................... 6

2.6 Frequency control services .......................................................................................................... 7

The model ......................................................................................................................................... 11

3.1 The governor .............................................................................................................................. 12

3.2 Turbine and waterways .............................................................................................................. 15

3.3 The grid ...................................................................................................................................... 16

Load disturbance signal generation .............................................................................................. 17

4.1 Method ........................................................................................................................................ 17

4.2 Results ........................................................................................................................................ 18

4.3 Discussion .................................................................................................................................. 19

4.4 Conclusion .................................................................................................................................. 20

The base case – today’s situation and how it can be improved ................................................ 21

5.1 Method ........................................................................................................................................ 21

5.2 Parameters to be studied ........................................................................................................... 23

5.3 The base case ............................................................................................................................ 29

5.4 Frequency quality – results ........................................................................................................ 29

5.5 Frequency quality – discussion .................................................................................................. 33

5.6 Wear on the hydropower units – results ..................................................................................... 34

5.7 Wear on the hydropower units – discussion .............................................................................. 35

5.8 Energy capacity and wear of the ESS – results ......................................................................... 36

5.9 Energy capacity and wear of the ESS – discussion ................................................................... 39

5.10 Conclusions .............................................................................................................................. 39

The future – a scenario with a weaker grid ................................................................................... 41

6.1 Method ........................................................................................................................................ 41

6.2 Results ........................................................................................................................................ 41

6.3 Conclusions ................................................................................................................................ 43

Potential technology for fast FCR-N .............................................................................................. 44

7.1 Batteries ..................................................................................................................................... 44

7.2 Flywheels .................................................................................................................................... 44

7.3 Supercapacitors.......................................................................................................................... 45

7.4 Wind power turbines ................................................................................................................... 46

Discussion........................................................................................................................................ 48

Conclusions ..................................................................................................................................... 50

Future work .................................................................................................................................... 51

References ........................................................................................................................................... 52

Appendix A – Model verification ........................................................................................................ 55

Appendix B – Analysis of frequency data ......................................................................................... 58

Appendix C – Evaluation of the estimation of the load disturbance signal .................................. 60

Appendix D – Comparison of frequency signals with and without fast FCR-N ............................ 61

Abbreviations

Description

aFRR Automatic frequency restoration reserve

EFR Enhanced frequency control. A frequency control service in the UK.

Ep-settings Controller settings used in turbine governors owned by Vattenfall AB

ESS Energy storage system

FCR-D Frequency containment reserve during disturbances

FCR-N Frequency containment reserve during normal operation

mFRR Manual frequency restoration reserve

NG National Grid, the TSO in the United Kingdom

SI Synthetic inertia

SOC State of charge

TSO Transmission system operator

Glossary

Guide vane Controls the flow of water through the turbine.

Head The vertical distance from the water surface of the dam to the

downstream water surface.

Penstock The conduit from the dam to the turbine.

Control system Manages and regulates the behaviour of a device or a system,

e.g. the power output of a power plant.

Feedback control system Uses the error between the actual output of the system and a

reference signal, which is the desired value of the output, to

determine the control signal to the system.

Rise time The time it takes for the step response to go from 10 % to 90 %

of the final value.

Step response The response, i.e. the output, of a system when the input signal

has the form of a step.

1

Introduction

Since the electrical power system cannot store more than a very limited amount of energy, the

consumption and production of electricity has to be almost equal at any given moment. When

the system is in balance, the grid frequency is kept stable. In the Nordic countries, electricity

is sold at Nord Pool, a market place for electricity, owned by the Transmission System

Operators (TSOs) in the Nordic and Baltic countries. At the spot market, electricity for every

operational hour is sold one day ahead, which means that there is a risk of discrepancies

between the power balance predicted at the time of trading and the actual balance in real time.

The main uncertainties lie in the load forecasts, i.e. the difficulty to know how much

electricity that will be consumed at a certain time [1]. During the last decades, a development

towards more unplannable variable energy sources, particularly wind and solar power, has

made the production less predictable as well. It makes the balancing even more difficult [2].

Because of these uncertainties in consumption and production there is a need for additional

reserves in the system. Reserves that can be used in times of imbalance, but also support the

system in the case of a larger disturbance, e.g. during an outage of a major component in the

system [1].

The Nordic TSOs are responsible for maintaining the system balance, which involves keeping

the frequency close to its nominal value of 50 Hz, and ensure a stable voltage level. To fulfil

this, the TSOs procure different ancillary services from other market players. Frequency

control is one kind of service. It is supposed to ensure that the grid frequency does not deviate

more than allowed from the nominal value [1]. This thesis focuses on frequency control

during normal operation, i.e. operation of the system within a frequency range of

49.9 Hz - 50.1 Hz. This range is referred to as the normal band. In the last decades, the

frequency quality of the Nordic power system has gradually deteriorated [2]. The number of

minutes outside the normal band has increased, and an oscillating behaviour of the grid

frequency having a period of 40-90 seconds, which will be referred to as the 60 seconds

oscillations, with a growing amplitude has been observed [3].

Possible explanations for the deteriorated frequency quality are firstly the deregulation of the

electricity market, secondly an increased share of electricity production from unplannable

variable energy sources and thirdly less inertia in the system [4]. The latter is a consequence

of more energy sources and electricity consuming units connected to the grid through

inverters, as mentioned mainly wind and solar power. Furthermore, the 60 seconds oscillation

increases the control work carried out by the hydropower turbines. Traditionally power

production has been provided by large grid connected synchronous machines, which naturally

has supplied the system with rotational inertia. This has made the grid relatively insensitive to

fast disturbances. In a scenario of a significantly higher share of inverter connected power

production the inertia decreases and as a result the grid frequency will be more volatile in

normal operation [5].

2

Having the deteriorated frequency quality and the 60 seconds oscillations in mind, there is a

need to look at the current frequency control services and examine possible alternatives to

improve the frequency quality and avoid increased wear and tear on the hydropower turbines.

1.1 Method and scope

The work is carried out through numerical simulations in Matlab Simulink. A model of the

Nordic power system and hydropower units delivering frequency control is used to simulate

the situation of today. Different methods to improve the frequency control are evaluated

regarding frequency quality and the work and wear of the units providing frequency control.

Finally the performance of the frequency control in a future scenario with a weaker power

grid is simulated. More specific descriptions of the methods are given continuously

throughout the report.

The thesis focuses on primary frequency control during normal operation, and will not study

the properties and performance of frequency control during disturbed operation. The model of

the Nordic power system is a simple one-area model. The grid is modelled as one rotating

mass and a frequency dependent load. All production is represented by one hydropower plant,

which consists of a turbine governor, a turbine and waterways. It can reasonably well

represent the dynamic behaviour of a Francis turbine delivering frequency control in normal

operation [6].

A new faster frequency control service that could be a support for the current frequency

control will be examined. The service is studied from a technical point of view, and possible

remuneration methods are left for future investigations. The service could be provided by

some kind of Energy Storage System (ESS). Other applications that the ESS could provide,

such as peak-shaving, intraday storage etc. is not within the scope of this thesis. At last, any

kind of cost optimisation of the ESS will also be left for future studies.

1.2 Previous research

Several studies have been carried out on how to improve the quality of the grid frequency, and

more specifically on how to improve the performance of the frequency control providing

units. Linn Saarinen at Uppsala University and Vattenfall R&D has studied the role of

hydropower as a provider of primary frequency control in a Nordic power system context [3],

[7], [8]. Her research also includes work on how less natural inertia and frequency dependent

loads would impact the frequency quality and the wear of the hydropower turbines. Related to

decreased inertia and damping she investigates how the introduction of synthetic inertia (SI)

can replace natural inertia and support the grid [5]. Inertia and damping are explained more in

detail in section 2.2 and 3.3.

3

Elin Dahlborg at Vattenfall R&D stresses the need to encourage good quality of provided

frequency control [4]. She suggests a remuneration method that not only remunerate the

quantity but also the quality of the provided frequency control.

The effects of a higher share of renewable energy sources in the power system and how the

current system needs to be adapted to meet this development is another common area of

research [9] - [11]. One possible solution is to use different ESS for frequency control and so

called peak-shaving, i.e. storage of energy during periods when the production normally

exceeds consumption (sunny or windy days with low consumption). This is investigated in

[12] - [14]. Wind power as a provider of frequency control and inertia has been studied

especially in [15], [16].

1.3 Outline of the thesis

This thesis is divided into ten chapters beginning with an introduction of the subject and a

brief presentation of previous research within this area. Chapter 2 gives a more thorough

background and introduces some relevant theory. In Chapter 3, the model used for the

simulations is described. The model uses the load disturbance of the power system as input

signal. How the load disturbance is estimated is explained in Chapter 4. Chapter 5 forms the

main part of the results, and contains method, parameters to be studied, results with

discussions and a conclusion. It analyses the performance of the frequency control today, and

suggests a new frequency control service that could support and improve the system.

Chapter 6 examines a future scenario with less inertia and damping in the system, but with

improved frequency control. Potential technology for the new frequency control service

suggested in Chapter 5 is briefly described in Chapter 7. The results are discussed and the

conclusions are summarised in Chapter 8 and 9 respectively. Finally, suggestions on future

work within this area are given in Chapter 10.

4

Background and theory

This work deals with the operation of the power system. The Nordic power system is an

interconnection of the synchronous power networks in Sweden, Norway, Finland and Zealand

(East Denmark). Within this area the frequency is close to uniform. It is further connected to

the Baltic countries and the continent through HVDC links. The Nordic countries’ energy

systems are characterised by different production mixes. Sweden has a combination of mainly

hydro- and nuclear power. Finland is dominated by hydropower and thermal power

production, including nuclear power. Norway has almost 100 % hydropower generation and

Denmark has a mix of wind and thermal power. However, the frequency control is carried out

mainly by hydropower plants.

For a better understanding of the results in later chapters, this chapter introduce some basic

concepts and explains some of the challenges the future power system is facing.

2.1 Swing equation

In case of a frequency deviation from the nominal frequency, the rotating machines connected

to the grid will provide or absorb kinetic energy to or from the grid. This increases or

decreases the speed of the machines according to

𝑃𝑚𝑒𝑐ℎ − 𝑃𝑒𝑙 = 𝐽𝜔𝑚

𝑑𝜔𝑚

𝑑𝑡,

(1)

the so called swing equation, where 𝐽 [kg∙m2] is the moment of inertia, 𝑃𝑒 [W] is the braking

electric power extracted by the grid, 𝑃𝑚𝑒𝑐ℎ [W] is the driving mechanical power supplied by

the turbines and 𝜔𝑚 [rad/s] is the angular speed of the machines. If 𝑃𝑒 increases, 𝜔𝑚 will

decrease and the derivative of the angular speed will be negative, i.e. the machines slow

down. To bring the system back to balance, the mechanical power 𝑃𝑚𝑒𝑐ℎ has to be increased.

As long as the frequency is lower than the nominal frequency, the machines need to be

accelerated further. This is done by increasing the driving force, for example the flow of water

through the turbine in a hydropower plant [17].

2.2 Inertia

An important property of the power system is its rotational inertia. Kinetic energy is stored in

the rotating masses in the system, which means that the more rotating synchronously

connected machines, the more inertia the system has. It will in turn contribute to better

frequency dynamics and higher stability in the grid [18].

5

The rotational energy is decided by 𝐽 and 𝜔𝑚 as

𝐸𝑘𝑖𝑛 =1

2𝐽𝜔𝑚

2 . (2)

The inertia constant, 𝐻 [𝑠], of a machine is defined as

𝐻 =

𝐸𝑘𝑖𝑛

𝑆𝐵

(3)

with 𝑆𝐵 [VA] as the rated apparent power of the generator. It tells for how long the machine

can provide its rated power solely using its stored kinetic energy [19]. In the Nordic system

the estimated stored rotational energy corresponds to between 4 and 7 seconds of the total

energy use of the system [18].

2.3 Static gain of a power plant (sv. reglerstyrka)

How much the power output from a power plant delivering frequency control is changed, ∆𝑃,

for a certain frequency deviation, ∆𝑓, is given as

𝑅 =

∆𝑃

∆𝑓,

(4)

and is measured in MW/Hz. Since there is no power plant large enough to provide all

frequency control work by itself, the work is divided on many plants across the grid. A

property of the turbine governor in a hydropower plant called the permanent droop, 𝐸𝑝, makes

this possible. The governor structure used by Vattenfall AB is a PI-controller with droop [6].

The droop, 𝐸𝑝, determines the static gain of a power plant. Due to differences in size and

capacities of the units, each unit has a different gain. The total static gain of the whole system

is the sum of the static gains of each individual component [17].

2.4 Welch's power spectral density estimate

To estimate the 60 seconds oscillation, the Matlab function pwelch is used. The function uses

Welch’s method for estimating either the power spectral density (PSD), or the power

spectrum (PS) of a signal. The PSD describes the squared magnitude of a signal (also referred

to as the power of a signal) per unit frequency. For a grid frequency signal, the unit of the

PSD estimate is Hz2/Hz. The PS is the estimated PSD scaled by the frequency. In the pwelch

function, the PS is obtained by specifying the spectrum type as ‘power’. The resulting

spectrum gives the squared magnitude of the signal at each frequency. For a grid frequency

signal, the unit of the PS estimate is Hz2.

6

For a given signal, Welch’s method divides the signal into overlapping or non-overlapping

sections of a given length. The Fourier transform is calculated for each section, and the

average of all transforms is decided. A window function can be applied to the signal, to

reduce the influence of the edge values in the calculations of the Fourier transform. The

default window function used in pwelch is a Hamming window [20].

As an example, a grid frequency deviation signal (non-realistic) is generated by adding two

sine waves of the same amplitude and different periods. The resulting signal is shown in the

upper graph in Figure 1. One of the sines has a period of 60 seconds, corresponding to a

frequency of 0.0167 Hz, and the other of 300 seconds, 0.0033 Hz. The lower graph shows the

PS of the signal. Two clear peaks with amplitudes of approximately 0.0025 Hz2 each can be

seen at 0.0033 Hz and 0.0167 Hz respectively.

Figure 1 An example of a power spectrum for a signal containing two added sine waves, generated by the pwelch

function in Matlab.

2.5 Challenges for the future power system

One of the biggest challenges for the future power system is the increased share of variable,

renewable energy sources, mainly wind and solar power. First of all, this production is more

difficult to predict and plan than conventional power production, traditionally thermal and

hydropower, which has dominated the system. Furthermore, most of these technologies are

not providing any inertia to the system since they in general are connected to the power grid

through inverters. Low levels of inertia make the power system more sensitive to disturbances

and the frequency dynamics faster. Especially operation with low consumption and a high

share of variable production from renewables, or operation with high consumption but low

variable production have been identified as extra problematic [21].

7

It becomes more difficult for the TSOs to predict how much frequency control they need to

procure when both the production and consumption are variable. For example, the forecasts of

wind power production are not accurate until a few hours before the operation hour. The risk

of shortage of frequency control resources at a large fault event such as line losses or power

plant outages increases. In the worst case scenario it comes to a total system blackout [19].

Large grid frequency deviations are especially harmful to thermal power plants. In case the

frequency drops below 47.5 Hz, frequency dependent motors cannot maintain vital process

flows and large units might disconnect to protect the machinery [18].

Other challenges of importance for a stable system operation are to avoid overproduction on

days of favourable solar and wind conditions, as well as to continuously ensure that there is

enough transmission capacity in the power lines [21]. Since these problems do not affect the

function and performance of frequency control specifically, they will not be studied further in

this thesis.

2.6 Frequency control services

As mentioned in the introduction, power consumption and production continuously have to be

almost equal. At a long time scale the electricity market is supposed to ensure this balance,

but within the operational hour and in situations of fault events the TSOs are responsible for

maintaining the system balance. To avoid imbalances, services targeted at bringing the system

back in balance and return the frequency to its nominal value are purchased [1].

Frequency control is commonly divided into primary, secondary and tertiary frequency

control, each carried out by units in the power system that are able to either change their

power output or change their load. Figure 2 gives an overview of the frequency control

market in the Nordic countries.

Figure 2 Scheme describing the different services at the Nordic frequency control market.

8

The focus of this thesis is on primary frequency control during normal operation, but the

following sections will briefly describe the properties of all different frequency control

services and the design of the Nordic frequency control market. It will also give a short

description of a new primary frequency control service that is being implemented at the

frequency control market in the United Kingdom (UK).

2.6.1 Primary control – FCR-N and FCR-D

As the frequency is uniform throughout the interconnected network, it is convenient to use as

control signal for the whole system. After a frequency deviation has been detected the primary

frequency control is automatically deployed to limit the deviation and stabilise the frequency.

It is generally activated after a few seconds and operates until the frequency is stabilised.

Normally the primary frequency control has no integral properties, which means a change in

system load will result in a steady state error, i.e. a steady state frequency deviation from the

nominal frequency [11]

Primary frequency control in the Nordic countries are provided by two different services:

Frequency Containment Reserve for normal operation (FCR-N) and Frequency Containment

Reserve for disturbed operation (FCR-D).

FCR-N is automatically activated for frequency deviations within the normal operation band

49,9 Hz - 50,1 Hz. Even though the Nordic countries all are connected through one common

grid the technical specifications for FCR-N differs between the countries [1]. In Sweden the

reserve shall be activated to 63 % within 60 seconds and to 100 % within 3 minutes for a

frequency step of 0.1 Hz [22]. In every operational hour the Nordic TSOs procure 600 MW of

FCR-N, but the total amount of FCR-N is estimated to be 753 MW [4]. The contribution from

each country is based on the electricity consumption from the previous year [1].

FCR-D handles larger disturbances and is activated when the frequency drops below

49.9 Hz. The reserve is dimensioned in such a way that if the largest power production unit

falls out, the system should still be able to keep the system frequency above 49.5 Hz (called

the N-1 criteria) [23]. To ensure continuous availability of FCR-D the reserve needs to be

restored within 15 minutes. This is done by activating the secondary and tertiary reserves.

2.6.2 Secondary and tertiary control – aFRR and mFRR

When the primary frequency control has stabilised the frequency, the secondary frequency

control is activated to restore the primary reserves and to bring back the frequency to 50 Hz

[11]. In the Nordic system, secondary frequency control is provided by an automatic service

called automatic Frequency Restoration Reserve (aFRR). It was first tested from 2013 to the

beginning of 2016. An improvement of the frequency quality was concluded and the service

was implemented again in September 2016. The largest risk of discrepancies between traded

9

energy and actual use is in the mornings and evenings when the load is changing more rapidly

than during the rest of the day. Therefore the reserve is active only a few hours in this time of

the day [6].

The last type of frequency control, tertiary frequency control, is a manual activation of

reserves and is called manual Frequency Restoration Reserve (mFRR). It operates also when

aFRR is not active, and on longer time scales, e.g. during long lasting disturbances due to

mispredictions of the weather or after the loss of a large power plant unit [22].

2.6.3 Enhanced Frequency Response

National Grid (NG), the TSO in the UK, has addressed the new challenges deriving from an

increased share of electricity production from renewable energy sources. To better manage the

transition from mainly conventional thermal power production to more renewable energy

sources, a new primary frequency control service is being implemented at the UK ancillary

service market. The service is designed by the NG and is called Enhanced Frequency

Response (EFR) [24].

The EFR is defined as a service that can provide 100 % of procured power capacity, either

positive or negative response, within 1 second or less after a registered frequency deviation of

0.5 Hz. The participating assets must provide or absorb active power proportional to the

frequency deviation, except within a defined deadband of ± 0.015 Hz from nominal system

frequency. Figure 3 shows a diagram of the technical specifications of the power response for

certain frequency deviations. Corresponding values are presented in Table 1.

Furthermore the assets must be able to deliver 100 % EFR capacity for a minimum of

15 minutes, given that it starts from its optimal state of charge. Since the service is supposed

to be symmetric, i.e. it can both provide and absorb active power and therefore respond to

both low and high frequency events, the optimal state of charge for a storage asset is at 50 %

of maximum charge level. In total NG has procured 200 MW EFR that is planned to be

installed and in operation at the beginning of 2018 [24].

10

Figure 3 A description of EFR. The diagram shows the reference behaviour (black line), upper and lower

operation limits (red and blue line) of EFR. Within the deadband of ± 0.015 Hz deviation from nominal system

frequency the asset is not obliged to provide proportional EFR capacity. Outside the deadband it must be able to

increase or decrease the active power of the system proportional to the frequency deviation [24].

Table 1 Corresponding response of EFR to a certain frequency deviation.

Δf [Hz] P/Pmax

± 0.5 ± 100%

± 0.25 ± 48.5%

± 0.015 Between -9 % and 9 %

11

The model

In Figure 4, one way to model frequency control is demonstrated. The model has been used in

studies of primary frequency control within Uppsala University and Vattenfall AB [4], [6],

and is used in this work as well. It is a so called one-area model, where the Nordic power

system is modelled as one hydropower unit representing all hydropower units delivering

FCR-N and a power grid represented by one rotating mass, corresponding to the inertia of the

system, and one frequency dependent load. A validation of the model is found in Appendix A.

Input to the system is the reference frequency deviation, 𝛥𝑓𝑟𝑒𝑓, and output is the frequency

deviation 𝛥𝑓. Measurement noise, grid frequency disturbance (oscillations etc.) and changes

in power production and load are considered as load disturbances and appears in the system as

a noise signal 𝛥𝑃𝐿. A negative 𝛥𝑃𝐿 means either a decreased power production or an increased

load. All signals with physical units are defined in Table 2. The per unit-system (p.u.) is used,

with bases given in Table 3. The parameters and their units are given in Table 4.

Figure 4 A one area model representing the Nordic power system. The grid is represented by one rotating mass

and all hydropower units providing FCR-N are aggregated into one unit consisting of one governor and one

equivalent hydropower plant (the turbine and waterways).

Table 2 Definitions of the signals in Figure 4.

Signal Description Physical unit

Δf Grid frequency deviation from 50 Hz Hz

Δfref Grid frequency deviation reference, 0 Hz Hz

ΔPL Load disturbance MW

ΔPhydro Deviation in power output from plant MW

ΔY Control signal, guide vane opening deviation %

Table 3 Per unit bases.

Base Value Applies to signal

fbase 50 Hz Δf, Δfref

Pbase 37650 MW ΔPL, ΔPhydro

Ybase 100 % ΔY

12

Table 4 The parameters used in the model in Figure 4.

System parameters Units (Physical units)

M 13 p.u. · s (GWs)

D 0.5 p.u./p.u. (MW/Hz)

Tw 1.5 s

K 1 p.u./p.u. (GW/%)

Ty 0.2 s

BL 0.001 p.u.

Governor parameters

Kp 1 p.u.

Ki 1/6 s-1

Ep 0.1 p.u.

Tf 1 s

3.1 The governor

The governor in Figure 4 is a PI-controller with droop, which is the controller structure used

by Vattenfall AB [4]. It responds to frequency deviations by giving the guide vane regulating

mechanism a signal to increase or decrease the guide vane opening, ∆𝑌. Thereby the flow

through the turbine is changed resulting in changed power output of the unit.

In a feedback control system, the basic concept of a PI-controller without droop is to make the

output signal of the whole system follow a reference signal as closely as possible. The

reference signal is used as input to the controller. The controller has a proportional part with

the gain 𝐾𝑝, and an integral part with the gain 𝐾𝑖. As a disturbance occurs, the proportional

part can partly compensate for the disturbance, but not eliminate it completely. The integral

part has an infinite static gain and can therefore increase the signal out from the controller, in

to the system, until the system output has reached the desired value [25].

The controller uses the error 𝑒 between the reference signal and the output signal of the

system to generate a signal 𝑢 according to

𝑢(𝑡) = 𝐾𝑝𝑒(𝑡) + 𝐾𝑖 ∫ 𝑒(𝜏)𝑑𝜏

𝑡

0

, (5)

which is the input to the system, in this case the hydropower plant which means

that 𝑢 corresponds to ∆𝑌. The reference frequency deviation, 𝛥𝑓𝑟𝑒𝑓, is 0 Hz, meaning no

deviation from the nominal frequency.

Droop characteristics, 𝐸𝑝, limits the static gain of the controller. It is introduced in the

governor to enable load sharing among the units participating in frequency control. As

mentioned in section 2.3, the required control work is divided on many hydropower units

13

distributed across the grid. The change in guide vane opening to a frequency deviation is

larger for a lower droop setting [26].

The hydropower turbine governor is modelled as in [4] and [8], with a first order low-pass

filter with a time constant, 𝑇𝑓, and a PI-controller with droop. During the time this thesis has

been carried out, the existence of the filter has been questioned. Recent research, for example

[3], has excluded the filter from the model.

After the PI-controller in Figure 4, there is a block representing the servo regulating the guide

vanes. It is also modelled as a first order low-pass filter and has the time constant, 𝑇𝑦, based

on measurements [7]. With the filter, the PI-controller with droop and the servo, the transfer

function from ∆𝑓 to ∆𝑌 becomes

𝐶(𝑠) =

𝐾𝑝𝑠 + 𝐾𝑖

(𝑇𝑓𝑠 + 1)(𝑇𝑦𝑠2 + (𝐸𝑝𝐾𝑝 + 1)𝑠 + 𝐸𝑝𝐾𝑖),

(6)

with the static gain

𝐶(0) =

1

𝐸𝑝.

(7)

3.1.1 Ep-settings

Depending on the controller tuning, i.e. the choice of the parameters 𝐸𝑝, 𝐾𝑝 and 𝐾𝑖, the

hydropower plant will contribute more or less to the frequency control. Vattenfall AB uses a

few standard settings for different operation modes, so called Ep-settings. Today Ep0 is the

least aggressive setting used for frequency control within normal operation. If more gain is

needed within normal operation the setting can be changed to Ep1 or Ep2. In disturbance

operation mode Ep3 is used.

In order to improve the performance of the supplied FCR-N, Vattenfall is changing these

settings so that fewer plants will participate in frequency control, but with a larger

contribution from each of the remaining plants. For plants not participating in frequency

control the parameters in Ep0 will be set to zero, and the standard governor tuning for

frequency control in normal operation will be Ep1. The result is the same amount of total

power output divided on fewer plants. The reason for this change is to decrease the impact of

backlash in the guide vane regulating mechanism [27].

Table 5 shows the governor settings for Ep0 and Ep1, which are used by Vattenfall AB.

Today the proportional gain, Kp, for Ep1 is 1, but it will be changed to 2.

14

Table 5 The turbine governor settings Ep0 and Ep1 used by Vattenfall AB. Today the proportional gain, Kp, for

Ep1 is one, but it will be changed to 2 [27].

Ep0 Ep1

Kp [p.u] 1 1 (2)

Ki [s-1] 1/6 5/12

Ep [p.u.] 0.1 0.04

3.1.2 Backlash

In measurements on a number of different hydropower plants made to analyse their dynamic

behaviour in frequency control mode, backlash in the guide vane regulating mechanism was

observed, and is therefore included in the model. The backlash is a non-linear phenomenon

that deteriorates the guide vane response to the control signal given by the governor [7].

Figure 5 illustrates this behaviour. According to measurements in [7] the size of the backlash

in the model, denoted BL in Figure 4, is given a value of ± 0.05 % of ∆𝑌 (0.001 p.u.). The size

differs between different plants.

Figure 5 The guide vane opening deviation signal and how the response is affected by the backlash in the guide

vane regulating mechanism. The blue line represents the signal given from the controller on how to change the

guide vane opening. The red line shows which opening deviation the regulating mechanism actually achieves.

If the control signal from the governor to the guide vane regulation mechanism has an

amplitude smaller than the backlash, the whole signal will be “eaten” by the backlash, and no

control action is taken. If the signal is large enough to come through the backlash, it will be

15

phase shifted with a decreased amplitude. The larger the signal is in comparison to the size of

the backlash, the smaller is the relative impact of the backlash.

When the droop is decreased, the response of the governor to a frequency deviation is a larger

guide vane opening signal ∆𝑌 to the turbine. Thus, if fewer plants conduct more control work,

small control signals and unnecessary wear on the hydropower units can be avoided.

3.2 Turbine and waterways

The behaviour of the turbine and the waterways in Figure 4 is represented by a non-minimum

phase system described by

𝐺𝑡𝑢𝑟𝑏(𝑠) = 𝐾

−𝑇𝑤𝑠 + 1

0.5𝑇𝑤𝑠 + 1

(8)

with

𝑇𝑤 =

𝐿𝑈

𝑔𝐻,

(9)

where 𝑇𝑤 [s] is the water time constant and K [MW/Hz] is the steady state gain from ∆𝑌 to

∆𝑃ℎ𝑦𝑑𝑟𝑜. Equation (8) is the transfer function from ∆𝑌 to the power output signal, ∆𝑃ℎ𝑦𝑑𝑟𝑜. It

defines how much a unit providing FCR-N will change its power output for a given change in

the guide vane opening.

The water time constant, 𝑇𝑤, represents the time needed for the water in the penstock to

accelerate from standstill to the velocity, 𝑈 [m/s], given a head, 𝐻 [m], and penstock length,

𝐿 [m] [26]. The respond of the power output after a change of the guide vane opening, will be

slower for power plants with larger 𝑇𝑤.

The steady state gain, K is normally a non-linear function depending on guide vane opening

and head [7]. A linearization of K is acceptable when the model is representing a small signals

performance of the turbine [26]. Since the turbines providing FCR-N only handles small

frequency deviations, this simplification of K is used.

The system is a non-minimum phase system due to the fact that its transfer function has a zero

on the right hand side of the imaginary axis. Non-minimum phase systems will respond to a

step signal by initially going in the opposite direction of the end value [26]. Compare to the

situation where a driver turns the steering wheel to the right, but the vehicle responds by first

turning left before it turns right. Non-minimum phase systems are therefore more difficult to

control than minimum phase systems.

16

3.3 The grid

The model of the grid is represented by a first order linear transfer function

𝐺𝑔𝑟𝑖𝑑 =

1

𝑀𝑠 + 𝐷

(10)

where 𝑀 is the inertia of the system and 𝐷 represents the frequency dependent load, also

called damping [26]. The input is the sum of ∆𝑃𝐿 and ∆𝑃ℎ𝑦𝑑𝑟𝑜. The output is the grid

frequency deviation, ∆𝑓. When the load disturbance is not fully compensated, a frequency

deviation arises. In the ideal case the output power from a hydropower unit would compensate

for all load disturbances, and the frequency would keep its nominal value of 50 Hz.

The power system contains a variety of loads. Some are purely resistive, such as most lighting

and heating. Others are frequency dependent, such as electrical motors. When their rotational

speed decreases, the frictional losses decreases, and consequently the load changes. Larger

values of 𝐷 means a higher share of frequency dependent loads in the system. It has a

stabilizing effect on the grid because when the frequency drops or rise these loads

automatically decrease or increase their power consumption.

More inertia gives a larger 𝑀 and means that the system is better equipped to handle

temporary imbalances. The values of 𝑀 and 𝐷, given in Table 4, are estimations made by the

Swedish TSO [8].

17

Load disturbance signal generation

To simulate the performance of FCR-N, a load disturbance signal is used as input to the

model. The actual load disturbance is unknown, therefore a method to estimate it is needed.

This chapter describes the method used to generate the load disturbance signal, followed by

the results, discussion and conclusions.

4.1 Method

The chosen method is inspired by [4], and it is based on the model described in Chapter 3

(Figure 4). A similar method is described in [6]. The model is rearranged so that the

frequency deviation signal is used as input, and the load disturbance, ∆𝑃𝐿, normally the model

input, is now the output signal. The frequency data used in the simulations are from the first

week of February 2012. At that time, aFRR was not used and it is assumed that the frequency

control was delivered by hydropower units with Ep0 as governor settings.

The chosen data set is intended to represent a week of relatively low frequency quality. In this

thesis the following three measures of frequency quality are used:

- the time outside the normal band

- the root mean square of the frequency deviation signal, RMSΔf

- an estimate of the 60 seconds oscillation.

These are further described in Section 5.2.1 - 5.2.3. During the week of consideration, the

number of minutes outside the normal band was 510, more than two times higher than the

weekly average of the year, which was 213 minutes. The RMSΔf was 53.9 mHz compared to

43.7 mHz for the year. On the other hand, the 60 seconds oscillation estimate in this week was

smaller than average, 0.56∙10-11 Hz2∙Hz compared to the average of 0.99∙10-11 Hz2∙Hz. A

summary of the frequency quality for all months in 2012 is found in Appendix B.

Figure 6 illustrates how ∆𝑃𝐿 is estimated. The power output, ∆𝑃ℎ𝑦𝑑𝑟𝑜, from the hydropower

unit represents the contribution of frequency control from FCR-N. The power difference

causing the frequency deviation is estimated by simulating the frequency deviation signal, ∆𝑓,

through the inverse grid. Subtracting ∆𝑃ℎ𝑦𝑑𝑟𝑜 from the power difference gives an estimate

of ∆𝑃𝐿. The frequency data used has a sampling frequency of 1 Hz, thus ∆𝑃𝐿 has a sampling

frequency of 1 Hz, i.e. 1 sample per second.

18

Figure 6 The Simulink model used to simulate the load disturbance, ∆𝑃𝐿. Frequency deviation ∆𝑓 is used as

input. The power output, ∆𝑃ℎ𝑦𝑑𝑟𝑜, from the hydropower unit is subtracted from the output from the inverse grid

and thereby it estimates ∆𝑃𝐿. An extra pole, 𝑇𝑔, is added to avoid a pure derivative in the inverse grid, which

otherwise would amplify the high frequency noise in ∆𝑓. The value of 𝑇𝑔 is chosen to make the simulated

frequency signal as similar as possible to the measured grid frequency.

An extra pole with the time constant 𝑇𝑔 is added to the inverse grid block. Without the added

pole, the inverse grid has a pure derivative. It amplifies the fast dynamics of the noise in the

frequency signal, which is not desirable. The choice of 𝑇𝑔 should preferably give a simulated

frequency deviation signal as similar to the measured grid frequency data as possible.

To decide the value of 𝑇𝑔, load disturbance signals of different values of 𝑇𝑔 are generated

according to Figure 6. These signals are one by one used as input signal to the model in

Figure 4 (Chapter 3). The simulated frequency deviation signals, corresponding to different

𝑇𝑔-values, are compared to the measured frequency deviation signal. The 𝑇𝑔 that gives the

most similar ∆𝑓 regarding the time outside the normal band, RMSΔf, and the 60 seconds

oscillation estimate is deemed to give the best estimation of ∆𝑃𝐿.

4.2 Results

After comparison of the frequency quality parameters for different values of 𝑇𝑔 [s], the value

of 𝑇𝑔 = 0.4 s is decided upon. As presented in Table 6, the frequency quality of the simulated

∆𝑓 is a bit lower than of the measured frequency deviation signal.

Table 6 Comparison of the frequency quality parameters for the measured and the simulated frequency deviation

signal. An extra pole with time constant Tg = 0.4 s is used in the inverse grid block in Figure 6 to estimate the

load disturbance signal.

Minutes outside the

normal band

RMSΔf [Hz] 60 seconds oscillation

estimate [Hz2∙Hz]

Measured 510 53.9 0.56∙10-11

Tg = 0.4 s 531 54.2 0.76∙10-11

19

For both larger and smaller values of 𝑇𝑔, the frequency quality parameters of the simulated ∆𝑓

differs more from the frequency quality parameters of the measured frequency deviation

signal. For larger 𝑇𝑔-values, faster dynamics of ∆𝑓 are lost. Smaller values of 𝑇𝑔 result in a

simulated frequency deviation signal that captures fast dynamics well, but the signal partly

becomes very volatile, with oscillations of a much greater amplitude than the measured

frequency data. In Appendix C, examples of the simulated ∆𝑓 compared to the measured

frequency deviation are given, along with the results of the frequency quality measures for a

number of different 𝑇𝑔-values.

The choice of 𝑇𝑔 is 2 s in [4], and 0.1 s in [6]. The difference will be further discussed later in

this chapter.

In Figure 7 the simulated frequency is plotted together with the real frequency signal from

measurements. The correlation is in general good. At some times, the simulated frequency

shows a more volatile behaviour than the measured, as can be seen between 150 and

200 seconds.

Figure 7 The simulated frequency when the estimated load disturbance is used as input (red graph) compared to

measured frequency data (blue graph).

4.3 Discussion

The choice of 𝑇𝑔 = 0.4 s is larger than in [6], but smaller than in [4]. When using the method

proposed in this thesis and a value of 𝑇𝑔 = 2 s, much of the faster dynamics get lost. Using

𝑇𝑔 = 0.1 s, results in a simulated frequency deviation signal of a partly very volatile

behaviour. When ∆𝑃ℎ𝑦𝑑𝑟𝑜 is generated as in Figure 6, a backlash is included in the model

after the turbine governor. In [6] the load disturbance signal is estimated from a pure linear

system. The difference between estimating ∆𝑃𝐿 from a linear system and a system with

backlash, might explain the different choices of 𝑇𝑔.

20

The biggest drawback of this method is that it is not general for a “typical behaviour” of the

load disturbance. Depending on parameters as weather conditions, level of inertia in the

system, and which hydropower plants that are providing frequency control at the moment, the

frequency quality will vary. This method generates a signal which is an estimation of the load

disturbance from a certain time in the past, in this case from February 2012. A way to

generate more generic data would be preferable.

4.4 Conclusion

By comparing the simulated frequency and measured frequency data in Figure 7, it can be

seen that the signals are not perfectly equal. At some times, the generated ∆𝑓 has a more

volatile behaviour than the measured frequency deviation. Since the purpose of the model is

to gain a load disturbance signal which is realistic, but not necessarily the same as the actual

load disturbance 2012, it is deemed to be an acceptable estimation of ∆𝑃𝐿.

In the following sections the generated load disturbance signal will be used to simulate the

performance of FCR-N today, together with a new faster frequency control service that is

called fast FCR-N.

21

The base case – today’s situation and how it can be improved

This chapter evaluates the situation today, regarding frequency quality and wear on the

hydropower units, and how it can be improved. By simulating one week of estimated load

disturbance, as described in Chapter 4, with Ep0 governor settings and a relatively strong grid

(𝑀 = 13 and 𝐷 = 0.5) the performance of the system is decided through a number of different

parameters. This will be the base case used as reference to see whether more fast frequency

control in the system can improve the situation, and if so, how much?

The fast FCR-N would be a service that can be provided by different energy sources, for

example batteries, flywheels or wind power. These three, along with supercapacitors, are

presented more in detail in Chapter 7.

Two different designs of fast FCR-N are investigated and their performance regarding

frequency quality and wear on the hydropower units is compared to the base case.

Furthermore, required energy capacity and wear of the ESS are examined.

5.1 Method

Figure 8 and Figure 9 illustrate the two fast FCR-N designs added to the system. Starting with

the proportional type in Figure 8, the 𝐾𝐸𝑆𝑆-block represents an ESS with pure proportional

response to a frequency deviation. To not demand infinite power capacity of the ESS, the

frequency deviation input to the 𝐾𝐸𝑆𝑆-block is limited. That means a constant power output

from the ESS when the frequency deviation exceeds a certain value. Two saturation levels are

used; at the normal band boundary ± 0.1 Hz as well as at ± 0.5 Hz.

Figure 8 Fast FCR-N is added to the system. The KESS-block represents the ESS, i.e. the fast FCR-N. Its response

is proportional to the frequency deviation. For deviations larger than the saturation level, it supplies a constant

power output. With increased response from the fast FCR-N asset, the power output of the hydropower unit is

decreased. For example, if KESS represents a power output of 400 MW/Hz, the response from the hydropower

units is decreased by 400 MW/Hz. The performance of the system for saturation levels of ± 0.1 Hz and ± 0.5 Hz

respectively are tested.

22

The second fast FCR-N type in Figure 9 is also proportional, but only outside a defined

deadband. Within the deadband, the asset delivering fast FCR-N is not active. Outside the

deadband, the response is proportional to the frequency deviation value minus the deadband

limit. For example, if the frequency deviation is 0.09 Hz and the upper deadband limit is

0.05 Hz, the value of the signal to the 𝐾𝐸𝑆𝑆-block is 0.09 Hz – 0.05 Hz = 0.04 Hz. The

saturation limit for this design is set at ± 0.5 Hz. The intended advantage of the deadband

design over the proportional design, is that it would be gentler on the ESS. The ESS assets

would not be active within the defined deadband, which means less charge and discharge

cycles and thus a longer life time.

Figure 9 Fast FCR-N with deadband. The ESS represented by KESS responds proportionally to a frequency

deviation outside a defined deadband. Deadband sizes of ± 0.05 Hz and ± 0.08 Hz are tested. There is a constant

saturation level at ± 0.5 Hz.

The main difference between the two designs is that when proportional fast FCR-N is added,

the power output of the hydropower unit is scaled by a factor 1 − 𝑥, where

𝑥 =

𝑃𝑓𝑎𝑠𝑡 𝐹𝐶𝑅−𝑁

753.

(11)

It means that if 60 MW fast FCR-N is introduced, the FCR-N delivered by the hydropower

plant is decreased to 753 MW – 60 MW = 693 MW (92 % of the original value). In other

words, fast FCR-N replaces some of the “traditional” FCR-N. That is not the case for the

deadband type. Fast FCR-N of deadband design is a service added to the system with

preserved amount of frequency control from the hydropower plant. This solution for the

deadband design is chosen to have a preserved power response within the deadband, without

being required to change governor settings of the hydropower turbine governor when the

frequency deviation signal exceeds the deadband limits.

It has been assessed that the dynamics of batteries and other ESS such as flywheels and

capacitors are orders of magnitude faster than conventional power generation [14]. The fast

FCR-N service is evaluated for two cases; instant full activation or full activation within

5 seconds. These response times are based on the technical specifications for the British EFR

[24] and experiments made on a 1 MW battery asset used for power system applications in

Switzerland [14], showing that the asset can make a step of 2 MW, from -1 MW (charging) to

23

1 MW (discharging), in less than one second. To simulate the performance when a slower

responding time is allowed, a 5 second delay modelled with the transport delay block in

Simulink is included after the 𝐾𝐸𝑆𝑆-block in variants, i) b. and ii) b..

In total six different variations of fast FCR-N are tested:

i) Proportional fast FCR-N with

a. no delay of the response allowed, saturation limit at ± 0.1 Hz,

b. 5 seconds delay, saturation limit at ± 0.1 Hz,

c. no delay, saturation limit at ± 0.5 Hz.

ii) Fast FCR-N of deadband type (all variants have a saturation limit of ± 0.5 Hz)

with

a. no delay, deadband within ± 0.05 Hz,

b. 5 seconds delay, deadband within ± 0.05 Hz,

c. no delay, deadband within ± 0.08 Hz.

The response from the fast FCR-N to a frequency deviation is varied from 0 MW/Hz,

meaning no fast FCR-N (the base case) to 2000 MW/Hz. If the frequency deviation exceeds

the saturation limit, the response will be constant. For fast FCR-N of proportional design with

a response of 600 MW/Hz and a saturation limit at ± 0.1 Hz, the power output will be 60 MW

for frequency deviations larger than 0.1 Hz. For a saturation limit at ± 0.5 Hz, and a response

of 600 MW/Hz, the power output is 300 MW when the frequency deviation exceeds 0.5 Hz.

As mentioned, in the case of proportional design, fast FCR-N replaces FCR-N delivered by

hydropower units. Within the saturation limits, the total gain of the system, i.e. the sum of

“traditional” and fast FCR-N, is 7530 MW/Hz. Because the power output of the fast FCR-N is

constant outside the saturation limit, the sum of the gains of FCR-N form hydropower and fast

FCR-N will be lower than 7530 MW/Hz outside the limits.

The deadband design has in turn a larger response than 7530 MW/Hz outside the deadband.

For example, a deadband limit of ± 0.05 Hz, a response of fast FCR-N of 600 MW/Hz and a

frequency deviation of 0.1 Hz, gives a power output of (0.1 - 0.05) Hz · 600 MW/Hz =

= 30 MW from the deadband fast FCR-N. Together with the power output of 753 MW from

the hydropower units, the total power output at a frequency deviation of 0.1 Hz is 783 MW.

5.2 Parameters to be studied

The performance of the system with the different fast FCR-N services is evaluated regarding

frequency quality, wear on the hydropower turbines and the energy capacity and wear of the

ESS.

24

The frequency quality is interesting for the TSOs in their role as responsible for the system

operation and purchaser of frequency control services. The frequency quality will be

determined by:

- the time outside the normal band

- the root mean square of the frequency deviation signal

- the 60 seconds oscillation, described by two measures:

i) the maximum gain of the transfer function from the load disturbance to

the frequency deviation

ii) a 60 seconds oscillation estimate based on spectral analysis.

The wear of the hydropower turbine is interesting for the power plant owner providing

frequency control. The parameters used to measure the wear are:

- the travelled distance by the guide vanes

- the number of load cycles of the guide vanes.

Finally, the required energy capacity and the wear of the ESS is of interest to the party

holding the ESS unit, also provider of fast FCR-N. Here the following three parameters will

be examined:

- the required capacity of the ESS

- the storage utilization

- the amount of control work of the ESS.

Results with following discussions are presented in Section 5.4 - 5.9. In the following sections

the performance parameters are described more in detail.

5.2.1 Time outside the normal band

One measure of the frequency quality used in this thesis is the time the frequency lies outside

the normal band, 49.9 – 50.1 Hz. It is a straight forward method, easy to measure, which is its

advantage. On the other hand, it does not say anything about the dynamics of the frequency,

and it does not say whether the frequency is just within the normal band, or perfectly at

50 Hz.

The Swedish TSO strives toward having no more than 10 000 minutes per year outside the

normal band. In 2016 this number was 13 862 minutes [28]. In this thesis, frequency data

from 2012 is used. Analysing the data for 2012 gives a number of the time outside the normal

band of 11 926 minutes. Figure 10 shows a situation where the frequency exceeds the upper

limit of the normal band.

25

Figure 10 A high frequency situation on February 1 2012. The two red lines mark the normal band, and it can be

seen clearly that the frequency exceeds 50.1 Hz at around 800 seconds. This measure does not capture the times

when the frequency is just below 50.1 Hz, and it does not describe that the frequency during this half hour is

constantly higher than the nominal frequency, 50 Hz.

5.2.2 Root mean square error

One way to measure how well the frequency matches the target of 0 Hz frequency deviation is

to calculate the root mean square of ∆𝑓. It uses the frequency deviation signal and describes

the typical deviation from the nominal value according to

𝑅𝑀𝑆∆𝑓 = √∑ ∆𝑓𝑡

2𝑛𝑡=1

𝑛

(12)

where 𝑛 is the length of the frequency deviation signal and ∆𝑓𝑡 is the frequency deviation at

time 𝑡. Preferably RMSΔf is as small as possible.

5.2.3 60 seconds oscillation

The observed oscillations of the grid frequency are of concern to the TSOs. It can be seen in

Figure 10 that the frequency has an oscillating behaviour. The amplitude is not large, but it

has increased during the last 10 years [3]. As mentioned the oscillations have a period of

between 40 and 90 seconds, but they are here referred to as the 60 seconds oscillation.

Two ways to determine how well the fast FCR-N handles the 60 seconds oscillation are used.

Firstly, the gain of the transfer function from the load disturbance to the frequency deviation

is studied. The maximum gain should be as low as possible, which implies that the system can

handle load disturbances of varying dynamics, i.e. both fast and slow changes in power

consumption and production.

In the simulations, fast FCR-N is represented by a constant, 𝐾𝐸𝑆𝑆, saturation blocks, and in the

deadband case, a deadband block. The saturation and deadband blocks give the fast FCR-N

non-linear properties. Plotting an amplitude curve of the transfer function in frequency

domain requires a linear model of fast FCR-N. Ignoring the saturation limit of the

26

proportional design, the ESS delivering fast FCR-N can be modelled as a constant, according

to

𝐺𝐸𝑆𝑆(𝑠) = 𝐾𝐸𝑆𝑆 (13)

where 𝐾𝐸𝑆𝑆 corresponds to the response of the ESS. The impact on the gain of the transfer

function will be evaluated for power outputs of the ESS of 400, 600, 1000 and 2000 MW/Hz

respectively. With the backlash omitted and proportional fast FCR-N added, the transfer

function from 𝑃𝐿 to ∆𝑓 becomes

𝐺∆𝑃𝐿→ ∆𝑓 =

𝐺𝑔𝑟𝑖𝑑

1 + 𝐺𝑔𝑟𝑖𝑑𝐺𝐸𝑆𝑆 + 𝐺𝑔𝑟𝑖𝑑𝐺𝑡𝑢𝑟𝑏𝐶.

(14)

The deadband fast FCR-N is not well represented by a linear model, and will not be evaluated

by this method.

The second method intends to give a comparable measure of the 60 seconds oscillation.

Welch’s power spectral density estimate function, pwelch, in Matlab is used to generate a

power spectrum of the frequency deviation signal. The integral of the frequencies taken from

10 to 90 seconds periods is calculated. The method is used in [4] to evaluate how different

governor tunings affect the frequency quality. Here, the measure will be referred to as the

60 seconds estimate. The unit of the 60 seconds estimate is Hz2·Hz, where Hz2 derives from

the unit of the amplitude of the grid frequency signal, because the unit of a power spectrum

estimate is in squared magnitude units of the time series data [20]. By calculating the integral,

the unit becomes Hz2·Hz. The last Hz corresponds to the frequencies used for the integration,

i.e. frequencies of the grid frequency deviation signal corresponding to periods of 10 to

90 seconds.

5.2.4 Guide vane travelled distance

This thesis focuses on frequency control in a Nordic context, where most of the frequency

control is provided by hydropower units. As a result of more variable renewable energy

sources, more control work is needed [29]. It could therefore be interesting to study whether

an introduction of fast FCR-N can support the system, not only by improving the frequency

quality, but also by reducing the wear on the hydropower turbines that is a result of increased

control work.

One measure of the amount of control work performed is the guide vane travelled distance,

𝑌𝑑𝑖𝑠𝑡. It is related to the sliding distance of the guide vane bearings, and thus an indicator of

the wear of the bearings induced by frequency control [6]. The result is calculated by

𝑌𝑑𝑖𝑠𝑡 = ∑ |∆𝑌𝑡+1 −

𝑛

𝑡=1∆𝑌𝑡|,

(15)

27

based on the guide vane opening deviation signal, ∆𝑌. The distance is then normalised by the

number of hours of the simulations, so that 𝑌𝑑𝑖𝑠𝑡 is given in percent per hour. Going from

closed to fully opened guide vanes in one hour would correspond to a travelled distance of

100 %/h.

5.2.5 Guide vane direction change

Another factor that may contribute to wear of the guide vane regulating mechanism, is the

number of direction changes of the guide vanes [6]. One load cycle is defined as two direction

changes of the guide vanes, and thus calculated as every second time the derivative of ∆𝑌

changes sign. It is measured in number of cycles/hour.

5.2.6 Maximum energy capacity of the ESS

The energy capacity of the ESS is of importance when optimizing the cost and the physical

size of the assets [13]. One way to determine the maximum energy capacity required is

suggested here.

The maximum energy capacity, Emax, can be determined by defining the time the asset must

be able to deliver power at its maximum operation point. If the asset provides both up and

down regulation, which means it can charge or discharge, the maximum energy capacity

becomes

𝐸𝑚𝑎𝑥 = 2 ∙ 𝑃𝑚𝑎𝑥 ∙ 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒, (16)

where Pmax is the maximum power output or power absorbed by the ESS. This method

calculates the required energy capacity of the ESS considering a worst case scenario. Most

likely, the fast FCR-N will not have to provide at its maximum capacity for such long periods

of time. Therefore next section is trying to find the actual energy capacity needed for an ESS

providing fast FCR-N.

5.2.7 Utilisation of the ESS

Looking at utilisation of the ESS can be another way to decide the energy capacity needed.

This method finds the maximum energy capacity for an ESS that is allowed to operate without

any other limitations than those specified by the designs of the fast FCR-N, and the time the

ESS is active. The purpose is to examine the difference in energy demand of the different

designs of fast FCR-N. In reality, no ESS has unlimited access to energy. Some kind of

control system is needed to recover the asset after it has been used. Here it is assumed that

28

some kind of recovery scheme, as in [5], has recovered the asset, and that the ESS in the

beginning of every new simulation starts from its nominal operation point.

Two days of load disturbance is divided into sections of 15, 30, 60 and 120 minutes

respectively and simulated separately. The integral of the power output from start to the given

time is considered as the assets state of charge (SOC). Depending on the system demand, the

asset charges or discharges. When charging the SOC increases, and when discharging the

SOC decreases. Figure 11 shows examples of the development of SOC for simulations of

different lengths, referred to as different time windows.

Figure 11 Example of the SOC for different time windows if the ESS is allowed to operate without any recovery

scheme. The black line represents the development of the SOC during 2 hours. For the blue line the SOC of the

ESS is reset to zero after one hour. Because SOC was below zero at the time of reset, the following hour result in

a lower Emax for the 2 hour time window, i.e. the black line, and a higher Emax for the one hour time window, blue

line. The 30 minutes time window, red line, it is reset every 30 minutes. After one hour, the blue and red lines

are reset at the same time, and the development is equal for the two simulations. During the following half hour,

SOC increases more than in any other 30 minutes period. It results in the same Emax for both the 30 minutes and

1 hour time window.

For every simulation the SOC is starting at a reference point equal to zero. Next the maximum

absolute value of the SOC is found for each simulation, and the largest value of all

simulations is considered as the maximum energy capacity, Emax, needed for that certain time

window and power output. Normally SOC is given as a percentage of the total energy

capacity. It calls for knowledge about the size of the energy storage. Here the purpose is to

determine how large energy capacity the ESS needs to have, and SOC is defined in MWh.

5.2.8 Wear of the energy storage unit

There are different ways to define the wear and life time of an energy storage device.

Commonly it is defined in terms of charge and discharge cycles. A deep discharge or full load

29

cycle is often referred to as when the device has been fully charged, then completely

discharged and fully charged again. For an ESS unit delivering frequency control this measure

is not perfectly adequate because the system does many shallow cycles, which are less

harmful for the device [30].

In this thesis, the size of the units providing fast FCR-N is not known. It is therefore not

possible to calculate the number of load cycles. Instead the wear of the ESS is measured in

amount of control work, ESSdist, performed by the ESS.

The total amount of work performed by the ESS, 𝐸𝑆𝑆𝑑𝑖𝑠𝑡, is calculated according to

𝐸𝑆𝑆𝑑𝑖𝑠𝑡 = ∑ |𝑆𝑂𝐶(𝑡 + 1) − 𝑆𝑂𝐶(𝑡)|

𝑛

𝑡=1.

(17)

To evaluate ESSdist for the different designs of fast FCR-N, proportional fast FCR-N with a

saturation limit of ± 0.1 Hz is used as a reference. The work of the other variants, i.e. with

larger saturation limit, with delay and with deadband, is presented in relation to the reference.

5.3 The base case

To evaluate whether the implementation of fast FCR-N has any positive effects on the system,

the performance of the different designs are compared to a base case, presented in Table 7.

The base case represents the situation today, assuming a relatively strong grid and that all

frequency control is provided by hydropower units with Ep0 governor settings.

Table 7 The base case used as reference when the performance of fast FCR-N is evaluated. In the base case the

grid is assumed to be relatively strong (𝑀 = 13 𝑎𝑛𝑑 𝐷 = 0.5). The hydropower unit has Ep0 settings. One

week of estimated load disturbance for the first week of February 2012 is used as input (see Chapter 4).

Performance parameters

Time outside the normal band 31 878 s (531 min)

RMSΔf 54.2 mHz

60 second oscillation estimate 0.76∙10-11 Hz2·Hz

Guide vane travelled distance 8.5 %/h

Number of load cycles of the guide vanes 25 # cycles/h

5.4 Frequency quality – results

In the following section the results of the simulations regarding frequency quality are

presented. When comparing the two services, it is important to be observant and remember

that for the proportional service the static gain of the system is kept constant within the

saturation limits. Added capacity of fast FCR-N reduces the power output from the “slow”

30

FCR-N delivered by hydropower. For the deadband service, the static gain increases outside

the deadband.

Figure 12 shows the change in the time outside the normal band.

Figure 12 In a) the change of the time outside the normal band is plotted as a function of the power output of the

proportional fast FCR-N, and b) shows the change for the deadband design. The best results are achieved by the

deadband design having a small deadband and no delay. It can be seen that the delay has a larger impact on the

results for the proportional design than for the deadband service. Hence, the deadband size is determining the

performance of this type. Note that the deadband design has preserved static gain of the “slow” FCR-N provided

by hydropower, resulting in an increased amount of frequency control in the system outside the deadband.

For the proportional type, a saturation limit of ± 0.1 Hz reduces the time outside the normal

band the most. All proportional variants improve the performance, but it seems to be a limit

where no further improvement is achieved. For power outputs larger than 600 MW/Hz, the

rate of change of improvement has slowed down. The best performance of all variants is

achieved by the deadband design having a small deadband and no delay. Comparing the best

results for the two different types, a power output of 2000 MW/Hz improves the time outside

the normal band by 26 % for the proportional service with saturation limit at the normal band

limit, ± 0.1 Hz. The deadband service with a deadband of ± 0.05 Hz achieves a 56 %

reduction. The impact of the time delay is smaller for the deadband design than for the

proportional design.

As mentioned, the week used for the simulations represents a week of relatively low

frequency quality. To see how well the fast FCR-N service would meet the goal of the

Swedish TSO of less than 10 000 minutes outside the normal band per year, one week of data

from August 2012 is simulated. The time outside the normal band of this data set corresponds

well to the average of the year (215 min for the week in August. 229 min is the average.). A

simulation is done with and without fast FCR-N and translated into a number representing the

whole year. The results for proportional fast FCR-N with a response of 600 MW/Hz, and a

saturation limit at ± 0.1 Hz, shows that the minutes outside the normal band during this week

in August decrease by 29%. Applied to the real frequency data from August 2012 it means a

31

decrease from 11 210 to 7973 minutes per year. It is an improvement large enough to fulfill

the goal of less than 10 000 minutes.

Continuing with the root mean square error of the frequency deviation in Figure 13, all

different fast FCR-N designs decrease the RMSΔf -value.

Figure 13 The root mean square error of the frequency deviation signal is decreasing for all service designs until

a power output of 1400 MW/Hz is reached. At this point a slight increase can be seen for the proportional

services having a saturation limit at ± 0.1 Hz.

For the proportional design the saturation limit is the important factor for reducing the RMSΔf.

Increasing the saturation limit results in better performance. For the ± 0.1 Hz saturated

proportional type and power outputs larger than 1400 MW/Hz, the RMSΔf is actually slightly

increasing again.

For the deadband design, the delay has almost no influence on the results, but a larger

deadband impairs the improvement. For a power output of 2000 MW/Hz and a deadband of

± 0.08 Hz, the RMSΔf is decreased by 2.2 %. For the same power output, but a deadband of

± 0.05 Hz, the decrease is 7.1 %, i.e. a more than three times better performance for the

narrower deadband.

Further on, the impact of fast FCR-N on the 60 seconds oscillation is investigated. In Figure

14, the amplitude curve of the transfer function from ∆𝑃𝐿 to ∆𝑓 is plotted for the base case

and for systems with different amount of proportional fast FCR-N. The results show that with

an increasing share of fast FCR-N, the maximum gain of the transfer function from ∆𝑃𝐿 to ∆𝑓

is reduced. For example, introducing fast FCR-N with a response of 600 MW/Hz reduces the

maximum gain by 43 %.

32

Figure 14 The amplitude curve of the transfer function from ΔPL to Δf is plotted. Introducing proportional fast

FCR-N to the system, here represented by a constant KESS, the disturbances in the range of frequencies with a

period of around 60 seconds is well damped. Note that the graph only describes proportional fast FCR-N.

The result of the second method, which uses Welch’s spectral density estimate to calculate the

60 seconds oscillation estimate, is shown in Figure 15. It shows, in accordance with the first

method, that fast FCR-N has a positive effect on the 60 seconds oscillation. The proportional

design decreases the 60 seconds estimate more than the deadband design. Allowing 5 seconds

delay of the power response has a negative impact for both designs. Increasing the saturation

limit for the proportional type gives better results, but the improvement is not large.

The rate of improvement decreases for larger the power outputs. After 600 MW/Hz, the rate

of improvement has slowed down for all variants.

Figure 15 The spectral analysis of the frequency deviation signal shows that the 60 seconds oscillation estimate

is decreased by fast FCR-N. The proportional design is better at handling the 60 seconds oscillations than the

deadband design. The delay is decreasing the accuracy of the response resulting in a more volatile signal.

An example of how 60 MW of proportional fast FCR-N with a saturation limit of ± 0.1 Hz

affects the frequency deviation signal is illustrated in Figure 16. The amplitude of the

oscillations in 𝛥𝑓 is reduced, resulting in a less volatile signal.

33

Figure 16 An illustration of the frequency signal with and without fast FCR-N in the system. When 60 MW

proportional fast FCR-N is introduced, the amplitude of the oscillations is reduced.

5.5 Frequency quality – discussion

A not so intuitive result is that the proportional design with a saturation limit of ± 0.1 Hz is

reducing the time outside the normal band more than the variant with a saturation limit of

± 0.5 Hz. Within the normal band, the response from both types are the same. When the

frequency deviation exceeds 0.1 Hz, the power output from the ESS becomes constant for the

narrower saturation limit, whereas the power output continues to increase proportional to the

frequency deviation for the larger saturation limit. The amplitude of the oscillations outside

the normal band is therefore better damped with a ± 0.5 Hz saturation limit. In situations

when the frequency is oscillating just around the normal band limit, it might happen that the

frequency signal stays outside the normal band for the type with ± 0.5 Hz saturation limit. The

more volatile signal from the ± 0.1 Hz saturation limit type is oscillating into the normal band.

An example of a situation like this is illustrated in Appendix D. These results verify that using

the time outside the normal band as a measurement of the frequency quality, is not capturing

all information about the frequency dynamics.

In this thesis, the deadband service has a design advantage over the proportional design due to

the fact it is implemented with higher static gain outside the deadband. A smaller deadband

means that the fast FCR-N is more active. The size of the deadband is therefore naturally the

important factor for the performance in respect to all performance parameters.

For the RMSΔf -value it seems like the delay has no impact on the deadband design. The delay

actually results in a less accurate response to frequency deviations, and this variant do not

reduce the amplitude of the oscillations as much as the no delay variant. In a similar manner

as for the time outside the normal band, the volatile behaviour of the signal is not captured by

the RMSΔf -value. For the delayed response the amplitude of the oscillation is bigger. It means

that the signal sometimes is coming closer to the nominal value, i.e. it has a smaller frequency

deviation, and sometimes it is further away. The difference between the two signals is not big,

and it seems like the times when the frequency deviation is larger for the delayed response is

cancelled out by the times of smaller deviations when RMSΔf is calculated by (12). That the

deadband design with a delay has a more volatile behaviour is on the other hand captured by

34

the 60 seconds oscillation estimate. Hence, it is a good complement to the time outside the

normal band and the RMSΔf when the frequency quality is evaluated.

The final result to be discussed here is the observation that the RMSΔf-value for the

proportional fast FCR-N with a saturation limit at ± 0.1 Hz and power outputs larger than

1400 MW/Hz is increasing again. Because the proportional design is replacing some of the

frequency control provided by the hydropower unit, the static gain (sv. reglerstyrkan) of the

system is 7530 MW/Hz as long as the frequency is within the normal band. When the

frequency exceeds the normal band, the power from the fast FCR-N is constant, and the total

response becomes smaller than 7530 MW/Hz. For example, if the narrow limited fast FCR-N

has a response of 2000 MW/Hz, the response from the hydropower unit is 5530 MW/Hz. At a

frequency deviation of 0.2 Hz, the fast FCR-N provides 200 MW, and the hydropower

provides 1106 MW. That is a response of 6530 MW/Hz. Thus at large frequency deviations,

too much of the hydropower FCR-N is replaced, which results in a weaker response of the

system and increased RMSΔf. The same problem does not occur for the ± 0.5 Hz saturation

limit because the static gain will be 7530 MW/Hz as long as the frequency deviation is not

larger than 0.5 Hz.

5.6 Wear on the hydropower units – results

This section presents the effects of fast FCR-N on the control work performed by the

hydropower units. The control work is assumed to contribute to wear of the hydropower units.

Figure 17 shows that the control work is reduced for all designs of fast FCR-N. The reduction

is however larger for the proportional type than for the deadband type.

Figure 17 The impact of introducing fast FCR-N on the control work. In a), the change in guide vane travelled

distance is presented and b) shows the number of guide vane load cycles. One load cycle corresponds to two

direction changes of the guide vanes.

35

For the travelled distance, the performance is similar for all variants of the proportional

service. The impact of the delay is of importance when evaluating the load cycles. The size of

the deadband has a large impact of the performance of the deadband service.

The best performance regarding both 𝑌𝑑𝑖𝑠𝑡 and the number of load cycles is gained by the

proportional design with a ± 0.5 Hz saturation limit. For 𝑌𝑑𝑖𝑠𝑡 there is not a big difference

between the proportional designs. A delay impacts the load cycles more than 𝑌𝑑𝑖𝑠𝑡 for both the

proportional and deadband designs. For the deadband type the results show that the size of the

deadband must be small to significantly reduce the control work of the hydropower unit.

Figure 18 shows an example of the guide vane opening deviation for the base case compared

to a system with 60 MW of proportional fast FCR-N with a saturation limit at ± 0.1 Hz. In

total, 𝑌𝑑𝑖𝑠𝑡 is reduced by 21 % and the number of load cycles by 41 %.

Figure 18 An example of the guide vane opening deviation during 15 minutes. The system with fast FCR-N has

less movement and fewer direction changes of the guide vanes.

5.7 Wear on the hydropower units – discussion

When fast FCR-N is introduced in the system, the ESS providing this service has properties

that are better at handling fast dynamics of the load disturbance signal than what the

hydropower units delivering FCR-N today have. Therefore the fast oscillations of moderate

amplitude is taken care of by the fast FCR-N. The hydropower turbine governor gets a less

volatile frequency deviation signal to work with. The hydropower units can therefore

concentrate on the disturbances of slower nature and compensate for them by providing large

amounts of energy.

The delay has some impact on the system, especially on the load cycles of the guide vanes.

When the guide vane opening signal is small and varies fast, the accuracy of the guide vane

response is decreased by the delay. This results in more control work, especially regarding the

load cycles, which only depends on the number of direction changes of the guide vanes. Since

the movements are only small adjustments, 𝑌𝑑𝑖𝑠𝑡 is not affected as much.

36

5.8 Energy capacity and wear of the ESS – results

If the ESS must be able to deliver at its maximum power capacity for a certain period of time,

the energy capacity needed will increase proportionally to the power output and the time. In

Table 8, examples of maximum energy capacities are calculated for power outputs of 400,

600 and 1000 MW/Hz. Required operation times of 15 and 60 minutes respectively are used.

A larger capacity is needed if the service is active also outside the normal band. For the

proportional design, the numbers in brackets represent a saturation limit of ± 0.5 Hz. The

deadband design is only evaluated for a saturation limit of ± 0.5 Hz. The number in brackets

represent a deadband size of ± 0.08 Hz. At a frequency deviation of for example 0.5 Hz, an

ESS providing deadband fast FCR-N will respond proportional to the deviation minus the

deadband limit, i.e. either to 0.5 Hz – 0.05 Hz = 0.45 Hz or 0.5 Hz – 0.08 Hz = 0.42 Hz.

Table 8 Examples of the energy capacity needed for fast FCR-N with different response, saturation limits,

deadband size and required operation times. For the proportional design, the numbers in brackets represent the

energy capacity needed for a saturation limit of ± 0.5 Hz. For the deadband design, the numbers in brackets

represent a deadband size of ± 0.08 Hz. The saturation limit for the deadband design is ± 0.5 Hz.

Required energy capacity [MWh]

Proportional design

Time 400 MW/Hz 600 MW/Hz 1000 MW/Hz

15 min 20 (100) 30 (150) 50 (250)

60 min 80 (400) 120 (600) 200 (1000)

Deadband design

15 min 90 (84) 135 (126) 225 (210)

60 min 360 (336) 540 (504) 900 (840)

Note that today the largest battery in the world has an energy capacity of 60 MWh [31], fast

FCR-N would preferably be provided by several units and the sum of their capacities would

correspond to the required energy capacity presented here.

The results of the utilisation method show that the actual maximum energy needed, Emax, is

highly dependent on the dynamics of the frequency. In Figure 19, Emax is plotted for different

fast FCR-N designs, time windows and power outputs. The upper graphs show Emax for two

days in February 2012. The lower graphs show Emax for two days in August the same year. In

both February and August the two hour time window generates the largest Emax. For time

windows of 30 and 60 minutes in February, Emax is the same, but in August the 60 minutes

time window has a larger Emax than the 30 minutes window.

37

Figure 19 The upper graphs represent the maximum energy capacity needed during two days in February 2012,

and the lower graphs represents two days in August the same year. Fast FCR-N of proportional design is shown

to the left, the deadband design to the right. The solid lines represent a ± 0.1 Hz saturation limit and the dashed

lines a ± 0.5 Hz saturation limit in the case of proportional fast FCR-N. In the deadband results, the solid lines

corresponds to a ± 0.05 Hz deadband size and the dashed lines to a ± 0.08 Hz deadband size. Note the different

scales on the y-axis.

This method shows that the energy need is determined by the dynamics of the frequency, and

not by the time the ESS is supposed to be active. However, it can be concluded that the

deadband design requires less energy capacity than the proportional design. A larger

deadband is decreasing the energy need even more. The difference between a ± 0.5 Hz and a

± 0.1 Hz saturation limit in Figure 19 is small. This means that a larger saturation limit not

necessarily increases the need of energy capacity, it depends on the frequency dynamics.

Regarding the wear of the ESS, the control work performed by the different fast FCR-N

designs is compared. As before, one week of load disturbance from February 2012 is used for

the simulations. The proportional design with ± 0.1 Hz saturation limit and no delay is used as

reference. Systems with fast FCR-N of 600 and 2000 MW/Hz power output respectively are

simulated. Table 9 shows the results presented in percentage change of control work, the

2000 MW/Hz results are written in brackets.

38

Table 9 The change in control work of the ESS compared to the proportional type of fast FCR-N with a

saturation limit of ± 0.1 Hz. 600 and 2000 MW/Hz power output respectively are investigated. The latter is

presented in brackets.

Fast FCR-N design Change in ESSdist [%]

± 0.1 Hz saturation limit, 0 delay 0 (0)

± 0.1 Hz saturation limit, 5 s delay 0 (0)

± 0.5 Hz saturation limit, 0 delay +2 (+2)

± 0.05 Hz deadband, 0 delay -78 (-81)

± 0.05 Hz deadband, 5 s delay -78 (-81)

± 0.08 Hz deadband, 0 delay -94 (-95)

It can be seen that the 5 second delay does not affect the amount of control work. For an

increased saturation limit the control work increases by only 2 %, thus for the proportional

type the work of the ESS is more or less the same for all variants. When looking at the

deadband design, the desired control work is reduced to between 78 % and 95 % of the

reference case.

In Figure 20, the power output and energy demand of a two hour simulation are plotted for the

different services. The ESS providing proportional fast FCR-N is continuously active,

whereas the deadband design only requires short times of activation of the ESS. The resulting

energy demand is therefore less for the deadband design.

Figure 20 A 2 hour simulation showing the power output and SOC of the different designs. Normally SOC is

given as a percentage of the total ESS capacity. Here the size of the ESS is unknown, and SOC is rather used for

examine the actual utilisation of the ESS. It is therefore given in MWh.

39

5.9 Energy capacity and wear of the ESS – discussion

Why the frequency characteristics are so important becomes clear when looking at Figure 11.

Each line represent the SOC of an ESS providing 600 MW/Hz proportional fast FCR-N.

When the frequency is too low, the ESS provides output power, i.e. it is discharging and the

SOC is decreasing. In high frequency situations the ESS is charging and the SOC increases.

Short before one hour the asset goes from discharging to charging, and charges for more than

half an hour. Since the SOC for the 2 hour simulation was low when the charging started, the

peak around 5000 seconds is lower than for the one hour simulation, which was reset at the

beginning of the hour. A half hour simulation also gets an absolute value of the SOC larger

than for the 2 hour simulation.

For the proportional design, ESSdist does not differ much between the different variants. This

is because ESSdist within the normal band increases at the same rate for both. The only time

ESSdist increases faster for the ± 0.5 saturation limit variant is when the frequency signal is

outside the normal band. First of all, that time is not long enough to change the result

significantly, and secondly, the ± 0.1 saturation limit variant is still providing a relatively

large constant power output. The difference in ESSdist outside the normal band arise from the

difference in power output between the constant signal and the signal that is still responding

proportional to the frequency deviation is small as long as the frequency deviations is not

much larger than 0.1 Hz.

The deadband type provides less frequency control since it is not active within the deadband,

and because the hydropower has preserved strength and provides more power than for the

proportional type. Consequently, the energy demand and control work of the deadband design

is smaller, and the larger deadband, the less control work.

Finally, for none of the simulations the maximum utilised energy is corresponding to the

suggested required energy capacity. Dimensioning the ESS according to Table 8 will likely

mean an over dimensioning of the system. Lower requirements on the energy storage capacity

may be justified and is an area for further investigations.

5.10 Conclusions

The overall conclusion is that fast FCR-N can improve the frequency quality and reduce the

wear on the hydropower units. The design of the service determines the performance

regarding the different parameters studied.

When the different proportional designs are compared, all variants contribute to improvement

of all parameters. The least improvement is seen when a 5 seconds delay is allowed. Since

there are battery storage systems that can go from no load to full load within a second [14],

the no delay-design is considered a feasible choice.

40

The narrow saturation limit of ± 0.1 Hz is reducing the time outside the normal band the most.

On the other hand, by increasing the saturation limit, the RMSΔf -value is decreasing. For the

other performance parameters, the difference between narrow or broad saturation limit is

small. Larger maximum power and energy capacities are required when a ± 0.5 Hz saturation

limit is allowed. In turn, the results show that the actual energy capacity needed depends

mainly on the dynamics of the frequency signal, and not on the saturation limits of the fast

FCR-N. Lower requirements on the energy storage capacity may be justified.

All performance parameters are improved also for the deadband fast FCR-N. The deadband

design has some advantages, for example, it does not demand as much work and energy

capacity of the ESS. Still, the deadband design is not damping the 60 seconds oscillation, nor

reducing the control work of the hydropower units as good as the proportional design.

None of the performance parameters except the utilisation of the ESS have linear dependency

to the power output of fast FCR-N. Therefore, it should be possible to find an optimal

capacity of the fast FCR-N service in relation to economic aspects, such as investment and

operational costs. It is beyond the scope of this thesis to develop a method to find this

optimum. However, 600 MW/Hz of proportional fast FCR-N with saturation limit at ± 0.1 Hz

will be considered the best design and hence investigated further. A narrower saturation limit

decreases the required power and energy capacity of the ESS. At a power output around

600 MW/Hz, the rate of change of improvement has slowed down for all parameters.

Proportional design is chosen because it improves the system performance for faster dynamics

of the frequency deviation and it is helps reducing the control work of the hydropower units.

Table 10 summarises the improvement of the frequency quality and the reduction of the

control work of the hydropower units when 60 MW of proportional fast FCR-N is introduced

in the system.

Table 10 A summary of the performance of the frequency control when proportional fast FCR-N with a response

of 600 MW/Hz and a saturation limit of ± 0.1 Hz is added to the system. Compared to the base case, all

parameters are improved.

Performance parameters with fast FCR-N

Change compared

to the base case

Time outside the normal band 26 995 s (450 min) -15 %

RMSΔf 53.5 mHz -1.3 %

Frequency deviation in 60 s oscillation 0.26∙10-11 Hz2∙Hz -65 %

Guide vane travelled distance 6.8 %/h -20 %

Number of load cycles of the guide vanes 15 cycles/h -40 %

41

The future – a scenario with a weaker grid

This chapter examines how different combinations of frequency control would perform in a

future scenario. It is assumed that the future power system will contain more wind and solar

power. The total natural inertia as well as the frequency dependent load will decrease as the

number of units connected to the grid through inverters are increasing [16].

The following sections describe the assumptions made regarding properties of the future

power system and future frequency control. The performance of different combinations of

FCR-N from hydropower units and fast FCR-N is evaluated for a future scenario.

6.1 Method

The grid parameters described in section 3.3 are decreased to represent a grid of less inertia

and frequency dependent loads. Today, a typical situation of a weak grid can happen in

summer nights when the consumption is low, and the production from renewable sources,

mainly wind power, is high. The Swedish TSO has estimated the values of inertia and

damping in such a situation to M = 8 and D = 0.4 [6]. Looking further in to the future, and

taking into account that a larger share of the power production and the load will be connected

to the grid through inverters, these values may decrease even more. For the future model both

the inertia M and damping D are reduced by half [5]. The new grid parameters become

M = 7.5 instead of 13, and D = 0.25 instead of 0.5.

Four different combinations of frequency control are evaluated regarding frequency quality

and wear of the hydropower units. The performance of the current FCR-N with governor

settings Ep0 is compared to the new Ep1 settings. The parameters used in the different

settings are presented in Table 5. Furthermore, both variants of governor tunings are tested in

combination with fast FCR-N.

The fast FCR-N evaluated here is 60 MW of proportional design with a saturation limit at

± 0.1 Hz, i.e. the service has a proportional response of 600 MW/Hz within the normal band.

When the frequency deviation exceeds the normal band, the fast FCR-N units deliver a

constant power output of 60 MW.

One week of load disturbance estimated by using frequency data from the first week of

February 2012 is used as input signal.

6.2 Results

In Table 11, the performance parameters describing the frequency quality and the control

work of the hydropower units are compared for the base case and four different combinations

42

of frequency control. The base case represents the performance of the system today, assuming

a relatively strong grid (M = 13 and D = 0.5).

Table 11 The performance of FCR-N in a future scenario compared to the base case. The base case represents

the performance of the system today, assuming a relatively strong grid (M = 13 and D = 0.5). Four different

combinations of frequency control are evaluated for a future scenario, in which both the inertia, M, and the

frequency dependent load, D, are reduced by half (M = 7.5 and D = 0.25). The results are presented as a

percentage change of the performance parameters compared to the base case. Ep0 represents the performance of

the system with the current Ep-settings. Ep1 represents a more aggressive tuning of the hydropower turbine

governors, which reduces the impact of backlash in the guide vane regulating mechanism. Both Ep0 and Ep1-

settings are also evaluated together with proportional fast FCR-N with a response of 600 MW/Hz and a

saturation limit at ± 0.1 Hz.

The base case Ep0 Ep0

+ fast FCR-N

Ep1 Ep1

+ fast FCR-N

Time outside

normal band

531 min +102 % -2 % +72 % -2 %

RMSΔf 54.2 mHz +15 % +2 % +11 % +2 %

60 seconds

oscillation estimate

0.76∙10-11 Hz2·Hz +623 % +3 % +417 % +1 %

Guide vane

travelled distance

8.5 %/h +185 % -4 % +533 % +200 %

Number of

load cycles

25 cycles/h +186 % -7 % +233 % +95 %

If no fast FCR-N is introduced in the system and the properties of the grid are weaker, the

frequency quality deteriorates and the control work increases. The more aggressive

Ep1-setting gives a higher frequency quality than Ep0-settings. Still, the time outside the

normal band is increased by 72 %, RMSΔf by 11 % and the 60 seconds oscillation estimate by

417 % compared to today, i.e. the base case. The guide vane travelled distance and the

number of load cycles are also increased significantly. Note that for the Ep1-settings, the

control work is concentrated to fewer plants.

Introducing fast FCR-N has a positive impact on the system. Even though the inertia and

frequency dependent load are reduced by 50 %, the frequency quality with fast FCR-N in the

system is almost the same as in the base case. The combination of Ep1 governor settings and

fast FCR-N contribute the most to improved frequency quality, but the difference between

Ep0 and Ep1 when fast FCR-N is introduced is little.

43

6.3 Conclusions

The results show that the worst case scenario from a frequency quality point of view is to

keep the current FCR-N unchanged. The control work of the hydropower units is on the other

hand increased when the governor settings are changed to Ep1. However, fewer plants would

participate in frequency control, and the wear would be concentrated to a smaller number of

units.

It is clear that an introduction of fast FCR-N is beneficial for the whole system. When fast

FCR-N is introduced, the difference in frequency quality between the different governor

tunings is small. It implies that the system has a need for some frequency control service that

can handle faster dynamics of the load disturbance, and that the dynamics of the hydropower

plant is to slow to do this in a good way.

Also, even though the governor tuning is better and fast FCR-N is implemented, the

frequency quality is approximately the same as in the situation today, i.e. the base case. It

points at the importance to find other solutions to compensate for reduced damping and

system inertia if the TSOs want the future system to have better frequency quality than today.

44

Potential technology for fast FCR-N

The following section will briefly present four different technologies which can be used for

fast primary frequency control. The four technologies are batteries, flywheels, capacitors and

wind power turbines. They are chosen because they are well known technologies, and in some

places already implemented in the power system.

7.1 Batteries

A battery energy storage system (BESS) converts potential chemical energy to electrical

energy. The basic battery cell has two electrodes (the anode and the cathode) and an

electrolyte. At the anode there is a surplus of negative charge, and the cathode in turn is

positive charged resulting in a difference in potential between them. When an external load is

connected to the battery electrons flow from the anode to the cathode giving rise to a current

[13]. For a more detailed description of different battery technologies such as lithium-ion or

flow batteries [13] is warmly recommended. The market for BESSs is increasing rapidly at

the moment, and it is difficult to estimate the cost or life time of a typical BESS. The

technology is continuously improving, the prices fall fast and numbers valid today may soon

be out of date.

A 22 MW battery owned by Vattenfall AB was one of the winning tenders of National Grid’s

procurement of EFR. The battery must, according to NG, be able to provide or absorb

maximum active power for at least 15 minutes. That means an energy capacity of 11 MWh for

the Vattenfall battery. The price is said to be 7.45 £/MW per procured hour of EFR, and the

asset shall have 100 % availability during the first 4 years [24].

7.2 Flywheels

Flywheels consist of rotating disks that are connected via a shaft to an electrical machine. The

electrical machine can operate as a motor or generator. When the system accelerates, i.e. the

electrical machine operates as a motor, electric energy is extracted from the power grid, and

the higher speed of the system, the more energy is stored. Opposite, when stored energy is

converted into electrical energy, the speed of the system is reduced [13]. The energy stored in

the flywheels is expressed in the same way as the rotating kinetic energy describing the inertia

(2), i.e.

𝐸𝑘𝑖𝑛 =

1

2𝐽𝜔2

(18)

where 𝐽 is the moment of inertia of the flywheel and the rotor of the machine to which it is

connected, and 𝜔 is the rotational speed. The energy capacity of the system is therefore

45

limited by the minimum and maximum rotational speed of the flywheels and the moment of

inertia.

The efficiency of modern flywheels is high, around 90 % at rated power. The cycling

capability is approximated to be between hundred thousand and ten million charge and

discharge cycles. The ramp rate is fast, meaning they can go from full discharge to full charge

within a few seconds. For short-term applications, e.g. frequency control, flywheels are well

suited, but since they cannot inject or absorb power at full load for more than a few minutes

they are not suitable choice for long term energy storage [13]. The two largest flywheel plants

providing frequency control are situated in New York and Pennsylvaina, USA, with a

capacity to deliver 20 MW each for 15 minutes [32].

7.3 Supercapacitors

The supercapacitor energy storage technology is based on electrostatically stored energy. The

cell of a supercapacitor is illustrated in Figure 21. It contains two conductor electrodes, an

electrolyte and a porous membrane through which ions can be transferred from one electrode

to the other. When a voltage is applied between the two electrodes both the electrodes and the

electrolyte becomes polarized, unlike a battery in which a chemical reaction occurs. Positive

charge from the cathode is transferred to the interface between the electrode and the

electrolyte. A layer of positive ions is formed. In turn, negative ions from the electrolyte are

moving towards the same interface, forming a negative layer of ions. These two layers are

separated by a layer of solvent molecules of the electrolyte (called inner Helmholtz plane). In

that layer an electric field is induced and potential difference arise between the positive and

negative side. The magnitude of the electrical potential, 𝑉 [V], and the capacitance, 𝐶 [F], of

the capacitor determines the energy storage capacity of the cell according to

𝐸𝑠𝑐 =1

2𝐶𝑉2. (19)

Different studies have estimated the life time of supercapacitors to 8 -17 years, and the

cycling capability to five hundred thousand and one million charge and discharge cycles.

Supercapacitors have high ramp power rates, and high efficiency (up to 80 %). The specific

power is comparable to flywheels, but 100 times higher than e.g. Li-ion batteries [13]. There

are only a couple of test projects in for example Ireland, and at the Canary Islands, where

supercapacitors are used for frequency control [32].

46

Figure 21 Illustration of a supercapacitor.

7.4 Wind power turbines

ENTSO-E (the European Network of Transmission System Operators for Electricity) will

present new technical requirements on the ability of wind turbines to provide frequency

control [2]. Wind power plants may also be required to in some way provide synthetic inertia

(SI). Some TSOs (Hydro-Québec in Canada and EirGrid in Ireland) have already specified

requirements in their grid codes on contribution of SI from wind farms.

To reach as high efficiency as possible wind power turbines conventionally operate at a point

where the power extracted from the wind is maximized. The working point where the

maximum aerodynamic efficiency is reached depends on the speed of the turbine and the

pitch angle, which is the direction of the wind in relation to the blade surface. By either

changing this angle or letting the turbine rotate at a higher speed than optimal, a suboptimal

working point is achieved. The plant has some margin to increase its power output when

needed for frequency control [13]. In Figure 22 the upper curve corresponds to an optimal

pitch angle, and the lower curve a changed pitch angle to reduce the power output. Point A is

the maximum power operating point. Point B represents so called overspeed operation and

point C is operation with pitched blades.

47

Figure 22 Power-rotor-speed curves illustrating working points for deloaded operation. Both curves represent the

power extracted from the wind by the same wind turbine at the same wind speed, but with different pitch angles.

When a wind turbine is used to provide SI it is the actual inertia of the turbine that is the

power source [5]. This works only for variable speed wind turbines, since it allows the rotor

speed to be slowed down. After a deceleration a recovery scheme is needed to return the wind

turbine to its optimal rotational speed as soon as possible [13].

48

Discussion

The designs of fast FCR-N suggested in this thesis are only two of many ways to design a

frequency control service providing fast frequency control and other technical solutions for

fast FCR-N are possible. The results show that to improve the frequency quality it is desirable

to make the service as fast as possible, but further studies are needed on how a service of such

a fast response affects other stability aspects in the power system.

Even though fast FCR-N improves the system performance, the improvement is moderate

when the grid becomes weaker. Implementing a service responding to the derivative of the

frequency deviation signal would act more like the natural inertia does today, and could

thereby compensate for the loss of natural inertia and damping.

It is assumed that the future development of the energy system is going towards more variable

energy sources, that the power system will contain more units connected to the grid through

inverters and that the system inertia and damping will decrease as a consequence. This is not

necessarily the case if other technical solutions are compensating for loss of natural inertia

and damping. There is an uncertainty in the choice of grid parameters in the future scenario in

Chapter 6. Reducing the inertia and damping by half might be too much, which has a negative

effect on the performance in Table 11. A more thorough sensitivity analysis is needed.

Regarding the retuning of the hydropower governor, the Ep1 governor setting has a 2.5 times

smaller droop, 𝐸𝑝, than the Ep0 settings. According to (7) that results in a 2.5 times higher

static gain. The Ep1 integral gain, 𝐾𝑖, is also 2.5 times larger than in Ep0. The proportional

gain, 𝐾𝑝, in the new Ep1 compared to Ep0 is on the other hand only 2 times larger. That

means that FCR-N provided by hydropower plants with Ep1 governor settings has a relatively

smaller proportional part than the Ep0 settings. Fast FCR-N of proportional design could

compensate for this reduction of proportional control in the system.

Furthermore, the different methods to estimate the control work of the hydropower units and

the ESS need to be stressed. The control work of the hydropower units is measured in terms

of movement of the guide vane regulating mechanism. The work of the ESS is in this thesis

related to the amount of energy it provides.

The wear on the hydropower units is assumed to increase with increased travelled distance

and direction changes of the guide vane regulating mechanism. The amount of frequency

control in numbers of delivered megawatt hours is not necessarily a relevant measure of the

wear. Theoretically, the frequency deviation could be constant, and thus also the power output

from the hydropower plant. This situation would result in a large amount of delivered energy,

but no movement of the guide vanes, i.e. no wear.

The operation of an ESS unit providing fast FCR-N would most likely induce wear of

different kinds and extent for different technologies. The method to measure the wear, ESSdist,

assumes that more control work in terms of provided energy is increasing the wear of the

ESS. It can be discussed for the case when wind turbines provides fast FCR-N. Probably

49

changing power output through changing rotational speed or pitch angel is what induce the

wear of a wind power turbine, not the amount of energy delivered. For battery storage

technologies, which do not have any moving parts, the chemical wear is the relevant factor to

study. Continual charge and discharge behaviour of the battery is assumed to increase the

chemical activity and contribute to the wear of the asset. The measure ESSdist can give a hint

about which design of fast FCR-N that contributes to most wear of the ESS, but the actual

wear depends on the technology used.

At last, it is not within the scope of this thesis to investigate remuneration methods for fast

FCR-N, but economic incentives is required to make potential fast FCR-N providers invest in

this kind of technologies. How fast FCR-N could be remunerated is a question to investigate

further.

50

Conclusions

Introducing a frequency control service with very fast response to frequency deviations can

improve the performance of the frequency quality in the Nordic power system and reduce the

wear on the hydropower units providing primary frequency control today. In this thesis a

service called fast FCR-N is suggested. Two different designs of fast FCR-N are examined,

proportional and deadband design. The proportional design has a pure proportional response

to frequency deviations, unless the frequency deviation signal is exceeding a saturation limit.

After the saturation limit the response will be constant. The deadband design is also giving a

proportional response, but only outside a defined deadband.

The advantage of proportional fast FCR-N is that it is continuously active and reduces the

amplitude of the 60 seconds oscillation. Thereby, the hydropower units are given a friendlier,

meaning less volatile, frequency deviation signal to work with, which reduces the control

work, and thus the wear on the hydropower turbines.

The deadband design is in turn not requiring as much work of the ESS. It is an additional

service, which does not replace any hydropower frequency control. As a consequence, the

total amount of frequency control outside the deadband is larger than for the proportional

design. Even though the strength of the response from the hydropower units is preserved, the

control work is reduced. As for the proportional design, the service improves the frequency

deviation signal, and for that reason the control work of the hydropower units decreases.

A future scenario is also investigated. It is assumed that the energy system will contain more

variable energy sources, such as wind and solar power, which replaces traditional power

production from thermal power plants. The natural inertia, provided by the large rotating

masses in the thermal power plants, will be reduced. In general more units will be connected

to the power system through inverters, resulting in less system inertia and less damping, i.e. a

reduced amount of frequency dependent loads in the system. Both inertia and damping have a

stabilising effect on the system. A scenario where the system inertia and the damping both are

reduced by half is examined. The results show that if the system has the same properties as

today, with almost all frequency control provided by hydropower units, the frequency quality

would deteriorate and the wear of the hydropower turbines would increase significantly. If

60 MW of proportional fast FCR-N is introduced in the system, the performance is improved.

Still, compared to the situation today, the improvement is moderate. Changing the settings in

the hydropower turbine governors and thereby improve the frequency control properties of the

hydropower unit, do not result in a significant improvement of the frequency quality.

The final conclusion is that the system has a need for some kind of faster frequency control.

The fast FCR-N designs suggested in this thesis could provide this. Still, if the power system

becomes weaker in the future, and the TSOs want the frequency quality to be better than

today, further actions need to be taken.

51

Future work

Before fast FCR-N can be introduced at the frequency control market, further technical and

economic questions have to be studied.

A market model that encourage possible providers of fast FCR-N to invest in batteries,

flywheels or other energy storage technology that can deliver fast FCR-N has to be developed.

The possibility to allow the energy storage system to provide more than one service, for

example both peak-shaving and frequency control, should be considered when designing the

model. Furthermore, specifications have to be made on the requirements of the energy storage

capacity of the fast FCR-N providing units.

Fast FCR-N is a frequency control service with a response much faster than the current

frequency control. Implementing this service might have an impact on for example inter-area

oscillations between countries. The effects of fast FCR-N on the power system stability within

a higher frequency range than what has been studied in this thesis has to be investigated

further.

Studies on suitable areas to place the fast FCR-N providing units, regarding frequency control

demand, power transmission capacity etc. have to be carried out.

The model of frequency control used in this thesis represents primary frequency control

during normal operation. Using a model which also includes frequency control during

disturbed operation (FCR-D) and secondary frequency control (aFRR), would give a better

representation of the system today, and a better picture of the behaviour of the frequency

control outside the normal band.

52

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[26] P. Kundur, Power System Stability and Control, New York: McGraw-Hill, 1994.

54

[27] L. Saarinen, Interviewee, About how to scale the controller parameters, and the change of

governor tuning of Vattenfall's tubine governors. [Interview]. 23 January 2017.

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http://www.svk.se/siteassets/om-oss/organisation/finansiell-information/arsredovisning-2016-

affarsverket-svenska-kraftnat.pdf. [Accessed 24 February 2017].

[29] W. Yang, P. Norrlund, L. Saarinen, J. Yang, W. Zeng and U. Lundin, “Wear reduction for

hydropower turbines considering frequency quality of power systems: A study on controller

filters,” IEEE Transactions on Power Systems, vol. 32, no. 2, pp. 1191-1201, 2017.

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[Accessed 25 02 2017].

55

Appendix A – Model verification

To verify the model of the hydropower governor and turbine, representing FCR-N in Figure 4,

the step response of each part is simulated. At a frequency deviation step of - 0.1 Hz the

system having Ep0 governor settings is expected to open its guide vanes by 2 %, resulting in

an increase of frequency control power by 753 MW. For Ep1 settings fewer plants provide the

same amount of frequency control, meaning a larger opening of guide vanes and a higher flow

through the turbines of these units. For Ep1 settings the guide vanes shall open by 5 % instead

of 2 % at a frequency deviation of - 0.1 Hz, but still giving 753 MW of power output.

The magnitude of the load disturbance step is decided through iteration until the step results in

a frequency deviation of - 0.002 p.u. (- 0.1 Hz), illustrated in Figure 23. It happens for a

disturbance step of - 0.021 p.u. (- 791 MW). The reason why a load disturbance of -791 MW

give rise to a frequency deviation of 0.1 Hz and can be compensated by only 753 MW is

because the system contains frequency dependent loads (damping). These loads decrease their

power consumption when the frequency drops. For a system with less damping, a -791 MW

load disturbance would result in a larger frequency deviation.

Figure 23 Frequency step response at a load disturbance of magnitude -0.021 p.u. (791 MW). The final value of

the frequency is 0.002 p.u. (0.1 Hz).

Simulating a disturbance step of - 0.021 p.u. (- 791 MW) gives the following results:

The guide vane opening response is plotted in Figure 24 and shows an opening of 0.02 p.u.

(2 %) for Ep0 and 0.05 p.u. (5 %) for Ep1.

56

Figure 24 Guide vane step response at a load disturbance of magnitude -0.021 p.u. (-791 MW). The guide vanes

open 0.02 p.u. (2 %) which is the expected opening for a frequency deviation of -0.1 Hz.

The power output response of the hydropower unit with Ep0 and Ep1 settings respectively is

plotted in Figure 25 and shows an output power of 0.02 p.u. (753 MW) for both settings. The

model is therefore assumed to behave as it is expected to.

Figure 25 Step response of the hydropower unit at a disturbance of magnitude -0.021 p.u. (-791 MW) which

corresponds to a frequency deviation of -0.1 Hz from its nominal value 50 Hz. The hydropower unit increases its

power output by 0.02 p.u. (753 MW) which is the expected static gain for a frequency deviation of -0.1 Hz.

57

When introducing proportional fast FCR-N, the total amount of frequency control should

preferably be the same (753 MW), and the frequency control provided by the hydropower

units shall decrease. Having 40 MW of fast FCR-N at a frequency drop of 0.1 Hz would

therefore result in 713 MW output power from the hydropower unit, which as seen in Figure

26 is true.

Figure 26 The power output from the hydropower unit and the fast FCR-N showing that when the fast FCR-N

provides 0.001053 p.u. (39.6 MW) at a frequency deviation of 0.1 Hz the hydropower has decreased its

contribution to 0.01896 p.u. (713.8 MW), which means that the total frequency control is 753 MW.

58

Appendix B – Analysis of frequency data

Frequency data from 2012 with a sampling time of 1 second is used. For each month, a power

spectrum is calculated using the Matlab function pwelch (described in Section 2.4) and plotted

in Figure 27. The 60 seconds oscillation is clearly visible. There is a peak at 0.0167 Hz, which

corresponds to a frequency of a time period of 60 seconds. Another peak can be seen around

0.01 Hz, corresponding to periods of approximately 100 seconds.

In Table 12, frequency quality data for each month are presented in terms of the frequency

quality parameters from section 5.2.1 - 5.2.3.

Figure 27 A frequency spectrum of the grid frequency 2012. Each line represents a month starting with January

at 1. For all months the spectrum shows a clear peak at 0.0167 Hz, which corresponds to frequencies with a

period of approximately 60 seconds. In the summer months the peak is slightly higher which is confirmed in

Table 12. The signal has almost no frequency content for frequencies larger than 0.1 Hz.

59

Table 12 Compilation of frequency quality parameters for each month of 2012.

Time outside

normal band

[min]

60 seconds

oscillation estimate

[Hz2∙Hz]

RMSΔf

[mHz]

January* 881 0.68∙10-11 43.7

February 1177 0.71∙10-11 46.4

March* 927 0.95∙10-11 42.9

April* 1047 0.96∙10-11 44.3

May* 1156 1.23∙10-11 44.4

June* 748 1.36∙10-11 41.2

July* 733 1.30∙10-11 42.1

August 824 1.29∙10-11 41.9

September* 1292 1.09∙10-11 45.5

October* 1132 0.88∙10-11 45.0

November* 1021 0.83∙10-11 44.0

December 987 0.57∙10-11 42.8

Total 11 926 min

Average 229 min

(week)

0.99∙10-11 Hz2∙Hz

(year)

43.7 mHz

(year)

* In these months, the data set had some parts where measured frequency data were

missing. In July, 47 190 seconds of frequency data were missing. In the other months

marked by *, between 301 and 7710 seconds were missing. The actual number of minutes

outside the normal band in 2012 might therefore differ from 11 926 minutes.

60

Appendix C – Evaluation of the estimation of the load disturbance signal

Frequency data from the first week of February 2012 is used to estimate a load disturbance

signal, ∆𝑃𝐿, used as input to the model described in Chapter 3.

The generation of ∆𝑃𝐿 is described in Figure 6 (Chapter 4). To avoid that the derivative part

of the inverse grid block is amplifying the fast dynamics of the noise, an extra pole of time

constant 𝑇𝑔 is added. How the choice of 𝑇𝑔 affects the simulated frequency deviation signal is

presented in Figure 28.

Figure 28 Examples of the simulated frequency deviation signals when different values of Tg is used to estimate

the load disturbance signal.

The choice of 𝑇𝑔 is determined by comparison of the frequency quality parameters presented

in Section 5.2.1 - 5.2.3. A value of 𝑇𝑔 = 0.4 s is decided upon. Results for other values of 𝑇𝑔 is

presented in Table 13.

Table 13 The frequency quality parameters for the measured frequency deviation signal compared to the

simulated frequency deviation signal.

Minutes outside the

normal band

60 seconds estimate

[Hz2∙Hz]

Root mean square

error [mHz]

Measured 510 0.56∙10-11 53.89

Simulated Δf with Tg-value [s]

5 604 1.30∙10-11 55.19

2 560 0.96∙10-11 54.60

0.5 533 0.76∙10-11 54.23

0.4 531 0.76∙10-11 54.22

0.3 537 0.77∙10-11 54.24

0.1 592 1.26∙10-11 55.03

61

Appendix D – Comparison of frequency signals with and without fast FCR-N

Figure 29 illustrates why the performance regarding the time outside the normal band is better

for the proportional fast FCR-N design of ± 0.1 Hz saturation limit than for ± 0.5 Hz

saturation limit. When the frequency deviation is larger than 0.1 Hz, the frequency exceeds

the normal band. Within the normal band, both designs respond in the same way. Outside the

normal band, the narrower saturation limit responds with a constant power output resulting in

a more volatile frequency signal. The larger saturation limit reduces the oscillations more, and

as a consequence, the frequency signal is kept outside the normal band at some points, for

example around 36 950 seconds in Figure 29.

Figure 29 Explanation of why the proportional fast FCR-N type of ± 0.1 Hz saturation limit result in better

performance regarding the time outside the normal band than the ± 0.5 Hz saturation limit. When the frequency

deviation is oscillating around the normal band limit, there are situations when the larger power output from the

fast FCR-N with larger saturation limit leads to a less volatile signal, and that the frequency stays outside the

normal band.