Dynamic transformers rating for expansion of expansion of existing wind farms

(1)

IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2019

Dynamic transformers rating for

expansion of existing wind farms

OSCAR DAVID ARIZA ROCHA

KTH ROYAL INSTITUTE OF TECHNOLOGY

(2)

of existing wind farms

Dynamisk lastbarhet hos transformatorer för expansion av

befintliga vindkraftparker

Author

Oscar David Ariza Rocha <odar@kth.se> KTH Royal Institute of Technology

Program

MSc Electric Power Engineering

Place and Date

KTH Royal Institute of Technology, Stockholm, Sweden ABB AB, Västerås, Sweden

June 2019

Examiner

Patrik Hilber

KTH Royal Institute of Technology

Supervisors

Kateryna Morozovska

KTH Royal Institute of Technology Tor Laneryd ABB AB Claes Ahlrot E.ON Energidistribution AB Ola Ivarsson E.ON Energidistribution AB

(3)

ii

Abstract

Distribution system operators face the challenge to connect users rapidly to the grid and the opportunity to reduce costs for new connections. A method to enhance net-work operation and planning is dynamic transformer rating (DTR), which considers load and temperature variations to increase the rating of the transformer while main-taining in safe operation.

This project investigates DTR application to an existing population of transform-ers connected to a wind park and proposes a method for adding new turbines to the grid using installed transformers. Five transformer locations and nine units belong-ing to E.ON AB are used to find the potential of DTR for network expansion.

A weather analysis reveals that simultaneous high wind speeds and high tem-peratures seldom occur. An aging estimation based on the IEC 60076-7 standard shows that the transformers for wind power applications are underused. Consider-ing the transformer thermal model, a sensitivity analysis shows that the parameters that mostly affect the aging rate are the moisture content, the hot spot factor, and the top-oil temperature rise. The maximum load to assure aging below 50 years is calculated for each transformer for different maximum hot-spot temperature levels showing that increasing the maximum allowed temperature reduces curtailment and increases aging. A single node analysis depicts the optimal expansion of wind power from a generator perspective, and a network analysis introduces further restrictions to the network. As a result, the optimal increase factor is around 30 to 50 % and is larger for higher hot-spot temperature limits.

Accurate weather measurements and transformer parameters are necessary to make a proper estimation of transformer aging to unlock transformer potential. To use fiber optic temperature sensors in new transformers and on-site temperature measurements can increase the rating of the transformer. A maximum allowed tem-perature of 110◦Cis conservative and limits the potential of the transformer for wind power applications. Finally, society benefits from DTR in wind power applications because there is a more efficient use of resources and additional renewable energy can be introduced to the network.

Keywords

(4)

Sammanfattning

Eldistributionsnätet står inför en utmaning att snabbt ansluta användare till nätet och en möjlighet att miska kostnaderna i nya ansultnigar. En metod för att förbät-tra nätverksdrift och planering är dynamisk lastbarhet hos förbät-transformatorer, eller

dy-namic transformer rating (DTR). Metoden beaktar belastings- och

temperaturvari-ationer för att öka transformatorns lastbarhet samtidigt som den upprätthåller säker drift.

Detta projekt undersöker tillämpningen av dynamisk lastbarhet till en befintling population av transformatorer kopplade till en vindkraftpark och föreslår en metod för att ansluta ytterligare turbiner till nätet med hjälp av befintliga transformatorer. Fem transformatorplatser och nio enheter som tillhör E.ON AB används för att un-dersöka potentialen för DTR inom tillämpningar för nätverksexpansion.

En vänderanalysis avslöhar att både höga vindhastigheter och temperaturer säl-lan uppstår samtidigt. En uppskattning av åldrandet baserad på IEC 60076-7-standarden visar att transformatorer för vindkraftstillämpningar är underanvända. Med avseende på den termisk transformatormodellen visar en känslighetsanalys att parametrarna som påverkar minskning av livslängden mest är fuktinnehållet, hot spot-faktorn och ökning av top-olja-temperaturen. Den maximala belastningen för att säkerställa en åldring under 50 år beräknas för varje transformator, för olika värden på den max-imala hotspottemperaturen. Detta visar att med ökning av den maxmax-imala tillåtna temperaturen minskar produktionsbortfall och ökar åldrandet.

En-nods-analys visar den optimala expansionen av vindkraft från en producents perspektiv, och en nätverksanalys introducerar ytterligare begränsningar för nätver-ket. Detta resulterar i en optimal ökningsfaktor på cirka 30-50% och är större för högre värden på den maximala hotspottemperaturen.

Noggranna vädermätningar och transformatorparametrar är nödvändiga för att göra en korrekt uppskattning av transformatorns åldrande. Att använda fiberoptiska temperatursensorer i nya transformatorer och platsspecifika temperaturmätningar kan öka transformatorns lastbarhet. En maximal tillåten temperatur på 110◦C är för konservativ och begränsar transformatorns potential för vindkraftstillämpningar. Samhället drar fördel av DTR i vindkraftstillämpningar eftersom det leder till en effektivare resursanvändning och att ytterligare förnybar energi kan introduceras i nätverket.

Nyckelord

(5)

iv

Abbreviation

DSO Distribution System Operator

DLR Dynamic Line Rating

DTR Dynamic Transformer Rating

DP Degree of Polimerization

Ei Energimarknadinspektionent: Swedish Energy Market Inspectorate

HSF Hot- Spot Factor

HST Hot Spot Temperature

IDW Inverse Distance Weight method

MAE Mean Absolute Error

NPV Net Present Value

OF Transformer Oil Forced cooling

ONAN Transformer Oil Natural Air Natural cooling ONAF Transformer Oil Natural Air Forced cooling OD Transformer Oil Directed cooling

RES Renewable Energy Sources RMSE Root-Mean Square Error SLES Sel Learning Expert Systems

(6)

Symbols

Symbol Meaning Units

A Arrhenius equation pre-exponential factor 1/h AHyd

Arrhenius equation pre-exponential factor for hydrolitic

process 1/h

AOxi Arrhenius equation pre-exponential factor for oxidation 1/h

Ar Rated Arrhenius equation pre-exponential factor 1/h

As Area m2

B Aging rate constant K

C Thermal capacity W · h/K

c Specific heat W · s/(kg · K)

cc Specific heat of the core W · s/(kg · K)

co Specific heat of the oil W · s/(kg · K)

cT Specific heat of the tank W · s/(kg · K)

cw Specific heat of the winding material W · s/(kg · K)

CIC Installed capacity W

Ct Cost of rewinding the transformer SEK

D Difference operation, in difference equations

DPpresent Present degree of polymerization —

DPnew New degree of polymerization —

Ea Activation energy kJ /mol

Ea,r Rated activation energy kJ /mol

EHyd Activation energy for hydrolitic material aging kJ /mol

EOxi Activation energy for oxidation aging kJ /mol

fp Probability density function —

gr

Average-winding-to-average-oil (in tank) temperature

at rated current K

gct Gravitational constant m/s

H Hot-spot factor —

Hz(t) Hazard function —

I Current A

ImLOL Impact of the loss of life SEK

ImDF Impact of dielectric failure SEK

ko Correction factor for the cooling mode —

(7)

vi

Symbol Meaning Units

k21 Transformer specific thermal model constant —

k22 Transformer specific thermal model constant —

K Load factor (load current/rated current) — L Total aging over the time period considered —

ma Mass of core and coil assemble kg

mT Mass of the tank and fittings kg

mo Mass of oil kg

mw Mass of windings kg

Oo Cooling mode correction in [33] model —

PBetz Theoretical maximum wind power W

Pe Eddy losses of winding at rated load W

Pm Mean production of a wind park W

PM Measured power W

PP Predicted power W

Pr Rated losses W

Pw Winding losses W

PW Power of an air mass W

P s Standard sea level atmospheric pressure kP a

P U L Per unit life —

R Ratio of load losses at rated load to no-load losses — Rair Specific gas constant for air J /(kg· K)

Rc Ideal gas constant (8.314) J /(kg· mol)

s Current density A/mm2

t Time in service h

vo Volume of oil l

V Relative aging rate —

x Exponential factor of oil —

y Exponential factor of winding —

Yc Portion of the core losses in the total transformer losses —

Yst Portion of stray losses in the total transformer losses —

Yw Portion of winding losses in the total transformer losses —

z Altitude above sea level m.a.s.l.

zref Rated altitude m.a.s.l.

z0 Surface roughness m

α Power law coefficient —

∆θh Hot-spot-to-top-oil gradient at the load considered ◦C

(8)

Symbol Meaning Units ∆θor Top-oil temperature rise at rated losses K

∆t Percentage of transformer lifetime difference between

the actual and reference value —

ϵ Maximum deviation between average value and measurement

in weather calculations —

ηT ot Total chain scissions in cellulose —

θ Temperature ◦C

θa Ambient temperature ◦C

θdor Average oil temperature at rated load ◦C

θh Winding hot spot temperature ◦C

θh,r Rated winding hot spot temperature ◦C

θo Top-oil temperature ◦C

θwr Average winding temperature at rated load ◦C

Θ Operating temperature K

σ Shape parameter of the Weibull distribution —

τo Oil time constant min

τw Winding time constant min

ν Wind speed m/s

νref Reference wind speed m/s

ρ Air density kg/m3

(9)

List of Figures

2.1 Transformer’s thermal diagram . . . 9

2.2 IEC 60076-7 block diagram representation of the differential equations 11 2.3 Wind power curve Class III normalized to rated power . . . 19

3.1 Flow diagram transformer aging . . . 25

3.2 Estimated temperature Substation 1 . . . 28

3.3 Histogram of the error temperature calculation . . . 29

3.4 Wind speed estimation for a week in April 2018 . . . 29

3.5 Histogram of the error in wind speed calculation . . . 30

3.6 Histogram of wind speed and temperature from Substation 1 estimations 31 3.7 Transformer 1 (63 MVA): load (a) and load duration curve (b) . . . 32

3.8 Transformer 1 (63 MVA): load (a) and load duration curve (b) . . . 33

3.9 Load Curve comparison between three different wind turbines models, αcalculation and transformer measured value . . . 34

3.10 Time based comparison between measured power and calculated . . . 34

3.11 Aging T1 base case . . . 36

3.12 Calculated highest HST of the studied period . . . 36

3.13 Sensitivity analysis regarding HSF for T1. . . 39

3.14 Sensitivity analysis of the aging based on the oil time constant for T1 . 40 3.15 Sensitivity analysis of the aging based on R for T1 . . . 41

3.16 Sensitivity analysis of the aging based on the top-oil temperature rise at rated losses for T1 . . . 42

3.17 Sensitivity analysis of the aging based on moisture level and type of paper for T1 . . . 43

3.18 Sensitivity analysis of aging based on the cooling mode . . . 45

3.19 Aging of T1 for different temperatures and hourly load . . . 46

3.20 Loss of life estimation for T1 . . . 49

4.1 Curtailment and aging for an increase of load by a factor B . . . 55

4.2 Curtailment and aging with the convolution method . . . 56

4.3 T1 and T5 revenue in the single node study . . . 60

4.4 T1 and T5 LOL in the single node study . . . 60

4.5 Imports, exports and cost of energy of the single node analysis . . . 61 x

(12)

4.6 One-line diagram of the network . . . 62 4.7 Flowchart depicting order of execution of the network analysis chain . 63 4.8 T5 revenue and LOL for the network study . . . 64 4.9 Curtailment in the network scenario and transformer T5 . . . 65 4.10 Imports and exports for the network analysis and unit T5 characteristics 66 E.1 3 winding transformer equivalent . . . 91

(13)

List of Tables

2.1 Aging rate constants . . . 5

2.2 Reaction parameters of Kraft cellulose paper . . . 6

2.3 Current and temperature limits for loading beyond nameplate . . . 14

3.1 Available data of the transformers to study . . . 26

3.2 Location 1 nearby weather stations . . . 26

3.3 Available weather stations and error in temperature and wind speed for the five different study locations . . . 32

3.4 Transformer specifications . . . 37

3.5 Transformer base aging, HST and loading . . . 38

3.6 HSF sensitivity for the population of transformers . . . 38

3.7 Transformer loss of life estimation based on different temperature mea-surements compared with the hourly taken meamea-surements . . . 46

3.8 Results for different loading and temperature scenarios . . . 48

3.9 Best temperature and loading scenario for the population of trans-formers excluding available load information . . . 48

3.10 Load study for the population of transformers . . . 49

3.11 Estimated and remaining lifetime of the population of transformers . . 50

4.1 Load duration curve for the new generator in T1 . . . 54

4.2 Load at which there is the first need for curtailment of power . . . 57

4.3 Load at which the expected aging is around 50 years . . . 58

4.4 Curtailment for the load in Table 4.3. . . 58

4.5 Cost of energy for the network analysis . . . 65

A.1 Transformer T1 and T2 specifications . . . 77

A.2 Transformer T3 specifications . . . 78

A.4 Transformer T5 and T6 specifications . . . 79

C.1 Original wind power scenarios for Location 1 . . . 86 xii

(14)

C.2 Reduced wind power scenarios for Location 1 . . . 86

D.1 Two winding transformers . . . 87

D.2 Bus data of the test system . . . 88

D.3 Generation data of the test system . . . 88

D.4 50 kV lines parameters . . . 89

D.5 Three winding transformers parameters . . . 89

(15)

Chapter 1 Introduction

Electric utilities face challenges related to better utilization of their infrastructure. A rapid increase in demand and connection points to the grid, the integration of in-termittent renewable generation and assuring a reliable supply of energy are among them. These challenges require the implementation of short and long term econom-ically feasible solutions to adapt to rapid changes in the network.

The power transformer is one of the most important components in a substation. It is the most expensive component and represents a bottleneck in terms of relia-bility; a power transformer failure impacts heavily the economics of power system operation [1]. Transformer aging and operational limits are primarily determined by insulation degradation, which is mainly determined by the winding hot spot temper-ature in oil-immersed transformers[2]. Loading conditions and weather conditions determine the heat flow in the transformer. As weather conditions change with time, the transformer capacity and life expectancy are varying as well.

Dynamic transformer rating (DTR) is a strategy to further extend the capacity of the transformer to meet the needs of a changing network. DTR has been defined as ”the maximum loading which the transformer may acceptably sustain under time-varying load and/or environmental condition” [3]. In this way, the transformer has a variable rating according to real-time measurement or estimates, without affecting its the life expectancy. If DTR is used, it is possible to use the transformer in a more efficient way by loading it to its true potential. Ultimately, it allows a higher loading, increases the use of the transformer with varying loads, and allows rapid deployment of new network connections [4].

Wind generation is highly volatile due to its dependency on wind speed. In many cases, the wind park transformers are designed for the peak load production of the farm [5]. This presents an efficiency problem because the transformer is not used at its full extent and operates below its nameplate rating 90 % of the time [6]. The im-plementation of DTR benefits a wind park as the transformers can be used at a higher extent and allows the expansion of an existing wind farm with no extra investment on new transformers. This project continues the previously research on thermal trans-former modelling, DTR applications, reliability and wind energy [7][8][9][10][11]. It

(16)

aims to define a method to specify the limits to which already installed transformers can be used for the expansion of wind parks based on DTR.

DTR for wind power applications has a considerable potential for the benefit of society. First, it is a more efficient use of transformers and allows a more sustainable transformer manufacturing because it reduces the material, energy and land required for the construction and installation of a new transformer. Second, a further incorpo-ration of renewable energy sources (RES) in the network allows a more flexible energy production and contributes to the decarbonization of the energy production. Third, it allows a faster deployment of projects and has the potential of reducing transmis-sion losses in the network depending on the configuration. An ethical consideration of the impact of expanding wind power projects on nearby communities that might not get a direct benefit from new generation is of concern. Additionally, there might be more profitable uses of land than wind power generation [12] .

In this document, Chapter 2 is a literature review on transformer thermal model-ing, DTR studies and applications, wind power load characteristics and grid expan-sion. Chapter 3 develops a method to make an assessment of the transformer aging based on the available data: first it estimates the weather conditions in the substa-tion based on nearby substasubsta-tion, then the relasubsta-tionship between wind speed estima-tion and the wind power on site is performed, followed by a sensitivity analysis on different inputs of the transformer thermal model, a study on different assumptions for the load, and an estimation of the current aging for the population of transform-ers. Chapter 4 explores the expansion scenario of the wind parks for the population of transformers. It starts by determining the expansion limits of the transformers and the expected lifetime under different thermal restrictions, followed by the study of maximization of wind power expansion in a distribution grid, and the financial ben-efits of DTR. Finally, Chapter 5 gives conclusions of the study and suggestions for the distribution system operators (DSOs) and manufacturers for the implementation of DTR, and future studies for academia.

This project is a joint project between the QED Asset Management group at KTH, ABB AB and E.ON Energidistribution AB under the context of SweGRIDS, where E.ON provides information on the population of transformers and ABB gives tech-nical knowledge in transformer theory.

(17)

Chapter 2 Literature review

2.1 Transformer basics

A transformer is a voltage changing device composed by a primary and a secondary winding, interlinked by a magnetic core. Electrical insulation, that can be in the form of oil and paper, is required to isolate the electric potential of each phase. Due to ther-mal losses of operation, a cooling system is also required. These two characteristics limit the maximum power a transformer can operate at.

The losses in a transformer can be split into no-load losses and load losses. The no-load losses are related to the magnetization losses in the transformer. This can be divided into eddy losses, produced by currents within the lamination of the core, and hysteresis losses consequence of the constant reversal of magnetization. Load losses are product of the electric resistance of the windings and stray losses. The resistance losses are the product of the square current and the resistance of the windings, I2_R_, and stray losses are caused by the leakage flux due to high currents. Stray losses are uneven and can cause hot spots when the flux is excessive, affecting the overall lifetime of the transformer [13] [14].

Insulation is required when there is a difference in electric potential between two points. The short distance between phases in a power transformer requires materi-als with dielectric strength to assure proper insulation. Large power transformers usually use paper as an insulating material, mainly kraft pulp paper. The dielec-tric strength of paper is related to the cellulose structure that is dependent on the molecule density of the structure. Additionally, nitrogen may be added to the cel-lulose chain to thermally upgrade the paper (i.e. increase the temperature the paper can resist). The highest temperature in the transformer is called the hot-spot temper-ature (HST). Given uniform moisture level in the transformer, it is the section of the transformer that experiences the highest degradation. The temperature of the trans-former is a combination of losses and oil flow. Due to transtrans-former construction, the highest electric field and losses are present in the top and bottom of the transformer. The HST tends to be on the top of the transformer, but it is not always the case. The temperature at which the paper presents a unitary aging (i.e. 1 day/day of the total

(18)

lifetime) is the rated hot-spot temperature. [15] establishes a hottest-spot temper-ature of 98◦C for non-thermally upgraded paper and 110◦C for thermally upgraded paper.

There are methods to control the temperature of the transformer and accelerate the dissipation of heat. The basic refrigeration starts by cooling the fluid at the radia-tor by heat exchange with the ambient. Then, the fluid goes up in the winding ducts, where the fluid absorbs the heat generated by the core and windings. The fluid exits with the top duct temperature and goes into the radiators. Pumps and fans can be used to increase the thermal exchange with the environment. A four letter system is used to describe the transformer cooling: i) the internal cooling medium can be liquid with flash point below or equal to 300◦ C (O), liquid with flash point above 300◦C (K) or without measurable flash point (L); ii) the internal cooling mechanism can be natural (N), non-directed flow (F) or directed flow (D); iii) the external cooling medium can be water (W) or air (A); iv) the external cooling mechanism can have nat-ural convection (N) or forced convection (F). As an example, an ONAF transformer has oil-natural ail-forced cooling[16].

2.2 Transformer aging rate and insulation

lifetime

When a transformer is overloaded, it may fail for two reasons: electrical breakdown or mechanical instability. An electrical breakdown can be caused by bubble formation in the oil or the reduction of the dielectric strength on paper due to the accelerated split of cellulose chains. The mechanical instability is produced by a reduction of mechanical strength of windings and coil deformation [17].

There are three main processes that affect the degradation of insulation paper: hydrolysis, oxidation, and pyrolysis. These processes are a function of the tempera-ture, moisture content, and oxygen content. Microcalorimetric studies have shown that the hydrolytic generation of cellulose is more temperature dependent than ox-idation [2]. With this in mind, under the same insulation paper conditions, higher temperatures results in higher aging. In a transformer, it is presented in the hot spot [18].

A measurement used for determining the quality of the paper is the degree of poly-merization (DP). DP is the average number of glycosidic rings in a cellulose macro-molecule and at the start of operation is usually 1000 DP. The number of rings is reduced with aging, thus reducing the paper mechanical and dielectrical strength. [2] states that a reduction to 35% retained tensile strength, or a reduction to 200 DP which is correlated with the retained textile strength, indicates the end of life of the insulation paper.

(19)

2.2. TRANSFORMER AGING RATE AND INSULATION LIFETIME 5 The relationship between temperature and insulation life is modeled with the Ar-rhenius reaction rate equation [15]. If the life of the insulation is treated as a per unit quantity, the per unit life, (PUL), is given by equation (2.1).

P U L = Aexp ( B θh+ 273 ) , [p.u.] (2.1) where A and B are empirical constants, and θh is the HST in [◦C]. Some values for

B based on different experimental conditions and end of life criterion are shown in Table 2.1. It is important that these values are experimental, and are not correlated between them.

Table 2.1: Aging rate constants [15]

Reference End Criterion B

Dakin[19] 20% tensile strength retention 18,000

Sumner [20] 20% tensile strength retention 18,000

Head [21] Mechanical/DP/ gas evolution 15,250

Lawson [22] 10% tensile strength retention 15,500

Lawson [22] 10 % DP retention 11,350

Shroff [23] 250 DP 14,580

Lampe [24] 200 DP 11,720

Goto [25] Gas evolution 14,300

ASA C57-92-1948 [26] 50 % tensile strength retention(θ = 120− 150◦C) 14,830

IEEE Std C57-92-1981 [27] 50 % tensile strength retention 16,054

IEEE Std C57-91-1981 [28] DT life test 14, 594

If a rated condition of aging is defined, it is possible to get the relative aging rate,

V, with equation (2.2). V = A Ar exp ( 1 Rc ( Ea,r θhr+ 273 − Ea θh+ 273 )) , (2.2)

where A is a paper related pre-exponential value in [1/h], AR is the rated A, Ea is

the required activation energy in [kJ/mol], Ea,r is the rated Ea, θhr is the rated hot

spot temperature in [◦C], Rc is the ideal gas constant, and θh is the actual hot spot

temperature in [◦C]. Ea= Ea,rand A = Aras it is assumed that the moisture content

does not change in time. The values of Ea and A for thermally upgraded and

non-thermally upgraded paper are shown in Table 2.2. Lower temperatures have lower aging rate than reference, whereas, higher temperatures result in a higher aging rate.

(20)

Lifetime can be halved or double for every 6◦Cto 8◦C. Thus, having a good estimation on the HST is fundamental to have a proper aging calculation.

Table 2.2: Required activation energy (EA) and environment factor for oxidation and hydrolysis of Kraft cellulose for thermally upgraded paper [2]

Paper type Parameter 0.5%H2O 1.5%H2O 3.5%H2O With Air

Non-thermally EA[kJ/mol] 128 128 128 89

upgraded paper A [h−1] 4.1· 1010 _1.5_{· 10}11 _4.5_{· 10}11 _4.6_{· 10}5

Thermally upgraded EA[kJ/mol] 86 86 86 82

paper A-value[h−1] 1.6· 104 3.0· 104 6.1· 104 3.2· 104 [15] has defined equation (2.3) for the relative aging of non-upgraded paper and equation (2.4) for thermally upgraded paper. The expected lifetime of a transformer is 20.5 years according to [29]. V = 2(θh−98)/6_, _(2.3) V = e ( 15000 383 − 15000 θh+273 ) . (2.4)

The loss of life (LOL) over a period of time is calculated with equation (2.5).

LOL =

∫ t2

t1

V dt, [h] (2.5)

[2] explores the estimation of present stage of aging based on laboratory experience. The present DP is estimated base on the starting value and the total chain scissions with equation (2.6).

DPpresent =

DPnew

ηT ot+ 1

, (2.6)

where DPpresent is the degree of polymerization of insulation at the time of the

analy-sis, DPnewis the DP value when the transformer is set in operation and ηT otthe total

chain scissions. ηT otis calculated with equation 2.7.

ηT ot = DPnew ( AOxie −EOxi RcΘ _{+ A} Hyde −EHyd RcΘ ) t· 365 · 24 (2.7) , where EOxiand EHydare the activation energy for oxidative and hydrolytic material

aging in [KJ/mol], AOxi and AHydare the corresponding contamination in paper for

oxidation and hydrolytic process, respectively, in [1/h], R is the molar gas constant, Θis the operating temperature in [K], and t is the time in service in [h].

(21)

2.2. TRANSFORMER AGING RATE AND INSULATION LIFETIME 7 Even though estimating the current DP value based on oil contamination mea-surements is a great indication on the aging and insulation conditions, the methods used for the sampling of oil have limitations which may not accurately indicate the condition of aging. A sample of oil might not be significant for describing all the oil in the transformer. Additionally, there is a constant interchange of oxygen and water in the insulation paper during operation[2]. This equation is informative, but further analysis of the topic is not in the scope of this project.

Studies on risk assessment of transformer failure and the economic repercussions based on HST are explored in [7]. The impact of LOL as a function of HST is given in equation (2.8). ImLOL = { ∆t t0Ct, θh ≤ θh,r 0, otherwise, [SEK] (2.8)

where ImLOLis the impact of LOL in [SEK], ∆t is the percentage of life difference for

the actual and reference value, Ctis the cost of rewinding the transformer in [SEK],

θh,ris the reference hot spot temperature in [◦C] and θhis the actual hot spot

temper-ature in [◦C].

Additionally, the impact of dielectric failure, ImDF, is defined by equation (2.9).

ImDF =

{

Ct, if a failure occurs

0, otherwise , [SEK] (2.9)

The risk associated with insulation, Risk(ImLOL|Load) in [SEK], is calculated

with equation (2.10).

Risk(ImLOL|Load) =

∫ T

0

∫ θhs

θh,r

P r(θh|Load) · ImLOL(θhs)dθdt, [SEK] (2.10)

where T is the period of time to study in [h] and P r(θh|Load) the probability of failure

at temperature θhgiven the value of load.

The risk of dielectric failure given the, Risk(ImDF|Load) in [SEK], is calculated

with equation ( 2.11 ). Risk(ImDF|Load) = ∫ T 0 ∫ θhs θhr P r(θhs|Load) · Hz(t|θh)· ∆t · ImDF(θhs)dθdt, [SEK] (2.11) where Hz(t|θ) is the hazard function determined by the probability density function

f (t)and cumulative distribution function F (t), which follow a Weibull distribution function depending on temperature. Hz(t|θ) is obtained from equation (2.12).

Hz(t1|θ) =

f (t1) 1− F (t1)

(22)

f (t) = 1 σte x−ex1 , (2.13) F (t) = 1− e−x1_, _(2.14) x = ((log(t)− µ)σ), (2.15) µ = B θhr − log(V ), (2.16)

where x is a stress as a function of time, σ is the scale parameter for the Weibull distribution (σ = 1/β), β is the shape parameter of the insulation material, and B the activation energy over the ideal gas constant. For distribution transformers, the shape parameter for dielectric strength in mineral oil is set to 3.62 based on acceler-ating aging tests and maximum likelihood method [30].

The total risk , RiskT OT, in [SEK] is obtained from equation (2.17).

RiskT OT = Risk(ImDF|Load) + Risk(ImLOL|Load), [SEK] (2.17)

2.3 Transformer thermal models

There are several models to evaluate transformer thermal behavior. These are mainly used to estimate the HST and the top oil temperature. Depending on the available information and the assumptions made, each model presents an advantage. Figure 2.1 shows a graphical interpretation of the oil and winding temperature. The HST is obtained by multiplying the gradient between oil and winding, by the hot-spot factor (HSF) H.

[15] presents two thermal models: IEEE top oil rise model or Clause 7 model, and IEEE bottom oil model or Annex G model. The first aims to calculate the oil and winding temperature for changes in the load without requiring an iterative proce-dure. This model does not consider changes in the ambient temperature and does not make a precise modeling of the load. The results of this method have proven to underestimate the HST under overload conditions, which lead to an underestimation of aging [3].

Annex G is a more complex model compared to Clause 7 model and makes a more accurate representation of transient loading conditions. This model considers the type of liquid, cooling mode, oil viscosity, resistance changes due to temperature change, ambient temperature changes and load changes. This model is more data-intensive compared with Clause 7 results.

IEC 60076-7 2nd edition model presented in [18] is the loading guide for mineral-oil-immersed power transformers from the point of operation temperatures and ther-mal aging. Two solutions of the differential equation are presented: the exponential

(23)

2.3. TRANSFORMER THERMAL MODELS 9

Figure 2.1: Transformer’s thermal diagram[18]. The y-axis represents the relative position and the x-axis the temperature. gris the the average-winding-to-average oil temperature in [◦C], H is the hot-spot factor and θhthe winding hot-spot temperature in [◦C].

equation model and the difference equation model. The step response of both solu-tion methods is the same as they come from the same set of differential heat transfer equations. The difference equation method is more suited for on-line monitoring of the transformer according to this standard.

A series of models were developed considering a thermal circuit equivalent of the transformer. These aimed to have a more accurate transformer’s temperature calcu-lation during the transient state based on data from the heat run test. A first model is proposed in [31]. This model is later improved in [32][33], in which the thermal ca-pacitances of the different components in the system are modeled and calculated. A more accurate calculation of the thermal constants of oil and windings is introduced. The authors claim better results than the IEEE Annex G method when transformers lack external cooling. A simplified model which only requires ambient temperature, top-oil and winding time constant, DC and eddy losses and the hot-spot temperature rise over ambient at rated current is proposed in [34].

Several studies comparing the methods of calculation have been done in [4], [35], [36], and [32]. The basic assumptions for all the models are: the oil temperature rises linearly from bottom to top; the temperature difference between the winding and the oil is constant along the windings and the temperature changes with the ambient temperature. The first parameter of comparison is the required data. The most data-intensive model is [32] model, followed the IEEE Annex G model; it is because they consider oil viscosity variation and have a more comprehensive modeling of top- and bottom-oil temperatures.

In terms of performance, the least accurate method is the IEEE Clause 7 model as it does not consider changes in load and ambient temperature. This is a significant

(24)

drawback for DTR applications and therefore is disregarded for the study. The com-parison between IEC model and Annex G is the most widely explored. In [35], IEC exponential solution method presents higher fluctuations compared with IEC differ-ence method despite coming from the same set of equations. In [4], IEC models and Annex G model present an error compared with the HST measured values. In [36], a seasonal comparison is done: in summer both models yield a similar and accurate es-timation of the HST. In winter, the models underestimate the HST as the IEC model is based on constant parameters and Annex G model does not consider changes in the operating oil volume in sub-zero temperatures. [8] and [9] calculate the difference between Annex G and IEC model calculations compared with an indirect HST mea-surement. Finally, [32] model has better results for transformers without external cooling and only applies zigzag cooling according to the authors.

Given that both Annex G model and IEC model yield similar results in terms of HST calculation, and that IEC model is less data-intensive compared with the IEEE model, it is considered for the calculations in this study. A more detailed description of the model is presented in subsection 2.3.1.

2.3.1 IEC thermal model

The block diagram representation of the IEC model is shown in Figure 2.2. The inputs of the model are the load K and the ambient temperature θa, which is used to calculate

the hot-spot temperature θh. It is also possible to obtain the top-oil temperature from

direct measurements instead of calculating it; in Figure 2.2 it is represented by the dotted line. The differential equation for the top-oil temperature is given by equation (2.18). [ 1 + K2_R 1 + R ]x (∆θor) = k11τo dθo dt + [θo− θa] , [K] (2.18)

where K is the loading in [p.u.], R is the ratio of load losses at rated current to no-load losses, x is the exponential power of total losses vs the top-oil temperature rise, ∆θor

is the top-oil temperature rise in steady state at rated losses in [K], k11is a thermal model constant, τo is the oil time constant in [min], θo is the top-oil temperature in

[◦C ] and θais the ambient temperature in [◦C].

The hot-spot temperature rise is given by the sum of two differential equations as shown in equation (2.19).

∆θh = ∆θh1− ∆θh2, [K] (2.19)

where ∆θhis the hot spot oil gradient in [K], ∆θh1is the differential equation defined

in equation (2.20), and ∆θh1is the differential equation defined in equation (2.21).

k21· Ky· ∆θhr = k22· τw· d∆θh1 dt + ∆θh1, [K] (2.20) (k21− 1) · Ky · ∆θhr = (τo/k22)· d∆θh2 dt + ∆θh2, [K] (2.21)

(25)

Figure 2.2: IEC 60076-7 block diagram representation of the differential equation transformer ther-mal model[18]. The s represents the differential operator

where y is the winding exponent, k21and k22are thermal model constants, ∆θhris the

rated hot-spot-to-top oil gradient at rated current in [K], and τw is the winding time

constant in [min].

Equation (2.22) gives the final hot-spot temperature .

θh = θo+ ∆θh, [°C] (2.22)

The recommended thermal characteristics for the model (i.e. x, y, k11, k22, τo and

τw) are given in [18].

The set of differential equations can be solved with an exponential equation and a difference equation. The latter is the selected method for this study as it is better suited for on-line monitoring due to applied mathematical transformation [18]. The first step is to assume a small time step D that should be at least half of the smallest time constant. Equation (2.18) can be rewritten as equation (2.23).

Dθo = Dt k11τo [( 1 + K2R 1 + R )x ∆θor− θo− θa ] , [K] (2.23) In this case, the operator D indicate a difference in the associated variable for each time step Dt. Then, nth_{value of Dθ}

ois calculated from the previous one with equation

(2.24).

θ(n)_o = θ(n_o −1)+ Dθ_o(n), [°C] (2.24) Equations (2.20) and (2.21) are rewritten to include the difference factor as equa-tion (2.25) and (2.26), respectively.

D∆θh1=

Dt k22τw

(26)

D∆θh2=

Dt

(τo/k22)

[(k21− 1) ∆θhrKy− ∆θh2] , [K] (2.26)

Following the logic of equation (2.24), equations (2.25) and (2.26) can be solved for the nth_{time step with equations (2.27) and (2.28).}

∆θ_h1(n)= ∆θ(n_h1−1)+ D∆θh1, [K] (2.27)

∆θ_h2(n)= ∆θ(n_h2−1)+ D∆θh2, [K] (2.28)

Equation (2.29) gives the total hot-spot temperature rise.

∆θ_h(n)= ∆θ_h1(n)− ∆θ_h2(n), [K]. (2.29) Finally, equation (2.30) gives the hot-spot temperature.

θ_h(n)= θ_o(n)+ ∆θ_h(n), [◦C] (2.30)

2.3.2 Calculation of the winding time constant

Both IEEE and IEC standards inform about different methods to calculate the ther-mal time constant for each specific transformer. IEC Annex E defines the time con-stant with equation (2.31).

τw =

mw· cw· gr

60· Pw

, [min] (2.31)

where gris the winding-to-oil gradient at the load considered in [K], mwis the mass

of the winding in [kg], cwis the specific heat of the material in [W s/(kg· K)] (390 for

Cu and 890 for Al), and Pwis the winding loss in [W ].

The winding time constant can be obtained from the heat-run test according to IEEE Annex G using equation (2.32).

τw =

mwcw(θwr− θdo,r)

Pe+ Pw,r

, [min] (2.32)

where θwris the average winding temperature at rated load in [◦C] , θdo,ris the average

temperature of oil in the cooling ducts at rated load in [◦C], Peare the eddy losses of

winding at rated load in [W ], and Pw,r are the winding resistive losses at rated load

in [W ]. Additionally, [15] suggests assuming a value for τw = 5[min]for all types of

cooling.

2.3.3 Calculation of oil time constant

IEEE, IEC and [32] models suggest methods to calculate the oil time constant. Clause 7 calculates the oil time constant based on the different component weight of the com-ponents of the transformer. First, the thermal capacity C for natural oil and forced-oil modes is calculated with equations (2.33) and (2.34), respectively.

(27)

C = 0.1323· (mc+ mw) + 0.0882· mT + 0.3513· vo for natural oil, [W · h/K] (2.33)

C = 0.06· (mc+ mw) + 0.04· mT + 1.33· vofor forced oil, [W · h/K] (2.34)

where mcis the mass of core in [kg], mwis the mass of the coil assembly in [kg], mT is

the mass of the tank and fittings in [kg], and vois the volume of oil in [l]. The top-oil

constant at rated load is obtained with equation (2.35).

τo=

C· ∆θor

Pr

, [h] (2.35)

where ∆θoris the top-oil rise over ambient temperature at rated load in [◦C], and Pr

is the rated loss in [W ].

A method suggested by the [18] in Annex E is based on the IEEE Clause 7 model and [37]. Equation (2.36) gives the thermal capacity.

C = (cw· mw+ cc· mc+

2

3cT · mT + ko· co· mo)/60, [W · h/K] (2.36) where cwis the specific heat capacity of the winding material (390 for Cu and 890 for

Al) in [W·s/kg ·K], mwis the mass of the coil in [kg], ccis the specific heat capacity of

the core (equal to 468) in [W·s/kg·]K, mcis the mass of the core in [kg], cT is the heat

capacity of the tank and fitting (equal to 468) in [W · s/kg · K], mT is the mass of the

tank in [kg], cois the specific heat capacity of the oil (equal to 1800) in [W· s/kg · K],

mo is the mass of oil in [kg], and ko is a correction factor for the cooling mode equal

to the ratio of average to maximum top-oil temperature rise. The time oil constant can be calculated using equation (2.35).

[32] suggests a model for the oil constant which is corrected for the relative losses of each component. The thermal capacity is calculated with equation (2.37).

C = (Yw· mw· cw + Yc· mc· cc+ Yst· mT · cT + Oo· mo· co)/60, [W · h/K] (2.37)

where Yw is the portion of winding losses in the total transformer losses, Yc is the

portion of core losses in the total transformer losses, Yst is the portion of stray losses

in the total transformer losses and Oo is a correction factor for the cooling mode:

0.86 for ONAF, ONAN and OFAF, and 1.0 for ODAF. Equation (2.35) is used again to determine the transformer oil constant.

2.3.4 Overload limits

Even if it would be possible to overload the transformer above its nominal value, there are limitations on current and temperature above the loading limit. Section 7 of [18]

(28)

explores these limitations in detail. One of the most important effects is that hot-spot temperatures exceeding 140◦C for moisture content of 2 % can create gas bub-bles which affect the dielectric strength of the transformer. High currents may affect transformer accessories and cause undesired oil expansion that increase the stress in the oil tank.

The transformer loading operation can be classified in: normal cyclic loading in which the transformer is expected to operate at rated conditions, long-time emer-gency loading resulting from prolonged outage of some system components that will not be connected before the transformer reaches a new and higher steady-state tem-perature, and short-term emergency loading, which is a heavy loading of a transient nature of one or more unlikely events which seriously disturb normal system loading. The limitations for each loading are presented in Table 2.3.

Table 2.3: Current and temperature limits applicable to loading beyond nameplate rating for medium and (large) power transformers [18].

Limit Parameter Normal Long-time Short-time Current [p.u.] 1.5(1.3) 1.5(1.3) 1.8(1.5) Winding hot-spot temperature and other metallic parts

in contact with cellulose insulation material [◦C] 120 140 160 Other metallic hot spot temperature [◦C] 140 160 180 Top oil temperature [◦C] 105 115 155

2.3.5 Temperature direct measurement

The hot-spot factor and location can be calculated during the transformer design pro-cess by running simulations. However, due to manufacturing variables, the exact lo-cation is difficult to determine and the magnitude may vary from the design. The way to have the most accurate representation of the hot-spot temperature is the installa-tion of fiber optic sensors in the radial spacers of the winding after the simulainstalla-tion to determine the hot-spot factor. The location of the sensors should be selected so that the maximum measured temperature rise is close enough to the real hot-spot temperature rise for safer operation of the winding.

For the temperature rise test, the recommended number of sensors is determined by the leakage flux [18]. For a leakage flux greater than 400 mWb/phase 8 sensors per winding should be used; if the leakage flux is between 150 mWb/phase and 400 mWb/phase, 6 sensors should be used; if the leakage flux is below 150 mWb/phase, 4 sensors per winding are recommended. The sensors should be inserted in the phase where the warm resistance curve is recorded. Nonetheless, the number of sensors should be selected according to the application. If the transformer is already manu-factured, thermocouples can be installed in the oil-pockets of the transformer casing and estimate indirectly from the top-oil temperature.

(29)

2.4. DYNAMIC TRANSFORMER RATING 15

2.4 Dynamic transformer rating

Transformer loading rating is determined by the operation of the device to be within its design temperature. Dynamic transformer rating makes the rating of the devices adaptive based on loading and environmental conditions. Three principles justify DTR: varying ambient temperature, the cumulative aging process and the oil thermal time constant.

In the traditional rating approach, an ambient temperature of 30◦C during a 24 h cycle is assumed. As shown in the thermal models, if the ambient temperature is below the rated temperature value, the transformer could be loaded to a higher limit without affecting the insulation lifetime[3][38]. Moreover, considering that aging is a cumulative process, the HST could be surpassed over some periods of time if the total aging of the transformer within a 24-hour period is still controlled. Intermittent loads can also benefit from DTR due to the inertia associated with the heating process. If the peak in the load is short enough (smaller than the oil time constant), the transformer won’t reach the thermal limit even if it is overloaded in terms of current.

To extract the full potential of a transformer by using DTR, an accurate real-time measurement of the load, ambient temperature, transformer’s oil temperature, and the transformer’s HST is desired. The possibilities of real-time measurements in a SCADA system and the employment of fiber optic temperature sensors inside the transformers allow greater accuracy of the method [3] [39].

2.4.1 Studies for implementation in wind power

[8] and [44] explore the economic benefits of implementing DTR in wind park ex-pansion. The examined transformers show little signs of aging and could increase their loading considerably without affecting the expected aging. [8] also analyzes the effect of load increase in the transformer in terms of aging. [10] performs an analysis of DTR from a network perspective. It focuses on how increasing the wind power ca-pacity affects a meshed network performance in terms of voltage stability and consid-ering a probabilistic reliability study. The conditions that caused high contingencies are isolated for future analysis. In [7], authors do a comparative net present value (NPV) calculation to determine the profitability of replacing a 19.4 MVA transformer with a 16 MVA dynamically rated transformer. [11] is a joint study of dynamic line rat-ing (DLR) and DTR day-ahead dispatch optimization problem based on dc-optimal power flow in the IEEE RTS 24 bus system which concludes that the joint strategy of DLR and DTR unlocks line and transformer constraints to a further extent.

2.4.2 Implemented project- FALCON

The flexible approaches for low carbon optimized networks (FALCON) is a project by the British company Western Power Distribution (WPD). The project is developed in Milton Keynes in England to increase the capacity during peak hours and introduce

(30)

renewable energy in the system. The introduction on dynamic rating, both in lines and transformers, is one of the solutions. The study is done in a population of 16 transformers operated at 33/11 kV or 11kV/400V. DTR is implemented and the HST is set not to exceed the transformer expected lifetime. The available studies are [4], [35], [40] and [41]. The main findings of the study are:

• After a sensitivity analysis, the winding and oil time constant, and the top and hot spot temperature are the most relevant variables in the aging.

• There is not a direct pattern of seasonal change in the parameters.

• The accuracy of ambient temperature is fundamental for the calculation of the HST.

The capacity day ahead is done using hourly weather forecast and interpolated to obtain 48-hour points. The error between the prediction and the actual measurement is in the range [-0.02, 0.05] p.u. The main results of the DTR are:

• The calculated values compared with the rated values are within 4% and 90 % of the time.

• Outdoor transformers are better suited for DTR.

• Transformers can be run 10 % above nameplate in winter and below nameplate in summer to meet the required unitary lifetime.

• Reducing the temperature in indoor transformer buildings may increase the transformer lifetime.

2.4.3 Implemented project- Unison

Unison Network Limited, a distribution company of New Zealand, implements DTR for load planning and long-term asset management and investment study. A total population of 50 transformers is dynamically rated in their network. The IEC model is used for the calculation of the HST. Substation measurements are performed and set to the SCADA monitoring system. Some of the faced challenges are the use of a customized algorithm for each transformer, and the lack of heat-run test of the transformers. In the study, additional tests are made to determine the heat-run test characteristics of the transformer. It concludes that maximum capacity is reached in the winter, achieving a maximum of 150 % above the rated value. The average capacity in the warmer months is 140% above the nameplate rating [42][43]

(31)

2.5. WIND POWER CHARACTERISTICS 17

2.4.4 Experience with self learning expert systems

The Dutch DSO Alliander studies the use of Self Learning Expert Systems (SLES) for the dynamic rating of power transformers. First, a transformer model based on the heat dissipation model, which considers the heat transfer function, is developed. This model considers sun radiation and wind convection to make the heat transfer calcu-lations. As the power transformers do not have a heat-run test, they are performed for the transformers in operation to be used as input in the model.

The algorithm is used to determine a parameter optimization based on historic load, ambient temperature, and top-oil temperature. Then, a capacity factor for the transformer under different conditions is obtained. With the set of data of historic load, top-oil temperature, ambient temperature and, optimized surface factors, a database is built. The database is used to determine the new top oil temperature for the thermal model for each transformer [39]. Authors claim the model accurately represents the top-oil temperature and does not have underestimations that the IEC model might have. This model is highly intensive on data and communication and requires the disconnection of the transformer for parameter determination which is not feasible for many transformers in the system.

2.5 Wind power characteristics

Wind power generation in Sweden represented 10.2 % of the total electricity produc-tion in 2016, with around 6.4 GW installed and a producproduc-tion of 15.4 TWh [45]. Wind power has presented a high growth in recent years which is partly explained by the fast construction time compared with traditional generation; a 50 MW plant can be built within 6 months [46]. This puts a constraint to DSOs which must react rapidly to the installation of wind power.

The power of an air mass, PW, in W, that flows at a speed ν in m/s through an area

Asis given by equation (2.38) [47].

PW =

1 2ρAsν

3_{, [W ]} _(2.38)

where ρ is air density in [kg/m3_{]. Equation (2.39) gives ρ as a function of altitude.}

ρ(z) = P s0 RairΘ exp ( −gctz RairΘ ) , [kg/m3] (2.39)

where ρ(z) is the air density as a function of altitude in [kg/m3_{], P s}

0is the standard sea level atmospheric pressure (101.3 kPa), Rair is the specific gas constant for air

(287.05 J/kg· K), gct is the gravitational constant (9.81 m/s), Θ is the temperature

(32)

The theoretical maximum power extracted from wind, known as the Betz limit, is given by equation (2.40) [49]. PBetz = 1 2ρAsν 3_{· 0.59, [W ]} _(2.40)

The wind power curve has the shape shown in Figure 2.3. The cut in speed de-pends widely on the type of turbine. The wind turbine reaches rated power between 12 and 16 m/s, and the cut-out is in the range of 20-25 m/s [47]. A composite IEC power curve using data from different manufacturers is proposed in [52]. The classes depend on the average wind speed following [50].

The impact of adding additional wind power has positive impacts on power quality and operation. First, increasing the number of wind turbines reduces the turbulent peaks caused by gusts, ultimately providing a smoother power production. Under ideal conditions, the variation of power output varies as n−0.5where n is the number of generators [47]. Additionally, if the geographical area is sparse, the power output is also smoothed as the weather condition vary depending on the spot. The mean production of a power park is given by equation (2.41).

Pm =

∫ CIC

0

xfp(x)dx, [W ] (2.41)

where Pm is the mean power production in [W ], fp the probability density function,

and CIC the installed capacity in [W ]. There are multiple factors affecting the power

generation of a wind generator, including the turbine construction, the height, the terrain, and the local wind speed. Therefore, it is not possible to make an accurate forecast of the individual production of a turbine based on a group.

The production pattern of wind is clearly highly dependent on the wind resource at the site, therefore, seasonal and diurnal variation is different in every site. In average, the capacity factor of a wind park onshore is between 30% and 50%. The available wind resource varies from year to year and lies between±15% of the average long-term yearly production [48].

Extreme ramp rates recorded for a 103 MW wind farm are 4-7 % of capacity in a second, 10-14% of capacity in a minute and 50 to 60 % in an hour [51]. Significant variations are more likely to occur in the range of 25% to 75% of the capacity.

Predictability of wind power production is important for scheduling of units and operating the network. Predictions from 1 to 24 hours ahead are necessary for op-eration. Day-ahead predictions are required to schedule of the units. Short term predictions (1-2 hours) keep up for the optimal amount of regulating capacity at the system operator proposal. The error in forecasting can be presented with the mean absolute error (MAE) and the root-mean-square error (RMSE). MAE and RMSE are calculated with equations (2.42) and (2.43).

M AE = Σ

n

i=1|PP,i− PM,i|

(33)

2.6. WEATHER DATA ESTIMATION 19

Figure 2.3: Wind power curve Class III normalized to rated power

RM SE =

√

σn

i=1(PP,i− PM,i)2

n , [W ] (2.43)

where PP is the predicted power, PM is the measured power, and n is the number of

samples. The typical RMSE for a single wind power plant in Germany related to the total installed capacity has an average day-ahead error of 13.5%, 10% as a minimum and 20% as maximum [53].

The service life of a wind turbine is expected to be 20 years[47], with the possibility to increase the operating lifetime up to 30 years [54].

2.6 Weather data estimation

The Swedish Meteorological and Hydrological Institute (SMHI) is the entity in charge of gathering meteorological data from weather stations across the country. Ideally, for DTR, the ambient temperature should be measured on site to reduce the mea-surement error. In reality, the substations are not located next to a weather station. Thus, an estimation based on nearby stations should be made.

There are various factors that might affect the temperature on-site such as the radiation, precipitation, pressure, topology and wind speed. Considering these fac-tors increases complexity without adding extra information to the study. A method to calculate the temperature on site is the inverse distance weight method (IDW). It is a simple distance weight estimate, which assumes that nearby stations represent in a better way the weather conditions of a specific site. [56] claims to obtain good results using the five nearest weather stations. The measurement estimate is given by equation (2.44).

(34)

ˆ

x = Σiwixi

Σiwi

, (2.44)

where ˆxis the IDW estimate, wiis the particular measurement of the ith station and wi

is the weight function derived from the inverse distance between the point of interest and the estimated location. wi is defined in equation (2.45).

wi =

1

d(y, yi)p

, (2.45)

where d is the distance between y and yi in [km], and p is a shape parameter. [56]

uses a simple IDW and [9] a squared method. For this analysis, a simple weighting is used.

Additionally, the air temperature changes with height. A correction factor is in-troduced in equation (2.46).

ˆ

xi

′

= xi− (h − hi)γ, [°C] (2.46)

where x′_iis the measured value after correction, h is the site height in [km], hithe

mea-surement station height in [km], and γ the Lapse rate; it takes a value of 6.5◦C/km

for the Troposphere [57].

The wind speed data recorded in the weather stations in Sweden is usually per-formed 10 meters above the ground. Yet, the wind turbines are at least 100 meters above the ground. The relationship between wind speed and height follows the wind power law profile [58], that is given by equation (2.47).

ν(z) ν(zr) = ( z zr )α , (2.47)

where ν(z) is the wind speed at height z in [m/s], νzr is the reference wind speed at

height zrin [m/s], and α is the power law exponent. There are several variables that

affect the wind speed with elevation such as the atmospheric stability, surface rough-ness, change in surface conditions and the terrain shape, which ultimately affect the selection of α. A value of α of 1/7 is proposed by [59], however, the value of α is highly variable. [60] proposed a method to calculate the value of alpha with equation (2.48).

α = 0.37− 0.088 ln (νref)

1− 0.088 ln(zref

10

) (2.48)

[61] proposed the correlation given in equation (2.49).

α = 0.096log₁₀z0+ 0.016 (log10z0) 2

+ 0.24, (2.49)

for 0.001m < z0 < 10m, where z0 is the surface roughness in m. [58] presents some values for roughness. The value for crops is 50 mm, for many trees, hedges and few buildings 250mm, and for forest and woodlands 500 mm.

(35)

2.7. GRID PLAN STUDIES 21

2.7 Grid plan studies

There are two main methods to perform generation expansion in grid studies: the single node study and the network study. Single node study considers only the ex-pected increase in demand. It aims to determine the exex-pected energy not supplied and the expected generation cost of the system given the availability of generators. This methodology does not consider network limitations. It is based on the equiv-alent generation of a power plant which is given by the convolution of states of the plant as shown in equation (2.50).

˜ Fg(x) = Ng ∑ i=1 pg,iF˜g−1(x− xg,i) (2.50)

, where ˜Fg is the load duration curve, Ng is the number of states of the power plant,

pg,iis the probability of state i, Fg−1is the equivalent load duration without the power

plant and xg,i is the outage compared to the installed capacity in state i [62].

For a wind power turbine, the number of generation scenarios can be large. Hav-ing a high number of scenarios increase the computational time considerably. Sce-nario reduction using probability distance aims to reduce the number of sceSce-narios to obtain an optimal solution close to the original scenario set. Considering the sce-nario Ω, it aims to determine a new scesce-nario subset Ωssuch that the reduced

proba-bility distribution is the closest to the original distribution. Two widely used heuristic algorithms are backward reduction and forward selection [63] .

Generation expansion considering the network sets network restrictions. It is use-ful to determine the effect that new generators have on the network. DC power anal-ysis is performed when only the power flow in the lines is of concern disregarding reactive power and voltage limitations. This method is a faster alternative to conven-tional AC power flow, which is based on non-linear differential equations and is used to determine reactive power flow, bus voltage magnitude and losses [64].

2.8 Conclusions from literature review

The literature review shows that a significant advance on DTR has been done. It is determined that the loss of life is the product of the HST and the insulation paper condition. Ideally, there would be a direct measurement of this temperature. How-ever, the temperature measurement is not always available and a calculation must be performed. The IEC thermal model has proven to yield acceptable results, but there is still a degree of uncertainty in the measurement; a safety margin should be con-sidered for the analysis. From the literature studied, the maximum allowed HST is set to the standard 110◦C. Yet, the standard suggests that the temperature can be increased up to 140◦C without any significant effects except an increase aging rate. Moreover, considering that the current limitations are given by oil expansion limits

(36)

and accessories, there is a reason to believe that these limits can be exceeded in DTR units if the corresponding modifications to the tank and accessories are made.

In terms of direct measurement, even if there is a fiber optic in the transformer, the HST should be calculated in the heat-run test for scheduling and used as a backup in case the measurement is not available during operation.

The characteristics of wind power, especially the variability in time, the low capac-ity factor and the short project lifetime, makes it a good candidate for DTR implemen-tation. An ideal analysis requires a small step to capture the variations of wind power in time. Nonetheless, the wind power information on site is not always available and some information is assumed.

Chapter 3 proposes a method to determine the loss of life estimation based on the transformer thermal model and considering wind power characteristics. It describes the results of sensitivity analysis for the transformer parameters and a method to handle temperature and load uncertainty. Chapter 4 uses the concept of accumulated aging and takes a grid plan approach to determine the optimal wind park expansion and calculate the benefit for society.

Dynamic transformers rating for expansion of expansion of existing wind farms

Dynamic transformers rating for

expansion of existing wind farms

OSCAR DAVID ARIZA ROCHA

of existing wind farms

Dynamisk lastbarhet hos transformatorer för expansion av

befintliga vindkraftparker

Abstract

Sammanfattning

Abbreviation

Symbols

Contents

List of Figures

List of Tables

Chapter 1

Introduction

Chapter 2

Literature review

2.1

Transformer basics

2.2

Transformer aging rate and insulation

lifetime

2.3

Transformer thermal models

2.3.1

IEC thermal model

2.3.2

Calculation of the winding time constant

2.3.3

Calculation of oil time constant

2.3.4

Overload limits

2.3.5

Temperature direct measurement

2.4

Dynamic transformer rating

2.4.1

Studies for implementation in wind power

2.4.2

Implemented project- FALCON

2.4.3

Implemented project- Unison

2.4.4

Experience with self learning expert systems

2.5

Wind power characteristics

2.6

Weather data estimation

2.7

Grid plan studies

2.8

Conclusions from literature review