Power system performance when implementing …kth.diva-portal.org/smash/get/diva2:1150174/FULLTEXT01.pdfPower system performance when implementing dynamic rating on a wind farm connected

IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 60 CREDITS

, STOCKHOLM SWEDEN 2017

Power system performance when implementing dynamic rating on a wind farm connected transformer

RIKARD KARLSSON

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING

Power system performance when implementing dynamicrating on a wind farm connected transformer

Kraftsystemanalys vid inforandet av dynamisk lastbarhetsmodell pavindkraftsansluten transformator

ISBN: 978-91-7729-554-9TRITA-EE 2017:139

Rikard Karlsson

Examiner: Patrik Hilber

Supervisors: Kateryna Morozovska, Malin Wihlen,

Olle Hansson, Tor Laneryd

Master ThesisKTH Royal Institute of Technology

School of Electrical EngineeringDivision of Electromagnetic Engineering

Stockholm, Sweden 2017

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I. ABSTRACT

In this study, dynamic transformer rating (DTR) is applied on a medium power transformer thatis in use in the regional transmission grid. The transformer’s rated apparent power is 63 MVA, itis connected between a wind farm at 22kV and the grid, Korsbarsdalen, at 135kV. Power systemanalysis are carried out on the grid, with the objective to test how DTR and increased wind poweraffects the grid performance with respect to reliability, voltage stability and active losses.

Historical measurements of ambient temperature and transformer loading is used to calculatefree transformer capacity based on unity life time loss. For the investigated transformer and giventime period the load can be increased without endanger transformer lifetime. The dynamicallyrated capacity exceeds the nominal capacity through the whole tested time period but DTR showsmost effective during winter when the ambient temperature is colder and therefore, has a coolingeffect on the transformer. DTR is used to calculate available transformer capacity but an increasedcapacity often comes with the expense of decreased lifetime and reliability. With the help of DTRthe current rate of transformer lifetime usage can be calculated and used as input to economicalanalysis where there is a trade of between reliability and profit from increased capacity.

Through the power system analysis procedure presented in this report it is possible to sortout the faults that are most probable to cause severe violations, this information can be used forefficient reinforcement of the grid. The contingency and reliability analysis can work as base tofind the solutions that will decrease the probability for violations most efficiently. Furthermore,the developed procedure can also be used when expanding the grid and to determine which gridalternative that will be most reliable.

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II. SAMMANFATTNING

I den har studien kommer en dynamisk modell for en transformators maxkapacitet anvandas isyfte att utvardera mojligheterna for utbyggnad av vindkraftsparken som ar kopplad till transfor-matorns lagspanningssida. Pa transformatorns hogspanningssida finns regionnatet, Korsbarsdalen.Med hjalp av den dynamiska modellen beraknas transformatorns varmaste punk. Dem varmastepunkten ar belagen pa ovre delen av transformatorns lindning. Det ar denna punkts temperatursom satter gransen for hur mycket strom som kan sandas genom transformatorn utan att resultera ioverhettning. Overstiger den varmaste punkten en kritisk temperatur finns risk for att transforma-torn livslangd forkortas. Konceptet dynamisk lastbarhet som bygger pa termiska modeller kallaspa engelska ,dynamic transformer rating (DTR).

Vidare utvarderas effekterna av DTR pa systemniva, Korsbarsdalens prestanda da DTR harimplementeras jamfors med det ursprungliga natets prestanda med avseende pa tillforlitlighet,spanningsstabilitet och aktiva forluster.

Historiska matvarden pa omgivningstemperatur och transformatorns last anvands for att beraknatransformatorns tillgangliga kapacitet, for det studerade tidsspannet kan transformatorn anvandasover dess nominella effekt. Pa vintern da omgivningstemperaturen ar lag kommer DTR till storstnytta, den kalla luften har en kylande effekt pa transformatorn vilket i sin tur betyder att en storrestrom kan sandas genom transformatorns lindningar utan att en kritisk temperatur uppnas.

Genom det presenterade tillvagagangssattet for systemkraft analyser kan de fel som har storstsannolikhet att resultera i allvarliga konsekvenser sorteras ut. Denna information kan anvandassom underlag for reinvesteringar saval som vid expandering av det befintliga natet.

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III. LIST OF VARIABLES

L loss of lifeV ageing rateΘh hot spot temperatureΘa ambient air temperatureΘo top oil temperature∆Θo top oil temperature rise over ambient∆Θh−o hot spot temperature rise over top oilqfe no load losses∆Θo,r top oil temperature rise over ambient at rated load∆Θh−o,r hot spot temperature rise over top oil at rated loadqcu load lossesRoil,th convection thermal resistance of oilC {oil} thermal capacity of oilK load factorR ratio of load losses to no load lossesk11, k22, k21 thermal constantsτo oil time constantτw winding time constantH hot spot factorgr gradient between medium winding and medium oil temperature at rated loadx oil exponenty winding exponentD Denotes a change in time∆ Denotes a change in temperatureΘb bottom oil temperatureλ failure rateµ repair time∗.sub subsystem description data file∗mon monitored element description data file∗.con contingency description data file∗.thr load throw over data file.dfx distribution factor data file∗.acc contingency solution output file∗.prb reliability outage statistic file

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IV. LIST OF TABLES

1 Thermal-Electrical Analogous Quantities [29] . . . . . . . . . . . . . . . . . . . . . 192 Current and temperature limits for loading beyond nameplate rating [15] . . . . . . 243 Sustained fault statistics for OH distribution lines . . . . . . . . . . . . . . . . . . . 314 Thermal model constants for 63 MVA medium power transformer . . . . . . . . . . 325 Dynamic rating for long- time overload during different ambient temperatures. The

initial load is 0,6 p.u, followed by a load step to K2 for eight hours then a load stepback to the initial load for four hours. . . . . . . . . . . . . . . . . . . . . . . . . . 37

6 Tested scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 PRA result bus 38- Voltages < 0,95 p.u . . . . . . . . . . . . . . . . . . . . . . . . 438 PRA result- voltage drop > 0, 03 p.u . . . . . . . . . . . . . . . . . . . . . . . . . 449 PRA result- overload of lines. 105% of lines rated MVA. . . . . . . . . . . . . . . 4410 Overall probability- original location . . . . . . . . . . . . . . . . . . . . . . . . . . 4511 Tested scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4712 PRA result- voltages < 0, 95 p.u. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4813 PRA result- voltage drop > 0, 030 p.u. . . . . . . . . . . . . . . . . . . . . . . . . 4814 PRA result- overload of lines. 105% of lines rated MVA. . . . . . . . . . . . . . . 4815 Overall probability- alternative location . . . . . . . . . . . . . . . . . . . . . . . . 4916 Worst contingencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4917 Branch losses for increased power injection at bus 38 . . . . . . . . . . . . . . . . 5218 Line losses for increased power injection at bus 61 . . . . . . . . . . . . . . . . . . 53

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V. LIST OF FIGURES

1 Block diagram representing the calculation of hot spot temperature [15]. . . . . . . 182 Equivalent thermal circuit for top oil temperature [17] . . . . . . . . . . . . . . . . 193 Temperature rise distribution diagram [30]. . . . . . . . . . . . . . . . . . . . . . . 224 Example of pv curve [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Procedure of performing probabilistic reliability asessment in PSS/E. . . . . . . . . 286 Example report of load curtailments grouped by effect. . . . . . . . . . . . . . . . . 287 Example report of load curtailments for each bus. . . . . . . . . . . . . . . . . . . 298 Example report of overloaded lines. . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Example report of voltage violation at busses. . . . . . . . . . . . . . . . . . . . . . 3010 Example report, showing probabilistic indices for all types of violations. . . . . . . 3011 Result from DTR model. the red line represents the measured top oil temperature

and the black line the loading of the transformer . . . . . . . . . . . . . . . . . . . 3312 Result from DTR model. the red line represents the measured top oil temperature

and the black line the loading of the transformer . . . . . . . . . . . . . . . . . . . 3413 Result from DTR model. the red line represents the measured top oil temperature

and the black line the loading of the transformer . . . . . . . . . . . . . . . . . . . 3514 Dynamic rating results with ambient temperature of 28 degrees, 12 hour simulation

and 0,6 p.u. initial load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3515 Dynamic rating results with ambient temperature of 28 degrees, 12 hour simulation

and step increase from 0,6 to 1 p.u. initial load. (a) shows Θh, Θo and Θa, (b showsthe load level, (c) shows the relative ageing, (d) shows the accumulative ageing). . 36

16 Dynamic rating results with ambient temperature of 20 degrees, 1,5 hour simulationand 0,7 p.u. initial load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38




20 Diagram of the subsystem, Korsbarsdalen, with bus name notations. . . . . . . . . 4121 PV curve of node 38, connection point for the transformer . . . . . . . . . . . . . . 4222 Diagram of subsystem Korsbarsdalen with contouring that shows the voltage level,

red is high voltage and blue is low voltage, ranging from 0,94 p.u. to 1,04 p.u. . . 4623 Diagram of subsystem Korsbarsdalen, added series line, bus 60, transformer, bus 61

and wind farm to bus 47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4624 PV curve of node 61, connection point for an alternative wind farm. . . . . . . . . 4725 Effect on bus 36 during increased power injection at bus 38 during the most critical

contingencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5026 Effect on bus 40 during increased power injection at bus 38 during the most critical



contingencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5129 Map of Korsbarsdalen with voltage angles, red is high angle and blue is low angle.

The lines in grey represents the five worst contingencies. . . . . . . . . . . . . . . . 52

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CONTENTS

I Abstract 1

II Sammanfattning 2

III List of variables 3

IV List of tables 4

V List of figures 5

1 Introduction 8

2 Dynamic rating 102.1 Benefits of dynamic rating . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Dynamic transformer rating . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Literature review 123.1 Most used methods for dynamic transformer rating . . . . . . . . . . . . . 123.2 Example of implemented project - flexible approaches for low Carbon op-

timised networks (FALCON) . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Example of implemented project- Unison Networks Limited (Unison) . . . 143.4 Summary of literature review . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Transformer theory 154.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 The electrical insulation and cooling system . . . . . . . . . . . . . . . . . 154.3 Lifetime calculations based on insulation degradation . . . . . . . . . . . . 17

5 IEC 60076-7, differential equation method 185.1 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.2 top oil and hot spot temperature . . . . . . . . . . . . . . . . . . . . . . . 195.3 Solution to the differential equations . . . . . . . . . . . . . . . . . . . . . 205.4 Thermal model constants . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.5 Overload limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

6 Power system analysis 246.1 Voltage stability analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.2 Contingencies and state space . . . . . . . . . . . . . . . . . . . . . . . . 256.3 AC contingency analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 266.4 Island mode after a contingency . . . . . . . . . . . . . . . . . . . . . . . 276.5 corrective action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.6 Probabilistic reliability assessment . . . . . . . . . . . . . . . . . . . . . . 27

6.61 System load probabilistic indices report. . . . . . . . . . . . . . 286.62 Bus load curtailment indices report . . . . . . . . . . . . . . . . 286.63 Branch flow overloading probabilistic indices report . . . . . . 286.64 Bus voltage violation probabilistic indices report . . . . . . . . 296.65 System problem probabilistic indices report . . . . . . . . . . . 29

6.7 Fault statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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6.71 Overhead lines . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.72 Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.73 Busses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7 Dynamic transformer rating- Result 317.1 Thermal model constants for the studied transformer . . . . . . . . . . . . 317.2 Verification of constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317.3 Load scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7.31 Long time overloading . . . . . . . . . . . . . . . . . . . . . . 347.32 short time overloading . . . . . . . . . . . . . . . . . . . . . . . 37

7.4 Evaluating possibility to increase wind farm size . . . . . . . . . . . . . . 39

8 Power system analysis- Result 408.1 Contingencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428.2 Increased wind generation at the original location . . . . . . . . . . . . . . 42

8.21 PV curve analysis for n-0 contingencies . . . . . . . . . . . . . 428.22 Probabilistic reliability assessment . . . . . . . . . . . . . . . . 43

8.3 Increased wind generation at alternative bus . . . . . . . . . . . . . . . . . 458.31 PV curve analysis for n-0 contingencies . . . . . . . . . . . . . 468.32 Probabilistic reliability assessment- result . . . . . . . . . . . . 47

8.4 Analysis of worst contingencies . . . . . . . . . . . . . . . . . . . . . . . 498.41 PV curve analysis of transformer original location during worst

contingencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498.42 PV curve analysis of transformer alternative location during worst

contingencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508.43 Voltage angle analysis . . . . . . . . . . . . . . . . . . . . . . . 51

8.5 Active power losses during n-0 contingencies . . . . . . . . . . . . . . . . 52

9 Summary of results and discussion 53

10 Conclusions 54

11 Future work 56

References 57

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1. INTRODUCTION

Dynamic rating (DR) is a method that lets the operator utilise a power component in thegrid more efficiently. Today, power components typically have a fixed maximum value for howmuch power they can transmit. However, with DR, the capacity of the component is constantlyevaluated depending on external factors such as ambient temperature, wind speed and load history.The component therefore can transmit more energy and make use of its true maximum capacity.Dynamic rating can be applied on overhead lines, cables and transformers, all of which require alot of material to produce and are expensive. By implementing dynamic rating the system operatorcan save money because the components don’t need to be replaced as often, this also benefitssociety in terms of lower tariff costs and a more reliable power supply. In addition, there areenvironmental benefits due to decreased use of resources involved in the production of powercomponents [1].

Dynamic rating can also help the grid to carry out temporarily higher loads. This is usefulbecause often there are load peaks, lasting only a short time and it is expensive to over dimensionthe grid to carry out these load peaks. With DR, components could potentially be used moreintelligently, avoiding the need to over dimension the grid. This is a particular issue in windpower where the electricity generation can be inconsistent due to varying wind speed. DR couldenable faster connection of load and generation, because the grid will be able to carry more powerwithout investing in expensive power components [2]. Also, if there is a failure in a line, cable ortransformer, DR might enable the rest of the grid to safely operate by rerouting the energy flowand disconnection of the load can be decreased or avoided [3].

This study will investigate DR applied on transformers (DTR). Transformers are one of the mostimportant and expensive components in the grid and are often the bottleneck in power systems [3].The transformer’s two main purposes are to transform voltage from a higher to a lower value or viceversa and also to electrically isolate loads [2]. When currents are sent through the transformerwindings they heat up, as does the insulation that surrounds the windings. Furthermore, it ismainly the insulation that ages in a transformer and does so dependent on temperature. Sendingmore power through the transformer windings will increase the temperature. If the temperature isincreased above the critical level, the insulation and hence the transformer will wear out faster andnot meet its designed lifetime. The most critical temperature is referred to as a hot spot temperature.It can be located at any point along the transformer windings, and its location depends on thetransformer design. Normally the maximum value of the hot spot is 97◦ or 110◦ [4].

It is the cooling effect on the transformer and hence on the transformer windings and insulationthat enables a new higher maximum capacity to be set, or in some cases, when it is warm, a lowermaximum capacity. The cooling effect mainly depends on the air temperature [4]. This makesDR in the Nordic countries interesting since during winter the temperature drops and the loadincreases [5], the transformer might be used at a higher capacity compared with the fixed maximumcapacity, because a lower ambient temperature will have a cooling effect on the transformer.

Traditionally power system robustness is determined by deterministic studies, where the outputis directly a result of the inputs , often using a n-1 criteria, so that the system should withstand aloss of one component without experiencing severe consequences. This method does not take intoconsideration the unpredictable nature of fault events. The sources of faults can be different, suchas weather, human factors, or material defects. Nevertheless, they all appear in a non-predictableway. Taking into consideration the unpredictability of faults introduces another dimension inpower system analysis. Risk is a function of probability and consequence. By representing everycomponent in the grid with a failure rate and a repair time, the risk for one or a series of eventscan be determined [6].

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In this study, dynamic rating will be applied on a medium power transformer that is in usein the regional grid. A dynamic rating model for the transformer’s true capacity will be designon temperature measurements and load flow data. Simulations, including the dynamically ratedtransformer, will be applied on the grid and the change in performance will be studied. The gridwill be exposed to a predetermined set of n-1 contingencies. The impact on voltage stability,overload and active losses will be evaluated from a probabilistic point of view.

This master thesis is a joint project between Ellevio, ABB and KTH, were Ellevio provides atransformer to be modelled and historical measurements of current and top oil temperature. ABBprovides technical knowledge in transformer theory and heat transfer.

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2. DYNAMIC RATING

This part of the report explains the fundamentals of dynamic rating (DR) and dynamic trans-former rating (DTR). Section 2.1, gives a general picture of DR and section 2.2, describes dynamicrating applied to transformers.

A. Benefits of dynamic rating

Dynamic Rating is a novel method to determine the true maximum capacity of overhead lines,cables and transformers. Power components have an ampacity limit which states the maximumcurrent that can be sent through the component. The current limit is designed so that the line,cable or transformer won’t reach their maximum design temperatures [7].

The consequences of exceeding the maximum designed temperature varies depending on thecomponent. For example, too high a temperature in overhead lines leads to the line sagging whichmay cause it to come in contact with underlying vegetation [7]. For cables, on the other hand, atoo high temperature leads to changes in the insulation’s dielectric properties and consequently anelectrical breakdown [8]. As a result of the relationship between current and temperature, powercomponents are often given temperature limits, referred to as thermal capacity or thermal rating.

The thermal limit is traditionally calculated using extreme values for ambient conditions, suchas temperature, wind speed, air pressure and air moisture. By considering the cooling effect ofexternal factors on the power component, its maximum capacity can be calculated [3].

In particular, the ambient temperature and load have an effect on the conductor temperature.When the ambient temperature is lower than that which the cable, line or transformer is designedfor, this means that a higher current can be sent through the power component without reachinga critical value of the conductor temperature [7].

Dynamic rating means that instead of calculating the maximum ampacity from constant ambienttemperature it will be the maximum allowed temperature that decides the ampacity. For dynamicrating, the concept of ampacity can be redefined from ”the maximum allowed current” to ”themaximum allowed current a component can transmit without reaching a critical temperature” [9].

Dynamic rating can have the potential to improve capacity utilisation and aid in life cycle assetmanagement as well as providing data to make cost efficient investments. Dynamic rating cantherefore be an important factor in the development of smart grids [3]. By implementing dynamicrating, new investments can be avoided and power components can be used more efficientlytherefore preventing negative environmental impacts through less use of raw materials; it can alsohelp to keep tariff costs low since the grid owner can avoid expensive reinforcement[2].

B. Dynamic transformer rating

The key factor when performing dynamic rating for transformers is the insulation; the lifetimeof a transformer is dependent on the degradation of the paper insulation. The insulation is placedaround the windings to electrically separate the wires from each other. There are two types ofinsulation papers, namely, non-upgraded insulation paper and upgraded insulation paper. Upgradedinsulation paper can withstand a higher temperature than non-upgraded insulation paper andhence ages slower when exposed to the same temperature as non-upgraded insulation paper.Conventionally the transformer lifetime is met when the hot spot temperature is 97◦ or 110◦ fornon-upgrade insulation paper and upgraded insulation paper respectively [10].

The name plate of a transformer states its rated power under certain conditions. If the transformeris operated at these conditions the maximum capacity will be the rated power and the rate ofinsulation degradation will be equal to one, in other words the design lifetime of the transformerwill be met. These conditions are:

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• rated frequency;• rated secondary voltage; and• an ambient temperature of 30◦.Which results in a hot spot temperature of either 97◦ or 110◦ depending on the type of insulation,

when rated power is applied [3].Using the transformer under these conditions results in that the designed lifetime is met. If

the transformer is operated at higher ambient temperatures and consequently a higher hot spottemperature, the insulation will degrade faster and the designed lifetime will not be met. If on theother hand the transformer is operated at a lower ambient temperature the insulation will degradeslower and the actual transformer lifetime will be longer than the design lifetime.

If the system operator has the knowledge of the current rate of insulation degradation hecan choose if carrying a higher load is worth the extra use of lifetime. Also, overusing thetransformer can be compensated by operating the transformer at a lower hot spot temperatureduring another time. The system operator can also have a constant load around the year, in thesummer the transformer insulation will then degrade faster than that which it’s designed for, butthis is compensated for during winter when the ambient temperatures are lower. Under lowertemperature conditions it could be possible to load the transformer over its rated power withoutreaching the transformers critical hot spot temperature and therefore degrading the transformerinsulation more slowly.

The transformer lifetime is a cumulative process, and knowing the current rate of insulationdegradation can help the system operator to better utilise the transformer [3].

The hottest temperature along the winding sets the limit, for the insulation degradation. It istherefore the most important temperature to find, the hot spot temperature is normally located atthe top part of the winding. The position and temperature of the hot spot depends on transformerdesign, ambient temperature, load losses and oil properties among others [9]. In some newtransformers, the hot spot temperature is measured thorough distributed temperature sensing (DTS),in this case a fibre optic cable is placed in parallel with the winding. DTS gives a temperatureprofile of the wingdings and hence the hot spot temperature can be accurately determined in bothlocation and magnitude. It is uncommon that transformers have a device to measure the true hotspot temperature [11]. The transformer in this study does not have any device to measure the truehot spot temperature.

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3. LITERATURE REVIEW

In this section of the report DTR will be presented and different solutions compared. Thefirst section, 3, gives an overview of the current most used methods for DTR. The last twosections, 3.2 and 3.3, demonstrate two examples of when DTR has been implemented by twoelectricity distribution companies, Western Power Distribution in England and Unison Limited inNew Zealand. Lastly, the main findings from the literature review are summarised in section 3.4.

Thermal rating is not a new concept, E. Norris presented a way to calculate transformer tem-peratures in “Thermal ratings of transformer”, published 1928 [12]. E Norris and M. Carruthersfurther developed the thermal model in “Thermal rating of transformers. Introduction of multiflowprinciple”, that was published 1969; the method in this study has many similarities with themethods that are used today [13]. These models are not designed to be used for real time dynamicrating but instead to perform tests on transformers and improve accurate dimensions. The accuracyof the early versions of thermal modelling is limited by the accuracy of measuring equipment atthat time.

A. Most used methods for dynamic transformer rating

Today, there are mainly two organizations that have developed standards for thermal models andloading guides for transformers, namely: Institute of Electrical and Electronics Engineers (IEEE)and International Electrotechnical Commission (IEC). IEEE has developed two standards, clause7 [14], which is a more simple method. The model assumes that the top oil temperature is thesame as in the cooling ducts during overload, this model does not consider that the viscosity ofthe oil changes with temperature; the model also has restrictions regarding changes in load andambient temperature [14]. The second IEEE method is described in annex G [14]. This methodhas no limitations regarding changes in ambient temperature and load and could be used for realtime monitoring of the transformer’s real capacity [14].

IEC has also developed two algorithms, described in IEC std. 60076–7 [15]. First, the expo-nential equation solution, which is designed for regular heat run tests. A heat run test is doneby the manufacture to ensure that critical temperatures are within threshold values. To solve thesecond order differential equations that describe the hot spot temperature, this method, requiresthat steady state has been reached between load steps. Thus, the input data to solve the secondorder differential equation is reduced from two parameters to one since the derivative of the hotspot temperature is zero [16].

The second solution described in IEC standard 60076–7 is called differential equation solution.It is a modified version of the exponential equation method. This method does not require the hotspot temperature to reach steady state values before a load change can be carried out [16].

The IEC differential equation model presents a way to solve the second order differentialequations that are derived from the school of heat transfer. The transformer heat transfer ismodelled in the same analogy as electric circuits, which will be described in section 5. However,G. Swift was first to develop the equivalent circuit for transformer heat transfer, his work is foundin [17], while the solutions for these differential equations are solved in IEC std. 60076-7 [15]and by D. Susa in [16].

Furthermore, there are many studies that are aimed to improve the IEC differential equationmodel. One improvement was developed by D. Susa and H. Nordman [16], they have developed amethod to calculate the thermal constants instead of selecting these depending on transformer size.The calculations of the thermal constants requires additional data from temperature tests duringcertain transformer loading. It is shown that the accuracy of calculated hot spot temperature canbe increased by using this method [16].

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Another study that further developed the IEC differential equation model was developed by J.Rosenlind [1]. Who has included the cooling effect of wind on the transformer and also the changein oil viscosity due to oil temperature change, to calculate a more accurate top oil temperature.

B. Example of implemented project - flexible approaches for low Carbon optimised networks(FALCON)

Falcon is a smart grid project run by the British company, Western Power Distribution (WPD).They operate in South West England, in the Midlands and in Wales, serving approximately 7,7million customers. The trial project was carried out in Milton Keynes, England. WPD expects anincrease of the peak in power during critical hours of the day. The increase is excepted due toa change in customer behaviour, such as increased usage of electrical vehicles and heat pumps.Also, a higher share of renewable energy in the system will give rise to load peaks. Load peakscan be dealt with by upgrading the system and increasing the capacity but these investmentsare expensive and often difficult to implement. Instead WPD is investigating other solutions forsolving future challenges [9].

The goal is to enable an increase of low carbon generation and to meet future requirements forthe grid, this is done by implementing five techniques [9]:• a utomatic load transfer- by changing the state of switching devices and hence directing

which substations supply specific loads, loses can be decreased and voltage stability andcapacity headroom increased [18]

• meshing network - circuit breakers are switched to feed loads from multiple locations. Thepurpose is to reduce losses, improve voltage stability, increase power quality and improvecapacity margins [19];

• battery storage at substations;• demand response service - contracts are signed with local industries and commercial cus-

tomers to either increase their production or decrease their elasticity consumption. The newplayers on the electricity market will get payed for carrying out the service of either providingelectrical power or decreasing their own usage of electricity during load-peaks. Smart metershave been installed to measure the amount of decreased usage or increased production. Animportant aspect of the new generation is that it is located closer to the consumer and, hence,won’t burden the distribution grid [9];

• dynamic rating of overhead lines, cables and transformers.The project included dynamic rating of over head lines and transformers. The voltage level

of the grid is 11 kV and the studied transformers operate at 33/11kV and 11kV/400V. Sixteentransformers are included in the study, all operate close to or over their rated capacity. As partof Falcons feasibility study, the most common standards for DTR was compared, namely: IEC60076, IEC 60354 and IEEE C57.91. Where IEC 60354 is an previous version of IEC 60076-7.According to WPD, IEC std 60076 gives the best results for their transformers [9].

The IEC 60076-7 standard is used for DTR. Historical measurements of top oil temperatureand current are used to validate the DTR algorithm for each transformer individually. In addition,the temperature measurements are validated throughout heat cameras. The limit for hot spottemperature is set to not exceed an ageing rate above the transformer’s designed lifetime [9].

Main findings regarding the DTR model:• sensitivity analysis shows the winding and oil time constants and the top oil and hot spot

temperatures have greatest impact of the result;• there is no direct pattern of a seasonal change in variables, such as the winding and oil time

constants and the top oil and hot spot rise over top oil temperatures;

14

• the accuracy of ambient temperature is important for accurate calculated hot spot values.After the model completion of the model the new capacity rating is calculated using the weather

data for a typical year. The result shows that during the coldest six winter months, when the loadis high the dynamic rating are higher than the static rating. This are usually the case for theremaining six summer months, although there were times during the summer when the staticrating exceeded the dynamic rating.

Moreover, to determine the available capacity for the next upcoming day, WPD uses hourlyweather data from BBC and interpolates an extra point for every half hour, resulting in 48temperature points per day. To approximate the temperatures for one week ahead, WPD uses theforecasted maximum and minimum temperature values and simulates each day with a sinusoidalcycle. The predicted day-ahead values are afterwards compared with the true dynamic capacity,as the real measurements of ambient temperature are known. The predicted errors are in the rangefrom -0,02 to 0,05 p.u. [4].

Main findings regarding the results of the DTR model:• Comparison of calculated hot spot temperature with measured hot spot temperature (optic

fibre) shows that the calculated values are within 4%, 90% of the time with especially highaccuracy for higher currents;

• outdoor transformers are more suitable for DTR, well ventilated indoor transformers can alsogave good results during the winter months;

• transformers can be run 10% above nameplate rating in winter and whilst during summerthey must run under their nameplate rating to meet the requirement of unity lifetime use;

• Reducing the temperature in indoor transformer buildings may increase the transformerlifetime;

More information can be found in: [9], [19], [20], [18], [4] and [21].

C. Example of implemented project- Unison Networks Limited (Unison)

The New Zealand based distribution company, Unison, decided in 2009 to invest in smart gridsolutions. As a part of the decision about investing in a smart grid they have implemented DTR.Unison is using DTR both for short-term, operational purposes such as load planning and alsofor long-term asset management and investment planning. In the long-term Unison predict theycan defer/avoid reinforcements, and hence save money on power equipment. Unison have 53distribution transformers of which 50 are dynamically rated. The transformers are in Hawkes Bay,Rotorua and Taupo regions of New Zealand’s North Island and supply 100,000 customers [3].

Unison are using IEC 60076-7, differential equation method for their transformers. Sensorsat each substation measure the required data which is then sent to the Supervisory Control andData Acquisition (SCADA) where it is processed in the DTR algorithm in real time. The outputis presented in the control room through the SCADA monitors and the operators can use theinformation for load management and outage response [3].

One challenge was that Unison have to customise the algorithm to all 50 transformers, thereare many different manufactures and the transformers are of different ages, some of which havehad a heat run test and some not. Modifications have been made to some transformers after theheat run test was completed. It is therefor a challenge to find accurate thermal model constants forall transformers. Unison addressed this problem by running additional tests on the transformerswith lacking information [3]. The transformer heat run test is described in section 4.

In the case study, [22], one of Unison’s dynamically rated transformers is further investigated.The transformer is a 10 MVA, 33/11kV distribution transformer. The simulation constraints are

15

according to IEC 60076-7 for medium power transformers and normal cycling, i.e. a maximumhot spot temperature of 120 ◦C and an maximum load current of 150%.

The result showed that the calculated rating is highest at low temperatures and low currentloading. The maximum capacity is reached in the summer when the ambient temperature droppedto under 30◦C, then reaching up to 150% or 15 MVA. During the warmer months, the averagecapacity was over 140% [22].

Moreover, the stored measured and calculated temperatures have in combination with gas testshelped Unison to identify the source of faults [22].

D. Summary of literature review

As of today, the most common used standard for DTR is the IEC differential equation model,both cases studies that have been considered uses the IEC method. Also, the data for the trans-former investigated in this study are obtained using an IEC based method. Therefor, the IECdifferential equation method are chosen for this study.

To implement the modifications that are presented in 3, additional data are needed. To includethe cooling effect of wind speed, accurate measurements of wind speed are required. The modelledtransformer in this study dose not have any wind speed measurements within a close distance,therefore, it is not possible to implement the modifications done by J. Rosenlind in, [1].

Moreover, the method for calculation of the thermal constants [16], requires additional mea-surements of temperatures during certain load levels. These measurements were not provided toEllevio by the manufacture and the thermal constants can not be calculated. Instead, standardvalues from the IEC 60076-7 standard, [15], were used.

The research done by Western Power Distribution [9], shows that the accuracy of calculated hotspot temperature is dependent on an accurate ambient temperature. The ambient temperatures inthis study are measured approximately 50 km away from the transformer; this can have an effecton the accuracy of calculated top oil temperature and loss of transformer life calculations.

4. TRANSFORMER THEORY

A. Construction

The transformers main parts are the core, the winding and insulation. The transformer has oneprimary side and one secondary side, each with different voltage levels. The voltage level at eachside depends on how many turns each winding has around its core legs. The core’s purpose is tolink the primary and secondary winding through providing a low reluctance path for the magneticflux and hence works as a link between the primary and secondary transformer side, inducing avoltage difference between the windings. The core is usually constructed with iron or steel whilethe windings usually consist of copper or aluminium [23].

Most transformers are filled with mineral oil, the oil works as both coolant and insulator [23],this will be further explained in the next chapter.

B. The electrical insulation and cooling system

Failures in the electrical insulation system (EIS) are the most common cause for transformeroutages and therefore an important subject to consider in transformer lifetime modelling. The majorconcern for transformer developers during the last 60 years have revolved around the insulation.In a constantly evolving market that demands higher voltage and power levels in combinationwith smaller units and lower prices, the insulation have been the major part of development in thetransformer industry. Furthermore, the transformer must have a good enough EIS so that it can

16

transmit unusually high electric stresses, such as a voltage spike caused by switching transientsor a lightning impulse [23].

For grid owners, the cost of not supplying the load to the customers often exceeds the actualcost for repairing the transformer. Therefore, reliability is also a key factor for both the gridoperator [23].

The electrical insulation system in large distribution transformers consist of oil and paper, whichare both subject to ageing [24]. Plastic materials such as cross-linked polyethylene have been triedbut are subject to treeing due to partial discharges [25] and are currently only used in transformerswith rated apparent power up to 2,5 MVA. The benefit of using cross-linked polyethylene aremainly a more compact design, lower fire risk and in some cases a lower manufacturing cost [10].

When partial discharges occur, it creates a hole in the insulation. An oil and paper based EIScan selfheal by filling this empty space with oil. In plastic materials on the other hand, the emptyspace will be permanent and increase the risk for future partial discharges and with time create atree-like pattern in the insulation [25].

Moreover, the insulation paper is made of cellulose. Cellulose is usually extracted from woodbut there has also been experiments when cellulose have been extracted from cotton. The woodgoes through a chemical process to filter out constituents, such as lignin, carbohydrates and waxes.Leaving the sought cellulose which is a high-polymer carbohydrate chain with glucose [23].

When the insulation paper is new, the glucose chain length is on average 1000 to 2000 butas the paper get exposed to high temperature, moisture and oxygen, the chain length decreasesand the paper becomes fragile [24]. The logarithm of the chain length is approximately a linearfunction of time and the process of ageing (decrease in chain length) is heavily enhanced bytemperature [26].

Furthermore, the chain length of the glucose is directly proportional to the insulation’s dielectricproperties. As the cellulose becomes shorter the dielectric strength decreases and the insulation ismore likely to have break through, resulting in transformer failure [23].

High temperature causes the paper-insulation to age above normal life ageing rate in two ways.Firstly, temperature increases the rate of chemical reaction that is also a function of time butis enhanced with temperature. Secondly, changes in temperature causes mechanical stress on thepaper insulation due to that the oil is expanding and contracting. Both phenomenon lead to changesin the insulation’s physical and electrical properties [24].

The oil in the transformer has two roles: it works as a coolant and as an insulator. The oil fillsup all empty spaces within the insulation paper and also between the conductor and the insulationpaper. Therefore, oil has both an impregnating effect on the paper and at the same time it increasesthe dielectric strength of the EIS [23].

The transformer is not 100% efficient, there are both losses resulting from resistance in thewindings and due to leakage flux in the core. Leakage flux occurs because not all the inducedflux by the primary winding gives rise to the same amount of power in the secondary winding,consequently, energy is lost in the core and it is said that the transformer has a leakage inductance.Losses associated with induction of flux in the core and wire-losses are commonly referred to asno-load and load losses respectively [23].

The losses constitute a heat-source in the winding and the core. Sending more power throughthe transformer will increase the load losses and hence the temperature in the core, resulting in afaster rate of glucose chain reduction of the insulation paper. It is therefore crucial that the heatis transported out from the transformer at a rate corresponding to that of the heat-source. The oilhas the right properties to transmit heat from the windings and the core and act as a coolant [23].

Furthermore, the viscosity of the oil changes with its temperature. As the oil heats up theviscosity decreases and the oil becomes even better at transferring heat, the viscosity decreases

17

exponentially with temperature [27].The oil circulates through the transformer and cooling duct either by natural flow or it can

be forced by pumps. The cooling duct can have forced air flow by fans or natural convection.Resulting in four standards for cooling [28]:• ONAN - Oil Natural Air Natural• ONAF - Oil Natural Air Forced• OFAF - Oil Forced Air Forced• OFAN - Oil Forced Air natural

A transformer can be equipped with both a pump and a fan but have these turned off during lowloads [28]. If there are no pumps in the transformer, then the flow of the oil depends only on theoil temperature, whereas if there are pumps, the oil flow does not depend on the oil temperature.

Similarly, if there are no fans in the cooling duct, natural convection will provide the air flow,hence the airflow in the cooling duct will be a function of the air temperature in the cooling duct.If, on the other hand, there is a fan in the cooling duct, the effect of convection can be neglected.This is because the velocity of air and oil during OFAF will exceed the velocity caused by naturalconvection of oil and air during ONAN.

The IEC differential equation model takes into consideration that the viscosity and naturalconvection changes with temperature by introducing the oil and winding exponents, x and y,these are further explained in section 5.4 [15].

C. Lifetime calculations based on insulation degradation

It is the insulation in the transformer that degrades and therefore ages the transformer. There aretwo types of paper insulation, namely, thermally upgraded insulation papers and insulation papersthat have not been thermally upgraded. Thermally upgraded paper has a higher resilience againsthigh temperature and keeps it’s tensile and bursting strength as well as its dielectric properties toa higher degree compared with not thermally upgraded paper [3].

As described in chapter 4.2, the degree of insulation degradation is a function of temperature.The standardised method is to calculate the insulation degradation at the hot spot , since it is atthis point that the insulation will degrade fastest.

In equation, (1) and (2), V, shows the relative ageing for non-thermally upgraded insulationpaper and thermally upgraded insulation paper receptively [15].

V = 2Θh−96

6 (1)

V = e15000

110+273−15000

Θh+273 (2)

Where Θh is the hot spot temperature in ◦C [15]. A hot spot temperature of 110◦C yields thatV is equal to one, meaning that if the hot spot is 110◦C throughout the whole operation time thedesigned lifetime will be met accordingly. For hot spot values under or over 110◦C the rate ofageing will change exponential according to (2), [14]. For every increase of approximately 7◦Cthe relative rate of ageing will be doubled.

If the transformer is operated at a relative ageing factor, V , equal to one through its operationtime, then it is predicted to last for 17,12 years [14].

Moreover, the loss of life for a certain time period, ranging from t1 to t2 is the accumulativefunction of the relative ageing, V, multiplied by the total time the transformer is operated at V ,according to (3), [15].

18

L =

∫ t2

t1

V dt (3)

Equation (3) is rewritten to (4), where, the sum of each relative ageing factor multiplied by theduration at the corresponding ageing factor gives the total loss of life for the studied time interval[15].

L ≈N∑n=1

Vn × tn (4)

5. IEC 60076-7, DIFFERENTIAL EQUATION METHOD

In this chapter the IEC std, 60076-7 differential equation method will be further explained, thegoal is to find the hot spot temperature. The hot spot temperature can be calculated in two ways,see Figure (1). The hot spot temperature is the sum of the top oil temperature, Θo, and the hotspot temperature rise over top oil, ∆Θh−o. The top oil temperature, Θo, can either be measuredand added directly to Θh−o or ∆Θo can be calculated as function of the load factor, K and thenadded with the ambient temperature, Θa, to get Θh. Both ∆Θh−o and ∆Θo are calculated as afunction of K, since the internal heat losses depends on the load factor. Generally, measurementsof Θo are used when calibrating the algorithm while ∆Θo is calculated when available capacityis determined in real time [15]. The top oil temperature rises over ambient will be calculated insection 5.2.

Fig. 1. Block diagram representing the calculation of hot spot temperature [15].

A. Heat transfer

This chapter describes the basics in heat transfer, which are used when the IEC, differen-tial equation method is derived. The heat-transfer calculations are based on an electrical-circuitmethodology where the electric quantities represents the thermal quantities according to Table 1,[29].

The oil constitutes an important component for the transformer cooling system, as a coolant theoil can be described with the two thermal parameters: heat capacity and thermal conductivity. Boththese are defined in volume and length, see Table 1. When a specific transformer is considered thequantities of length and volume are known and hence the thermal capacity and thermal conductivitycan be calculated as thermal capacitance and thermal resistance [17].

19

TABLE 1THERMAL-ELECTRICAL ANALOGOUS QUANTITIES [29]

Thermal ElectricalProperty Symbol Unit Property Symbol Unit

Heat Q joule charge q coulombTemperature Θ K Voltage U voltTime t s Time t s

Heat-flow rate dQdt

= q W Current i ampere

Thermal capacity ρS joule/m3,K Capacity c farad/m3

Thermal conductivity k W/m,K Conductivity 1/r 1/ohm, mThermal capacitance Cth Ws/K Electrical capacitance C ohmThermal resistance Rth K/W Electrical resistance R faradLength l m Length l m

Temperature gradient dΘdl

= ∆Θ K/meter Voltage gradient dUdl

volt/m

Rate of temperature rise dΘdt

= DΘ K/s Rate of voltage rise dUdt

volt/s

Furthermore, the heat-flow rate, q, and the temperature, Θ, in Table 1 represent an ideal heatsource and an ideal temperature source, respectively. In the same analogy as the electrical lawsfor resistance and capacitance the laws for thermal resistance and capacitance in heat transfer iswritten as in (5) and (6).

Θ = Rthq (5)

q = CthdΘ

dt(6)

In similar to electric capacity that stores energy as electric charges, thermal capacity storesenergy as heat. Consequently, if the temperature, Θ, in (6) changes, the heat flow rate, q, do notchange immediately but instead as dependent on time and the thermal capacitance of the mediumwhere the heat is transferred in.

B. top oil and hot spot temperature

In following calculations the top oil rise over the ambient and hot spot temperature rise overtop oil temperature will be defined.

Fig. 2. Equivalent thermal circuit for top oil temperature [17]

Figure 2 shows the thermal equivalent circuit for the top oil temperature in a transformer, whereRth,oil is the thermal resistance of the oil, Cth,oil is the thermal capacitance of the oil, Θa and

20

Θo is the ambient and the top oil temperature respectively, lastly qfe and qfe represents the lossesin the windings and the core i.e. the load and no-load losses. Applying Kirchhoff’s current lawon the circuit in Figure (2) yields the differential equation for the top oil temperature[17].

qfe + qcu = CoildΘo

dt+

1

Roil,th[Θo −Θa] (7)

Equation (7), is then rewritten to (8).[1 +K2R

1 +R

]x∆Θor = k11τoil

dΘo

dt+ [Θo −Θa] (8)

The hot spot over top oil temperature is reached in a similar manner but instead of the top oiltemperature rise over ambient the hot spot rise over top oil is used. These differential equationsare solved in chapter 5.3.

C. Solution to the differential equations

The differential equation method is a reworked version of the exponential equation method[15]. Both the differential and the exponential calculation methods are derived from the disciplineof heat transfer and the electric circuit analogy. In following calculations, ∆Θo, is calculated andadded to, Θa, according to the solid line in figure 1 and according to (9).

Θh(t) = Θa(t) + ∆Θo(t) + ∆Θh−o(t) (9)

Where:

∆Θo(t) = ∆Θoi + (∆Θo,final)−∆Θoi)× f1(t) (10)

∆Θh−o(t) = ∆Θh−oi + (∆Θh−o,final)−∆Θh− oi)× f2(t) (11)

Where, ∆Θoi, is the initial value of top oil over ambient temperature and ∆Θh−oi is the initialvalue of hot spot rise over top oil temperature. ∆Θo,final and ∆Θh−o,final denotes the final,steady state temperature rise for an arbitrary load, K, R denotes the ratio of load losses at ratedcurrent to no-load losses.

∆Θo, final =

[1 +K2R

1 +R

]x×∆Θor (12)

∆Θh− o, final = ∆Θh− or ×Ky = H × gr ×Ky (13)

Furhtermore, gr is the temperature rise from average oil to average winding temperature andH is the hot spot factor, see Figure 3, r represents values at rated load. The relative increase ofthe top oil temperature rise is described by, f1, as per unit of the steady-state value. f2 describesthe relative increase of the hot spot to top oil gradient as per unit of the steady-state value. Inother words, f1 and f2 is factor that denotes how much of the steady state value that has beenreached at time, t.

f1(t) =(1− e−t/(k11×τo)

)(14)

f2(t) =

[k21

(1− e−t/(k22×τw)

)−(k21−1

)(1− e−t/(τo/k22)

)](15)

21

Where, k11, k21 and k22 are thermal constants and tauo and tauw represents the oil andtime winding constants respectively. f2 is the solution of a second order differential equationand requires two initial values to be solved. In the exponential calculation method above it isassumed that the derivative of the hot spot temperature is zero before every new load step orchange in ambient temperature so that the required input data is reduced from two to one. In thedifferential equation method, this problem is instead solved by taking the difference of two firstorder differential equations:

∆Θh−o = ∆Θh1 −∆Θh2 (16)

where:k21 ×Ky ×∆Θh−or = k22 × τw ×

d∆Θh1

dt+ ∆Θh1 (17)

(k21 − 1)×Ky ×∆Θh−or = τo/k22 ×d∆Θh2

dt+ ∆Θh2 (18)

Where, x is the oil exponent and y is the winding exponents, x and y compensates for naturalconvection, hence, if the transformer is operated as OFAF x and y equals one. These constantswill be further explained in chapter 5.4. The exponential solution of differential equations, (17)and (18) are:

∆Θh1 = ∆Θh1i + (k21 ×H × gr ×Ky −∆Θh1i)×(1− e−t/(k22×τw)

)(19)

∆Θh2 = ∆Θh2i + (k21 ×H × gr ×Ky −∆Θh1i)×(1− e−t/(τo/k22)

)(20)

The differential equation method is then reached throughout Taylor series, (21).

1− e−∆t/τ = 1−∞∑n=1

(−∆t/τ)n

n!≈ ∆t/τ (21)

Combining (10), (14) and (21) yields (22), where DΘo is a change in the top oil temperatureduring the small time step, ∆t.

DΘo =∆t

k11τoil

[[1 +K2R

1 +R

]x∆Θor − [Θo −Θa]

](22)

The top oil temperature for a time t is then calculated with (23), where n-1 is the top oiltemperature for the previous time step.

Θo = Θo(n− 1) +DΘo (23)

Combining (19) and (20) with (21) yields (24) and (25).

D∆Θh1 =∆t

k22τw×[k21 ×∆Θh−orK

y −∆Θh1

](24)

D∆Θh2 =∆t

(1/k22)τo×[(k21 − 1)×∆Θh−orK

y −∆Θh2

](25)

Where:∆Θhr = H × gr (26)

22

H represents the hot spot factor, see Figure (3). Finally, ∆Θh1 and ∆Θh2 for a specific timeis calculated with (27) and (28).

∆Θh1 = ∆Θh1(n− 1) +D∆Θh1 (27)

∆Θh2 = ∆Θh2(n− 1) +D∆Θh2 (28)

The initial values for Θo(0), ∆Θh1(0) and ∆Θh2(0) are calculated with equation (8), (17)and (18) respectively, by assuming steady state at start and hence setting dΘo

dt , d∆Θh1

dt and d∆Θh2

dtequal to zero.

D. Thermal model constants

Figure 3 illustrates temperatures in the transformer where g is the gradient between the averageoil and the average winding temperature, ∆Θom is the average oil temperature, ∆Θwm is theaverage winding temperature. g is assumed to be constant for the winding height. To find thehot spot along the wire, which is usually at the top of the winding, a correction factor, H, isintroduced. In equation, 29, g is calculated for rated power. ∆Θo is the bottom oil temperature[30].

Fig. 3. Temperature rise distribution diagram [30].

Moreover, to obtain values for the temperatures in Figure (3), a heat run test is done. Theheat run test is usually carried out by the manufacture, to ensure the buyer that the transformertemperature limits are within threshold values. During the heat run test the ambient temperature,the bottom oil temperature, the top oil temperature and the hot spot temperature are determinedfrom cold start until temperatures have reached steady state at rated power. Usually, the bottom oil,top oil and ambient temperature are directly measured while the hot spot temperature is calculated.

As described before, the hot spot temperature can also be measured by means of optic fibre[16]. More detail of how the heat run test is performed and how the hot spot factor is calculatedare found in the IEC std. 60076-2, Power transformers - Part 2 [30], an alternative method to

23

calculate the hot spot factor was developed by D. Feng and Z Wang in [31]. The hot spot factorfor the transformer that are tested in this study was received from the manufacture data sheet.

gr = Θwmr −Θomr (29)

The average winding temperature is calculated in (30), [16].

Θwmr =R1

R2(Θk + Θa)−Θk (30)

Where R1 is the resistance at rated load but before the winding has become hot, often referredto as cold resistance, R2 is the resistance after that rated load have been applied long enoughfor the resistance to have a steady-state value and Θk is the factor depending on the conductormaterial, for copper and aluminium the value is 235◦C and 225◦C respectively. Moreover, theaverage oil temperature at steady state and rated load is calculated as the average of bottom oiltemperature Θb and the top oil temperature, Θo [30].

The oil time constant is calculated as:

τo =C ×∆Θom × 60

P(31)

Where P is the losses at the studied load and C is the thermal capacity. The Thermal capacityis derived in IEEE standard C57.91-1995, [14]: The oil time constant for ONAN and ONAF iscalculated as:

C = 0, 132mA + 0, 0882mT + 0, 400mO (32)

Where mA is the mass of the core and coil, mT is the mass of the tank and mO is the massof the oil. The winding time constant is calculated as:

τw =mw × c× g

60× Pw(33)

Where Pw is the winding losses, mw is the mass of the winding and c is the thermal constantfor the winding, for copper c is 390 Ws/(kgK). For accurate result the time step, ∆t, needs to beshorter then τw

2 [15].The exponential constants x and y depends on the cooling setting of the transformer. If the

transformer is an ONAN/ONAF the oil circulation will depend on the oil temperature, hencealso depend on the load and the load-losses. Therefore the change in for example DΘo in, (22),does not increase linearly with increasing K [16]. The phenomenon with natural convection areexplained in more detail in section 4.2.

The loss constant, R, is calculated as the ratio of load losses at rated current, Pk, to no-loadlosses P0, [15].

R =PkP0

(34)

Moreover, to calculate the thermal constants k10,k22 and k21 the data from a heat-run test isneeded, a method to calculate these parameters is presented in, [16].

E. Overload limitsTable 2 shows the recommended limits for loading over nameplate rating of medium and large

power transformers according to the IEC guide [15].The limits are often not reached simultaneously, either the current, hot spot or top oil limit is

reached and then sets the limit for the other parameters. The most critical temperature is for thehot spot ; if the oil exceeds 140 ◦C there is risk of bubble formation and the oil might start toboil [15].

24

TABLE 2CURRENT AND TEMPERATURE LIMITS FOR LOADING BEYOND NAMEPLATE RATING [15]

Normal cyclic loadingCurrent [p.u] 1,5Winding hot spot temperature [C◦] 120top oil temperature [C◦] 105Long-time overloadingCurrent [p.u] 1,5Winding hot spot temperature [C◦] 140top oil temperature [C◦] 115Short-time overloadingCurrent [p.u] 1.8Winding hot spot temperature and metallic parts incontact with cellulosic insulation material [C◦] 160

top oil temperature [C◦] 115

6. POWER SYSTEM ANALYSIS

In previous theory we have looked in to how transformers maximum capacity varies withtemperature and a method for calculating the transformers true capacity was defined in section 5.The theory in this section focuses on how the grid performs when DTR is implemented and thewind park size is increased.

Traditionally power system robustness is determined with deterministic studies, where the outputis directly determined by the inputs, often using a n-1 criterion, so that the system should withstanda loss of one component without experiencing severe consequences. This method does not takeinto consideration the unpredictable nature of fault events.

The source for faults can be many, such as, weather, human factors, or material defects.Nevertheless, they all happen in a random fashion, taking into considerations the unpredictabilityof faults introduces another dimension in power system analysis. By representing every componentin the grid with a failure rate and a repair time the probability and consequence for one or a seriesof events can be determined [32].

Mainly two power system simulation tools will be applied in this study, both using the softwarePSS/E by Siemens. The first is to study voltage stability during an expansion of the wind farm,this study is done by drawing the PV curve, which shows the relationship between active powerand voltage.

Secondly, the grid will be exposed to a predetermined set n-1 contingencies. The impact onvoltage stability, overload and losses will be evaluated from a probabilistic point of view, usingProbabilistic Reliability Assessment (PRA), in PSS/E [6].

The procedure and theory behind these two power system tools will be explained in this chapter.Firstly, by presenting a method to draw the PV curves in section 6.1. Secondly, by defining thestate case and contingencies in section 6.2, followed by the procedure to perform the PRA analysis.In order to perform PRA analysis it is first required to test all defined contingencies, this is donein section 6.3, the result from the contingency analysis is used to calculate the probability forviolations in section 6.6.

A. Voltage stability analysis

Using the DTR algorithm the maximum capacity of the transformer can be evaluated but it isnot certain that the connection point can receive more active power and an increased wind farmsize, the PV curve is used to test the connection point’s ability to receive more active power.

25

Figure (6.1), provides an example of a PV curve or nose curve as it is sometimes called. Thecurve in Fig (6.1) shows the bus voltage change during an increased injection of active power. Asthe active power is increased the voltage drops until a critical point is reached and the subsystemwill experience a voltage collapse. Usually the critical voltage limit is reached before voltagecollapse, the critical voltage is an arbitrary limit set by the grid operator, commonly the criticalvoltage limit is 0,9 p.u. Furthermore, P0, is the initial load level of the bus and P1 is the potentialload level, hence, P1 − P0 is the load margin that can be increased before voltage collapse [33].

Fig. 4. Example of pv curve [33]

In PSS/E the PV curve is drawn by first defining two subsystems, namely, a source subsystemand sink subsystem, these subsystems are defined in the Subsystem description data file (*.sub)which will be further explained in section 6.3. The source subsystem defines all busses where theactive power is to be increased [34]. In this study, the active power will only be increased onebus at the time, the bus which the wind farm is connected to.

The sink subsystem defines all busses that will absorb the extra power from the source sub-system. The sink subsystems busses can either increase their existing loads or decrease theirgeneration of active power to meet power balance [34]. In this study the rest of the grid, apartfrom the bus that the wind farm is connected to, is included in the sink subsystem and the existingloads will be increased to meet power balance in the studied grid.

Moreover, increasing the generation at one bus will usually have greatest affect at the closestsurrounding busses but will also effect the whole power system, it is therefore necessary to draw thePV curve for all studied busses in system. As the active power in, fig (4), is increased the voltagedrops faster, it is not safe to operate too far to the right, because, the derivative of the voltagebecomes heavily negative and a little change in active power can result in voltage instabilities orin worst case a voltage collapse [33].

If the voltage deviates too much from rated voltage at a bus, it could cause problems for thecustomers. For example, machines could be stalled, and other voltage sensitive equipment couldface problems. Also, a low voltage gives less margin in case of a fault and hence the risk forvoltage collapse increases with low voltage [33].

B. Contingencies and state space

The base case of a power system consists of the initial grid. Apart from the base case thereare often multiple contingency cases. The base case and the contingency cases are said to form

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the state space. The state space describes all states that the system can be in, it follows that thesum of the possibilities of each case to occur equals one or 100%, the system is always in a stateeven though it is not functional or not fully functional. By investigating the contingency statesand removing components and performing power flows the state space can be studied, removingone component is referred to as n-1 contingency, removing two components is referred to as n-2contingency and so forth [35].

For a system with two components there are four states and a maximum contingency of n-2.Often there is a need to perform reliability analysis on subsystems and the number of componentscan be extensive. For a system with 30 components there are millions of states if all n-30contingencies are to be investigated. Therefore, it is often not possible to investigate the wholestate space. Instead, the most important contingencies are chosen to represent the state case [35].

Often in contingency analysis, two alternative grid layouts are compared to determine the mostreliable alternative, as in this case, when the system including the dynamically rated transformeris compared with the same system that does not include the dynamically rated transformer. Itmight then not be relevant to study the entire state case, it is instead more important that the twoversions of the grid are exposed to the same set of relevant contingencies so that the result canbe compared [6]. This theory has been implemented in this study, where n-1 contingencies formachines, lines and busses along with the base case are assumed to form the state case and willbe used for all scenarios.

C. AC contingency analysis

The AC contingency analysis (ACCC) function in PSS/E performs a full ac power flow solutionfor a specified set of contingency cases [34]. In this section, the procedure to perform an ACCCwill be described. The results are stored in a binary file and used in the probabilistic reliabilityassessment (PRA) analysis. The power flow is performed either by fixed slope decoupled Newton-Raphson iterative algorithm [6].

To perform PRA analysis the first step is to do an ACCC. PSS/E needs five files to run theACCC, these files can be programmed in various ways, such as with Python or in a text file. Therequired files and their functions are[34]:

1) Subsystem description data file (*.sub)- Defines which part of the system that will bemonitored.

2) Monitored element description data file (*mon)- Describes what is going to be monitored,for example, loading of branches and bus voltage magnitudes. Each element can be specifiedindividually or all components of the same type in the defined subsystem can be specifiedall together.

3) Contingency description data file (*.con)- All contingencies are specified in this file. Forexample: loss of a line, increased or decreased load or loss of a machine.

4) Load throw over data file (*.thr)- All actions that can reduce the impact of a contingencyare defined in the thr- file. Such actions can be load transfer, open or close a line or add ageneration unit. The file is built upon an if arguments, for example: if there is overload ona specific line an alternative line will be opened or a specific load will be decreased.

5) distribution factor data file (*.dfx)- This file is generated with a function in PSS/E wherethe *.sub, *.mon and *.con files are combined into the *.dfx file.

When these files have been programmed the ACCC can be carried out, the results from theACCC are saved in the Contingency solution output file (*.acc). With the *.acc file, reports onvoltage violations, voltage collapse, overload and more can be generated, it is also this file thatwill be used in the PRA analysis.

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D. Island mode after a contingency

If one or more busses operate in island mode, i.e. are not connected to the swing bus, after acontingency the whole island will be considered as lost unless a dispatch mode is chosen. Forexample, all generation and load connected to busses that are in island mode after a contingencywill contribute to the loss of load and loss data. By choosing an alternative dispatch mode, PSSEwill select the generation unit with highest generation to become the swing bus for the island. Ifthe swing bus can’t supply all loads on the island and a deficiency in generations exist, then theload will be divided on the rest of the generation units in the island, according to (35), [34]

P 1GEN,i = P 0

GEN,i + pi × deficiency (35)

Where P 0GEN,i is the dispatch of unit i, P 1

GEN,i is the new dispatch of unit i and pi is theparticipating factor of unit i. If there is still a generation deficiency after that all generation unitson the island are operating at their maximum capacity, load shedding will be done. Load sheddingmeans that the load at all busses on the island is shed proportionally until load and generationare met. Load shedding occurs according to (36), [34].

P 1LOAD,i = P 0

LOAD,i +P 0LOAD,i∑P 0LOAD,i

× deficiency (36)

E. corrective action

After a contingency, it is likely that the grid has violations. With the function, corrective actionin PSSE, these violations are minimised through a series of actions. Such actions can be to adjusttap positions at transformers, machine phase angle adjustment, off-line generator activation andswitched shunt controls. The procedure is done with a series of load flows where above actionsare implemented until the violation is minimised, this is done for each contingency with violationin the state case [34].

F. Probabilistic reliability assessment

Once the ACCC is completed and the *.acc file is obtained the PRA analysis can be carried out.The acc file contains information about voltage violations, overloads and loss of loads for eachcontingency that was programmed in the *.con file. In the PRA function in PSS/E, the probabilisticindices for each of these fault events are calculated separately and there are also over all resultsfor each type of violation, for example the probabilistic number of hours with overload for alllines during one year including all contingencies. PRA also requires one additional file, apart fromthe *.sub, *.mon, *.con and *.dfx file; the reliability outage statistic file(*.prb). This file containsinformation about failure rate and repair time for each of the components that are included incontingencies, such as line, buss and machine statistics. The necessary files to perform the PRAare mapped in Figure 5. It should be noted that these report do not give the probability for faultsto occur; the report shows the probability for violations to occur due to failures. If the probabilityfor faults would be calculated it would therefore, result in a higher probability than the results inthe PRA analysis done in this study.

There are altogether six PRA reports: System load probabilistic indices, bus load curtailmentindices, branch flow overloading probabilistic indices, bus voltage violation probabilistic indices,contingency summery probabilistic indices and system problem probabilistic indices. Each of theseare explained in section 6.61 to section 6.65.

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Fig. 5. Procedure of performing probabilistic reliability asessment in PSS/E.

1) System load probabilistic indices report.: The system load probabilistic report, shown inFigure (6), displays a summary of all faults in the studied system with respect to loss of load.Each loss of load falls into its corresponding group depending on load size. For example, in thegroup 10-20 MW there are 0,0906 faults per year, each fault lasts for 13,7 hours, the probabilityfor loss of load ranging from 10-20 MW is 1,2 hours per year, the interrupted power per year is4,94 MW which results in an expected unserved energy of 23,87 MWH per year, in this case thereis only one contingency that causes this fault. The farthest right column shows which contingencyhas the highest contribution of loss of load for that range. The last row shows the load probabilisticindices for the entire subsystem.

Fig. 6. Example report of load curtailments grouped by effect.

2) Bus load curtailment indices report: The bus load probabilistic indices report, Figure (8),is similar to the system load probabilistic indices report, but instead of being grouped in effectranges, the loss of load for each bus is shown. The top column shows the probability for loss ofload for Korsbarsdalen, the values for this column are the same as in the last column in Figure(6).

3) Branch flow overloading probabilistic indices report: The report in Figure 8, shows over loadof lines and transformers. The first row displays the overall result for the subsystem, Korsbarsdalen.In the rest of the rows each line or transformer are represented as from which bus they aregoing from and to. Apart from the frequencies of events, duration of fault and probability that

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Fig. 7. Example report of load curtailments for each bus.

was explained in the previous section, impact and maximum violations in percentage are alsodisplayed. Maximum violation is defined as a predetermined overload of the lines rated MVA.Worst contingency shows which contingency caused the worst violation.

Fig. 8. Example report of overloaded lines.

4) Bus voltage violation probabilistic indices report: The bus voltage probabilistic report,Figure 9, shows two types of violations. Firstly, the probability for voltages under a definedlimit, in this case 0.95 p.u. Secondly the probability for a voltage drop beyond a defined limit, inthis case 0.03 p.u. The structure is the same as for the previous reports but max violations andworst contingency shows the magnitude of the violation in p.u. and which contingency causedthe worst violations, respectively.

5) System problem probabilistic indices report: The last probabilistic report, fig 10, displays asummary of all other probabilistic reports. The last row, subsystem Korsbarsdalen total, shows thetotal probability for voltage and overload violations as well as voltage collapse and loss of load.This report is not from the same simulation as the other report, hence the values in the summaryreport cannot be compared with the previously shown reports.

G. Fault statistics

The fault statistics that are used in this reliability assessment analysis are derived by Elforsk[32] and ENTSOE [36]. Elforsk have compiled data for the Swedish grid from the following gridoperators: Fortum Distrubution (Ellevio), Vattenfall EON and Svensk Energi, the data is collectedfrom 2004 until 2007 [32].

Faults can be categorised in two groups; momentary faults and sustained faults. Momentaryfaults are of the character that they will clear themselves when the component is re-energised.Sustained faults on the other hand will require reparation. The minimum downtime for a fault tobe classified as a sustained fault is three minutes. The sustained faults for each component arerepresented with a fault frequency, λ, in occasions per year and a repair time, µ, in hours. Inthis study only the sustained faults will be considered. The data for failure rate and repair timehave either been automatically registered by a computer software of the grid operator or manually

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Fig. 9. Example report of voltage violation at busses.

Fig. 10. Example report, showing probabilistic indices for all types of violations.

collected by repair and maintenance personnel. The faults causes that are included in the failurestatistics are [32]:• Weather related (tree falls, snow, wind, ice, thunder, rain)• External influences (environment related, animal, digging, sabotage, salt, traffic)• Material defect• Technicale related• Dimensioning failure• Operation and people related (lack of maintenance, overloading, improper method, improper

montage, faulted operation)In this study faults on lines, machines and busses are included as contingencies and therefore

need to be assigned a λ and a µ to perform the PRA analysis. Fault statistic for the includedpower components are shown below.

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1) Overhead lines: Faults on over-head (OH) lines can occur either at the connection pointsor on the actual line, therefore the failure rate and repair time for the connection point and onthe line are separately represented in PSS/E [32]. All 135 kV lines in this study are assumed tohave the same fault frequencies per kilometre and the same repair times. The statistics that havebeen used in this study are represented in Table 3.

Moreover, the studied grid mostly contains OH-lines, even though parts of the branches arecables. The exact information of which branches are cables or which parts of branches that arecables were not know, for the reliability data it will therefore be assumed that all branches areOH- lines. Since the goal is to compare different layouts and scenarios it does not matter thatcables have also been approximated as OH-lines; all layout and scenarios will be subject to thesame fault statistics and same set of contingencies.

TABLE 3SUSTAINED FAULT STATISTICS FOR OH DISTRIBUTION LINES

λ µConnection caused faults 0,0166 faults/yr 8 hours [6]Line faults 2,2 faults/(100 km, yr) 15 hours [36]

Falling trees is the most common cause of failure for overhead lines [32].2) Machines: The failure rate and repair time for generating units are, λ = 0, 01 [failures/year]

and µ = 336 hours [6].3) Busses: According to Elforsk, [6], the failure rate and repair time for busses is 0,0008

faults/year and 15 hours respectively. The reason that the failure rate is so low is that it is veryseldom that a whole substation is out of service. PSS/E simulates a bus fault as the probabilityfor all incoming branch-connection points to break [34].

7. DYNAMIC TRANSFORMER RATING- RESULT

This section of presents the result regarding the transformer and how maximum loadabilitychange with the implementation of dynamic rating.

The transformer tested in this study is a 63 MVA , medium power transformer. The transformeris working at 135/23 kV, it is connected to a wind farm at the low voltage side whilst the gridKorsbarsdalen is on the high voltage side.

A. Thermal model constants for the studied transformer

In the previous section, the different techniques for DTR and thermal models were comparedand the IEC differential equation model was selected. In this section, the required constants willbe determined from three sources, namely: from the manufacture data sheet, the IEC std. 60076-7and from the heat run test that was performed by the manufacture.

Table 4, presents the thermal model constants for the modelled transformer along with thesource of each value. The DTR algorithm is implemented in MATLAB.

B. Verification of constants

In this section the calculated top oil temperature, ∆Θo, will be compared with measurementsprovided by Ellevio. The data provided by Ellevio consists of top oil temperature and currentmeasurements; the current is measured on the high voltage side. Measurements reach from March2016 until December 2016.

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TABLE 4THERMAL MODEL CONSTANTS FOR 63 MVA MEDIUM POWER TRANSFORMER

Parameter Symbol Value SourceOil exponent x 0,8 IEC 60076-7Winding exponent y 1,3 IEC 60076-7Thermal constant k11 0,5 IEC 60076-7Thermal constant k21 2 IEC 60076-7Thermal constant k22 2 IEC 60076-7Oil time constant τo 150 IEC 60076-7Winding time constant τw 7 IEC 60076-7Average oil to average winding gradient gr 16,2 eq. (29)hot spot factor H 1.13 Manufacturetop oil temperature rise ∆Θo,r 53,0 Manufacturehot spot temperature rise ∆Θh−o,r 18,3 eq. (26)Loss factor R 12,8 eq. (34)

The ambient temperature, Θa, that is used in these calculations is from a weather station ownedby SMHI [37], it is located approximately 50 km away from the transformer location.

The first step is to verify that the algorithm is correct and secondly to verify that the constantshave been appropriately chosen. To verify the algorithm, a known case is used. The case is fromthe IEC std. 60076-7, it provides ambient temperature and load level for 40 time steps, each threeminutes long. The correct calculated top oil and loss of life is also presented in the guide [15].Calculated top oil and loss of life values calculated from the algorithm used in this study arecompared with the correct answers from IEC guide. The result was a perfect match, hence it canbe concluded that the algorithm is correctly implemented.

Figure 11 shows the calculated top oil temperature in light blue and the measured top oiltemperature in red. As can be seen there is a temperature gap between the measured and thecalculated top oil temperature. In shape, the calculated and measured temperatures are similar butthe measured values are too high compared with the calculated.

In Figure 12, the measured top oil temperature has been shifted down ten degrees, over these42 days there is an average difference between the downshifted measured top oil temperature andcalculated top oil temperature of 1,7 C◦. Figure 13 shows the same graph as 12 but zoomed inon the hours 700 to 830.

The underlying reason for this temperature difference could be that the measurements from theheat run test, done by the manufacture, are faulty. During the heat run test two sensors were used,the sensors then measured 79,9 C◦ and 81,2 C◦ when the top oil had reached steady state at ratedcurrent, the ambient temperature was 27,3 C◦.

Using the derived algorithm in this study under the same conditions, e.g. an ambient temperatureof 27,3 C◦ and a load factor, K, equal to one, results in a top oil temperature of 80,3 C◦, whichis in line with measured top oil temperature during the heat run test done my the manufacture.Since the derived algorithm itself has been verified with an example from the IEC guide it can beconcluded that it must be the constants that are the reason for the deviation between the calculatedtop oil and the measured top oil temperature from Ellevio, in Figure 11.

Many of the parameters used for the DTR model are calculated from the heat run test, a fault inthe heat run test would therefore affect the whole model. That the calculated top oil temperatureis similar to the measured top oil during the heat run test, supports the theory of a fault in themanufacture’s heat run test. If the input data is faulty, then the model built upon the input datawill also be faulty.

A second explanation for the difference in calculated and measured top oil temperature couldbe that the temperature sensor in the transformer is not working correctly or is not located at its

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Fig. 11. Result from DTR model. the red line represents the measured top oil temperature and the black line the loadingof the transformer

correct spot which could also result in a constant temperature fault.A third explanation for the difference could be that the ambient temperature is measured

approximately 50 km away from the transformer since the ambient temperature has a direct effecton top oil temperature. It is though unlikely that the difference would be as great as ten degreesand it is also unlikely that the difference in ambient temperature would be constant over time.

To get to the bottom of this problem, further measurements of ambient temperature at thetransformer location and additional measurements of the top oil temperature would have to beperformed. For time reasons, it was not possible conduct this measurement during this study. Soas to be ensured that the hot spot temperature is not calculated too low which could result intransformer failure if the DTR algorithm were implemented, a ten degrees safety margin will beused throughout all DTR calculations.

C. Load scenarios

In this section, the developed DTR algorithm will be used to test transformer behaviour duringdifferent load levels and for different ambient temperatures. Moreover, the initial load has an impacton the transformers maximum dynamic capacity, especially for short time emergency loading. Thisis because there is a time delay of the hot spot temperature when the load is increased, for a shorttime it can therefore be possible to have a considerably higher loading rating than compared withthe static rating.

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The DTR algorithm that has been used here is slightly modified to calculate how much theload can increased from a certain initial load. The algorithm is programmed in MATLAB. Theuser makes a series of choices where the ambient temperature, initial load and simulation time areset. The program then calculates the top oil temperature, hot spot temperature, maximum relativeageing and the total use of lifetime. The loading factor is gradually increased until any of thelimiting values are reached; in between every load increase the start values for the initial load areset. Simulation can be performed for long time overloading and short time overloading, the limitsfor these are defined in Table 2.

1) Long time overloading: Figure (14), shows an example of how the result is displayed inMATLAB. For the simulation in Figure (14), the ambient temperature is 28 ◦C, the initial load is0,6 p.u. and the total simulation time is 12 hours. The first column shows the simulation number,the user can use this number to choose to draw graphs for a specific load increase, the secondcolumn shows the new loading, K2, the third and fourth column show the maximum hot spotand top oil temperature during the whole simulation time, the fifth column shows the maximumrelative ageing and the last column shows the use of lifetime for the 12 hours. At time zero thereis a load step from the initial load to the new load, K2, the transformer is then run at load levelK2 for eight hours and then there is again a load step back to the initial load.

For the long-time overload the limits is according to IEC std. 60076-7, a maximum hot spotand top oil temperature of 140 and 115 degrees respectively and a maximum load level of 1,5p.u, see Table 2.

In Figure (14), the load is increased by 0,5 p.u. for each step. For long time over loading theinitial load is not as important as for short time over lodging since the simulation time is so long

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so that a steady state value for the top oil and hot spot temperature is reached.

Fig. 14. Dynamic rating results with ambient temperature of 28 degrees, 12 hour simulation and 0,6 p.u. initial load.

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Step 10 in, fig (14), shows an load increase from 0.6 p.u. to 1 p.u, after that steady state hasbeen reached. At the new load level the hot spot temperature is approximately 110◦C and hence,the relative loading approximately one. Consequently, if the ambient temperature is 28 ◦C orlower the relative ageing will be below one. Figure (15), displays graphs for load scenario nine,graph (a), shows the hot spot, top oil and ambient air temperature, as can be seen a steady stateis reached after about five hours. The relative ageing for 0,6 p.u. is almost zero but increaseswhen the hot spot temperature increases after the load step. The hot spot and top oil temperaturedrops fast after the load has been decreased and hence also the relative ageing, resulting in thatthe accumulative ageing does not change much after that the load has been decreased. The totalaccumulative ageing for the 12 hours of operation is 6,79 hours.

Fig. 15. Dynamic rating results with ambient temperature of 28 degrees, 12 hour simulation and step increase from 0,6to 1 p.u. initial load. (a) shows Θh, Θo and Θa, (b shows the load level, (c) shows the relative ageing, (d) shows theaccumulative ageing).

Load scenario 14, in fig (14), is for a step change to 1.25 p.u. Load scenario 14 is the highestthat the load can go with given ambient temperature, increasing the load level more would implythat one or more of the criteria for long time overload in Table 2, would be breached.

Table 5, shows a summation of simulations done in the same analogy as for Figure 14 and(15). First a load step from 0,6 p.u. to the new load, K2, that is run for eight hours followedby a load step back to 0,6 p.u. In Table 5, these simulations are done for six different ambienttemperatures, ranging from -10◦C to 35 ◦C. Θh,max and Vmax denotes the maximum hot spottemperature and maximum relative ageing during the 12 hours. While, L, denotes the total lossof life for the 12 hours. The blank boxes in Figure (5), means that one of the limits for long timeoverloading have been reached; no results are presented for these scenarios.

For the simulations done with an ambient temperature of -10◦C, a load increase to 1,4 p.u.results in a maximum relative ageing of 2,1, running the transformer continually at this load foran arbitrary time length results in a consumption of double the amount of transformer lifetime.However, in Figure (15), there is a time delay between the step change in load and the changein hot spot temperature. Consequently, increasing the load from 0,6 to 1,4 p.u. for the used

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TABLE 5DYNAMIC RATING FOR LONG- TIME OVERLOAD DURING DIFFERENT AMBIENT TEMPERATURES. THE INITIAL LOAD IS0,6 P.U, FOLLOWED BY A LOAD STEP TO K2 FOR EIGHT HOURS THEN A LOAD STEP BACK TO THE INITIAL LOAD FOR

FOUR HOURS.

K[p.u.] Θa [◦C] -10 0 10 20 30 350,7 Θh,max [◦C] 44,3 54,3 64,3 74,3 84,3 89,3

Vmax 0 0 0 0 0,1 0,1L [h] 0 0 0 0,2 0,6 1,0

0,8 Θh [◦C] 53 63,0 73,0 83,0 93,0 98,0Vmax 0 0 0 0,1 0,2 0,3L [h] 0 0 0,1 0,4 1,3 2,2

0,9 Θh,max [◦C] 62,3 72,3 82,3 92,3 102,3 107,3Vmax 0 0 0,1 0,2 0,5 0,8L [h] 0 0,1 0,3 1,1 3,2 5,4

1,0 Θh,max [◦C] 72,3 82,3 92,3 102,3 112,3 117,3Vmax 0 0 0,2 0,5 1,3 2,1L [h] 0,1 0,3 1 2,9 8,3 13,8

1,1 Θh,max [◦C] 82,8 92,8 102,8 112,8 122,8 127,8Vmax 0,1 0,2 0,5 1,3 3,6 5,7L [h] 0,3 1 2,9 8,3 22,4 36,1

1,2 Θh,max [◦C] 93,4 103,9 113,9 123,9 133,9 138,9V 0,2 0,5 1,5 3,9 9,9 15,5L [h] 1,0 3,1 8,8 23,6 60,4 95

1,3 Θh,max [◦C] 105,4 115,4 125,4 135,4Vmax 0,6 1,7 4,6 11,5L [h] 3,5 10,0 26,3 66,9

1,4 Θh,max [◦C] 117,5 127,5 137,5Vmax 2,1 5,5 13,8L [h] 11,7 30,9 77,8

1.5 Θh,max [◦C] 130,1Vmax 7,0L [h] 38,0

time scenario results in a total lifetime use of 11,7 hours, close to unity lifetime since the totalsimulation time is 12 hours.

The result for ambient temperature of 20◦C, and a load step to 1,1 p.u. see Table (5), resultsin a total lifetime use of 8,3 hours, which is 3,7 hours under unity lifetime.

Moreover, Table 5 clearly shows the relationship between increased load, ambient temperatureand loss of life for the tested transformer, up to a hot spot temperature of 100◦C, the relativeageing is small but above 100◦C the it increases fast. The relative ageing is doubled for everyincrease of seven degrees hot spot temperature.

Already at an ambient temperature of zero ◦C, it is not possible to utilize the higher limit of1,5 p.u. before the hot spot limit is reached and for an ambient temperature of 35◦C the hot spottemperature limit is reached at a load increase to 1,2 p.u.

2) short time overloading: In this section, the transformer behaviour will be evaluated duringshort time overload. The limits for short time overload are hot spot and top oil temperature of160◦C and 115◦C respectively and a maximum loading level of 1,8 p.u, according to the IEC std.60076-7. Hot spot temperature above 140◦C can cause gas bubble formation in the oil, hence,risking a decreased dielectric strength that can lead to electric breakdown in the insulation. [15].But for theoretical purposes the hot spot limits are set to 160◦C, as in the IEC standard.

Figure (16) shows the DTR result for a simulation done for 1,5 hours and with an ambienttemperature of 20◦C. First there is a load step from the initial load of 0,7 p.u to the increasedload, K2. The transformer is operating at load level, K2 for one hour, then it is again a load

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Fig. 16. Dynamic rating results with ambient temperature of 20 degrees, 1,5 hour simulation and 0,7 p.u. initial load.

step back to the initial load of 0,7 p.u. For an ambient temperature of 20◦C it is not possibleto increase the load level to 1,8 because the hot spot temperature limit is then reached. We willnow look at load step 11, in Figure (17), as can be seen, the hot spot temperature does not reachsteady state. The initial load level is, therefore, in short time over load of great importance forthe transformer maximum loadability.

A lower initial load means that a higher increased load is possible, for a short time because ofthe time delay between a change in load and the hot spot temperature. The hot spot temperature,in Figure (16), decreases fast as soon as the load is decreased, the time delay only exits for anincreased load step and not for a decreased load step; when the load is decreased the hot spottemperature also decrease. The system operator can take advantage of the time delay and use thetransformer at above its name plate rating in case of emergency, but only for short time period.

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D. Evaluating possibility to increase wind farm size

Ellevio has provided current measurements for ten months, ranging from February to December2016. The current and air temperature is, used to calculate the load level of the transformer andit are investigated if the load can be increased without endangering the transformer lifetime.

Figure (18) shows the load level for the ten months. The maximum loading during the tenmonths is 0,87 p.u. and the average loading is 0,29 p.u.

The constructed DTR algorithm is used to calculate the lifetimes for this time period, the resultis shown in Figure (19). In the previous section, where loss of life was calculated for a range ofdifferent scenarios we can see that a hot spot temperature below 100◦C did not contribute muchto the loss of life. The maximum hot spot temperature for these ten months is 104,3◦C and mostof the time lower than that. Consequently, the total loss of life for the ten months is only 8,3hours, see Figure (19).

By iteration, where the load is gradually increased, a new load level can be found. The limitfor the new load level is set so that no threshold values for long time overloading is not exceedednor should the life time exceed unity. The maximum load limit is reached when the wind farmhave been expanded by 76%. Increasing the wind farm size with 76% resulted in a lifetime use

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7211 hours, which is close to unity, there are 7344 hours from February to December.


8. POWER SYSTEM ANALYSIS- RESULT

This section, will investigate how DTR affects the grid. To utilise the increased maximumcapacity from DTR an increased wind farm size is simulated and hence an extra injection ofactive power to the transformers low voltage side.

A work procedure to determine the effects on the grid due to the extra injected power will bepresented. The first step is to investigate how much more active power the surrounding nodes tothe connection point of the dynamically rated transformer can receive. From the DTR result wecan conclude that the transformer in many cases can be used at a higher capacity than the fixedrated power but it is not assured that the grid can transmit the extra power, this is first determinedby studying the PV-curve.

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Next, DTR is evaluated in terms of reliability. The probability of under or over voltage atbusses and overload in lines are calculated and compared with the case of the original, fixed ratedtransformer.

The studied grid is a 135 kV grid located in Sweden, see Figure 20, its exact location isnot presented due to company security reasons; throughout this report the area is referred to asKorsbarsdalen and is a part of Ellevio’s regional grid. Korsbersdalen consists of 55 busses, 32machines, 23 loads and 53 lines. It is the power components of Korsbarsdalen that are included ascontingencies in the PRA analysis. Korsbersdalen has interconnections with the rest of the Nordicpower system but the change in power flow with the surrounding grids during contingencies werenot included in the ACCC analysis. The interconnections can be seen as perfect machines andload that does not change due to a change in voltage.

Fig. 20. Diagram of the subsystem, Korsbarsdalen, with bus name notations.

Originally the dynamically rated transformer is not located in Korsbarsdalen, the choice oftransformer is limited by the transformers with enough data to build the DTR model. Moreover,to perform interesting power system analysis the grid cannot be too small. These two requirementslead to the dynamically rated transformer are, in theory, moved to Korsbarsdalen and replaced atransformer with almost the exact same properties located between bus 37 and bus 38. Throughoutfollowing calculations and simulations, the transformer between bus 37 and bus 38 will be referredto as the original location of the transformer.

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A. Contingencies

For n-1 contingencies, all lines, busses and machines are included with the fault statisticspresented in section 6.7. In total there are 157 contingencies, part of the purpose of performingthe PV curve and PRA analysis is to determine which of these 157 contingencies cause mostproblems and to calculate the probability of these problems occurring, therefore narrowing downthe 157 contingencies and focusing on the most critical.

B. Increased wind generation at the original location

To utilise the dynamically rated transformer, a higher generation is required. Therefore a numberof scenarios with an increased amount of wind power generation is investigated. In this chapter,the PV curve is used to test Korsbarsdalens voltage stability during increased load.

1) PV curve analysis for n-0 contingencies: The original place for the studied transformer isbetween bus 37 and bus 38 in Figure 20, the wind farm is connected to bus 38. The most criticalbusses to investigate are the busses near bus 38, but an increased generation at bus 38 have aneffect on the whole subsystem. Therefore, the PV curve is drawn for all busses in Korsbarsdalen,a selection of eight PV curves are shown in Figure 21.

Bus 38 is selected as the source subsystem and the rest of Korsbarsdalen as sink subsystem,meaning that the increased generation is done at bus 38, and to meet power balance, the existingloads in Korsbarsdalen are increased. Bus 40 and bus 36 are the most effected busses but also thevoltage levels at busses far away from bus 36 are effected from the increased power generationin bus 38.

Fig. 21. PV curve of node 38, connection point for the transformer

Bus 40 is most affected by the increased generation and is therefore the bus that will set thelimit of how much the generation can be increased in bus 38. The relationship between voltagedrop and increased generation is almost linear until 40 MW extra power is injected, after that thederivative of the curve become heavily negative and drops quickly until voltage collapse at 87

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TABLE 6TESTED SCENARIOS

Senariolabel

Totalgeneration [MW ]

Increasedgeneration [MW ]

Loading%

Deteriorationrate (15 C◦)


A1 43 0 68 0,02 0,08A2 65 22 103 1,02 3,56A3 85 42 135 36,86 103,66A4 105 62 167 1114,45 2612,8

MW. From a voltage stability perspective, we are likely to see voltage violations after 50 MWextra power have been injected, because the defined critical voltage limit of 0,95 p.u. is reached.

Moreover, the PV curves in Figure 21, are drawn with all system component in service, ascontingencies are tested these curves are likely to change for the worse, this phenomenon will beinvestigated later on in this study. In the next section, the performance in Korsbarsdalen duringan increased generation in bus 38 is evaluated for n-1 contingencies.

2) Probabilistic reliability assessment: PRA analysis is carried out for the original location. Thefirst scenario to be evaluated is the base case, which is a generation of 43 MW, it corresponds to aloading degree of 68% for the transformer. The second scenario is when the transformer operatesat 103% of rated power, the corresponding effect of wind power is then 65 MW. The worst casethat is tested is when the transformer operates at 167 % or 1,667 p.u current, the size of thewind farm is then 105 MW. All tested scenarios are listed in Table 6, total generation is the totalamount of wind power and loading of transformer is the percentage of which the transformer isloaded, compared with its rated power at one per unit voltage.

When the loading percentage of the transformer is calculated, it is assumed that the voltage atthe transformer low voltage side do not change during the increased increment of wind power,this approximation results in slightly higher percentage, since the apparent power is a functionof voltage and current. However, the voltage level changes differently depending on what typeof contingency the grid is exposed to. The calculating transformer loading level from constantvoltage therefore works as a good indicator.

Furthermore, for each tested scenario the wind park is expanded, to meet power balance theextra generation is divided among the other machines in Korsbarsdalen, i.e. the existing machinesdecreases their generation.

The first type of violation is under voltage at busses, see Table 7. Under voltage is defined asvoltage levels below 0,95 p.u. For scenario A1, there are 1,89 occasions per year that cause undervoltage, the average length of each occasion is 9,9 hours, the probability for under voltage is 18,8hours per year and there are in total four contingencies that cause under voltages.

All ready for A1 there are two voltage collapses, it means that the system does not have n-1redundancy for the base case without any extra injected power.

TABLE 7PRA RESULT BUS 38- VOLTAGES < 0,95 P.U

Scenariolabel

Freq.[OC/Y ]

Duration[H]

Probability[H/Y ]

Worstviolation [p.u.]

worst cont. No. ofcont.

No. of voltagecollapse

A1 1,89 9,9 18,8 0,907 LOSELINE37 4 2A2 2,17 9,9 21,5 0,905 LOSELINE37 5 2A3 1,57 9,9 15,5 0,904 LOSELINE55 4 3A4 1,79 9.9 17,7 0,900 LOSELINE55 5 8

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For A2 the probability of under voltage increases to 21,5 hours per year and there are fivecontingencies causing this violation. For the next scenario, A3 there is instead a decrease inprobability for under voltage, there is also a decrease in the number of contingencies causingunder voltage from five to four contingencies. On the other hand, the number of voltage collapseshave increased, there are now three contingencies that cause voltage collapse compared with twocontingencies for A2. As we move from scenario A2 to A3 there is one contingency that in A2only caused a voltage violation that is in A3 instead causing a voltage collapse.

The decrease in under voltage probability gives the appearance that the grid is improving fromscenario A2 to A3 but a voltage collapse is a more critical problem then a voltage violation.The last scenario A4, has in total eight voltage collapses and therefore causes extensive systemproblems for many fault types. Consequently, increasing the wind power generation to 105 MWrequires extensive grid reinforcement. Furthermore, the worst violation is increasing from 0,907p.u. to 0,900 p.u. throughout scenarios A1 to A4.

The next report, Table 8, shows voltage drops above 0,03 p.u. A voltage drop of 0.03 p.u. mightnot be a critical violation unless it results in under voltage or voltage collapse. However, it t canbe a good indicator of how voltage resistant Korsbarsdalen is to faults during increased injectionof active power.

TABLE 8PRA RESULT- VOLTAGE DROP > 0, 03 P.U

Scenariolabel

Freq.[OC/Y ]

Duration[H]

Probability[H/Y ]

Worstviolation[p.u.] worst cont. No. of

cont.No. of voltagecollapse

A1 2,19 9,9 21,7 0,096 LOSELINE55 6 2A2 2,27 9,9 22,4 0,098 LOSELINE55 7 2A3 4,04 9,9 40,2 0,100 LOSELINE55 8 3A4 3,98 10 39,6 0,104 LOSELINE55 7 8

We see an increased probability for a voltage drop thorough scenario A1 to A3 and then aslightly fall from A3 to A4 where there is an increase in voltage collapses from three to eight.The reason for the increased probability of voltage drop is that there is also an increase of thenumber of contingencies causing this violation, six contingencies for A1, seven for A2, eight forA3 and then a decrease in both probability and number of contingencies for A4.

The last report, Figure 9, shows the probability for overload of lines. Overload of lines is definedas load above 105% above the line’s rated apparent power. Ellevio has two different ratings forlines, one summer rating and one winter rating. The summer rating is lower than the winter rating;a warmer air temperature results in the lines start to sag at lower currents. The summer ratingis used for the PRA analysis. The report for over load of lines shows a similar pattern as for

TABLE 9PRA RESULT- OVERLOAD OF LINES. 105% OF LINES RATED MVA.

Senariolabel

Freq.[OC/Y ]

Duration[H]

Probability[H/Y ]

Worstviolation%



A1 4,60 13,1 60,4 141,3 LOSELINE30 6 2A2 6,35 12,3 77,9 145,6 LOSELINE30 8 2A3 4,91 12,9 63,6 146,7 LOSELINE30 7 3A4 5,47 12,6 69,0 147,2 LOSELINE30 8 8

under voltage. For scenario A1 the probability of overload is 60,4 hours per year and there aresix contingencies that cause this violation. There is an increase in probability from A1 to A2 andthen a decrease from A2 to A3 due to the voltage collapse. The worst violation is increased from141,3% to 147,2% through A1 to A4.

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For all studied violations: under voltage, voltage drop and overload, there are three differentcontingencies that cause the worst violations. Namely, LOSELINE37, LOSELINE55 and LOSE-LINE30, these contingencies represent faults of branches. The worst contingencies are defined inTable 16 and will be further discussed in section 8.4.

TABLE 10OVERALL PROBABILITY- ORIGINAL LOCATION

Scenario Freq.[OC/yr]

Duration[h]

Probability[h/y]

A1 7,02 12 84,4A2 8,85 11,6 102,6A3 8,30 11,7 97,1A4 7,58 15,7 119,0

Table 10, displays the overall probability for violations, where voltage and overload violations aswell as voltage collapse are included. When moving from scenario A1 to A4 there is an increasedprobability for violation of 41%.

C. Increased wind generation at alternative bus

In this section, an alternative location for a wind farm is investigated. First by looking at thecontouring diagram of Korsbarsdalen to locate an area with strong voltage, secondly by analysingthe PV curve and third by performing PRA of the system with an increased generation at thechosen bus.

At the original transformer location there is already a wind farm and we investigated if thetransformer’s true capacity could be utilised through an increased wind farm size. At the alternativelocation, the scenario is instead that an investor wants to invest in a wind farm and to avoid overdimension of the transformer, DTR is implemented.

The aim is to get a comparison of how differently the grid reacts to modifications depending onthe location of the changes. But more importantly to present an analysis procedure for evaluationof the effect of wind power and extra injected active power to the grid.

Furthermore, the alternative spot is investigated only for theoretical purposes and it has notinvestigated if it is piratically possible to build a wind farm at given location.

Figure 22, shows voltage levels at different regions in Korsbarsdalen. The colour red meansthat there is high voltage in the area and blue that there is low voltage, the scale goes between0,94 to 1,04 p.u. The darkest blue parts in Figure 22 are generation units, separated from the135 kV grid by transformers. By adjusting the taps in the transformer, a suitable voltage level isachieved on the secondary side, i.e. the 135 kV side. These most blue parts are, therefore, notcritical from a voltage stability point of view.

In the section 8.2, an increase of generation at bus 38 is evaluated. By looking at the con-touring diagram in, fig 22, we can see that the voltage there is low compared to other areas inKorsbarsdalen, busses 39, 40 and 41 have particularly low voltage; that these busses are voltagesensitive is also shown in the PV-curve, Figure 21.

An area with higher voltages can be seen in the bottom of Figure 22. For theoretical purposesbus 47 will be tested in the same manner as bus 38. The series components that are connectedto bus 36 are copied and connected to bus 47, the transferred components consist of a seriesconnected line, bus, transformer, bus and the wind farm according to Figure 23.

The original generation of 43 MW at bus 38 is left as originally. The two new busses that havebeen introduced are named 60 and 61, the transformer is connected between bus 60 and 61 andthe wind farms is connected to bus 61.

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Fig. 22. Diagram of subsystem Korsbarsdalen with contouring that shows the voltage level, red is high voltage and blueis low voltage, ranging from 0,94 p.u. to 1,04 p.u.

Fig. 23. Diagram of subsystem Korsbarsdalen, added series line, bus 60, transformer, bus 61 and wind farm to bus 47.

1) PV curve analysis for n-0 contingencies: Bus 61 is denoted as source subsystem and therest of Korsbarsdalen as sink subsystem. To keep power balance in the system the original loadsin Korsbarsdalen are made larger, and the increased generation is divided among these loads. ThePV-curve is drawn for all busses in Korsbarsdalen, a selection of eight curves are shown in Figure24.

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Fig. 24. PV curve of node 61, connection point for an alternative wind farm.

The system shows good response with regards to voltage stability increasing the active power atbus 61. The voltage level for bus 47, which is the closest bus to the alternative location, changesmarginally for extra injected power up to 120 MW after that the voltage changes more rapidlyuntil voltage collapse when around 200 MW of active power is in injected.

Bus 40 has low voltage from the beginning and even though it is located a long distance awayfrom bus 61 it is still affected by the increased generation in bus 61. The voltage change forother nearby busses to 61, as for example bus 50 and 53, are stable and change little until anextra generation of 190 MW is reached. Similarly to the PRA analyses for bus 39, the generationwill be increased to 105 MW, corresponding to 167% of transformer current compared with thefixed rated current, this increase will, according to the results in Figure 24, not cause any voltagerelated problems for Korsbarsdalen when all its components are in service.

2) Probabilistic reliability assessment- result: Because there is no wind farm connected to bus47 originally there will be two extra scenarios when PRA analysis is performed for the alternativelocation. The first scenario, B1, is for zero extra injection of active power, hence B1 is the sameas A1. All scenarios are listed in Table 11. The extra injected power at bus 61 is divided amongthe existing machines in Korsbarsdalen; which will decrease their generation.

TABLE 11TESTED SCENARIOS.

Senariolabel

Increasedgeneration [MW ]

Loading%



B1 0 0 0 0B2 15 24 0 0B3 35 56 0 0B4 65 103 1,02 3,56B5 85 135 36,86 103,66B6 105 167 1114,45 2612,8

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The first PRA result to be analysed is probability for under voltage, see Table 12. Increasingthe injected power from scenario B1 to B3 has no effect on the probability for faults but theworst violation changes slightly for the worse. There are two voltage collapses for scenario A1to A3. From scenario B3 to B4 when the extra injected power is increased from 65 to 85 MWthe number of voltage collapses is reduced to zero.

TABLE 12PRA RESULT- VOLTAGES < 0, 95 P.U.

Senariolabel

Freq.[OC/Y ]

Duration[H]

Probability[H/Y ]




B1 1,89 9,9 18,8 0,907 LOSELINE37 4 2B2 1,89 9,9 18,8 0,909 LOSELINE37 4 2B3 1,89 9,9 18,8 0,899 LOSELINE37 4 2B4 1,86 9.9 18,4 0,904 LOSELINE37 5 0B5 1,86 9,9 18,4 0,905 LOSELINE37 5 0B6 1,86 9,9 18,4 0,904 LOSELINE37 5 0

Table 13, shows busses with a voltage drop above 0,03 p.u. The probability for a voltage dropincreases from 21,7 hours per year to 31,2 hours per year. As mentioned before, a voltage drop initself might not cause any system problems, in this case the probability for under voltage decreasesand at the same time the number voltage collapses go to zero. Overall, from a voltage stabilityperspective the system is not sensitive to an increased injection of active power to bus 61, evenduring contingencies.

TABLE 13PRA RESULT- VOLTAGE DROP > 0, 030 P.U.

Senariolabel

Freq.[OC/Y ]

Duration[H]

Probability[H/Y ]




B1 2,19 9,9 21,7 0,096 LOSELINE37 6 2B2 2,27 9,9 22,4 0,094 LOSELINE55 7 2B3 2,53 9,9 25 0,098 LOSELINE37 7 2B4 3,15 9.9 31,2 0,100 LOSELINE37 9 0B5 3,15 9,9 31,2 0,099 LOSELINE37 9 0B6 3,15 9,9 31,2 0,099 LOSELINE37 9 0

The last report, in Table 14, describes the probability for overloaded lines. Both the number ofcontingencies causing overload and the worst violation decrease through B1 to B6.

TABLE 14PRA RESULT- OVERLOAD OF LINES. 105% OF LINES RATED MVA.

Senariolabel

Freq.[OC/Y ]

Duration[H]

Probability[H/Y ]

Worstviolation [%]



B1 4,60 13,1 60,4 141,3 LOSELINE30 6 2B2 4,3 10 42,5 134,4 LOSELINE30 4 3B3 2,85 10 28,5 126,5 LOSELINE30 2 2B4 3,47 10 34,7 129,6 LOSELINE31 4 0B5 3,47 10 34,7 135,5 LOSELINE31 4 0B6 3,47 10 34,7 129,7 LOSELINE31 4 0

Korsbarsdalen seems to benefit from extra injected power to bus 61, the two voltage collapsesthat existed originally disappear and if more than 65 MW active power is injected to bus 61 thesystem reaches n-1 redundancy. Also, the probability and magnitude of overloaded lines decreases.

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TABLE 15OVERALL PROBABILITY- ALTERNATIVE LOCATION

Scenario Freq.[OC/yr]

Duration[h]

Probability[h/y]

B1 7,02 12 84,4B2 6,81 12,1 82,2B3 5,61 9,9 55,8B4 5,61 9,9 55,8B5 5,61 9,9 55,9B6 5,61 9,9 55,8

Table 15, shows the overall probability for violations, where voltage, overload and voltagecollapse are included. As the wind farm size is increased from scenario B1 to scenario B6 theprobability for violation decreases with 34%.

The most problematic violations for the alternative location are LOOSELINE37, LOSELINE55,LOOSELINE30 and LOSELINE31, all of which represent a fault in a branch, these contingenciesare defined in Table 16. In the next section, we will consider why these contingencies causesystem problems and propose some solutions for higher reliability in Korsbarsdalen.

D. Analysis of worst contingencies

In this section results regarding both the original and the alternative location will be shown.Table 16 shows a summation of contingencies that give rise to the worst violations during thePRA analysis for both the original and the alternative location.

We will now continue the investigation of the most critical contingencies by drawing the PVcurves for the most critical contingencies and for the most affected busses. The most affectedbusses are the ones closest to the source subsystem and also bus 40, that have shown poor voltageresponse in previous simulations.

TABLE 16WORST CONTINGENCIES

Contingeciy From bus To busLOSELINE30 14 33LOSELINE31 33 34LOSELINE32 34 5LOSELINE37 39 40LOSELINE55 42 43

1) PV curve analysis of transformer original location during worst contingencies: Again,we look at the increased injection of active power to bus 38, but now considering the worstcontingencies. Figure 25, shows the voltage response at the closet bus, bus 36. Comparing theseresults with the PV curves that are drawn with n-0 contingencies, in Figure 21, shows that lessactive power can be injected before voltage collapse; contingencies have a negative effect onvoltage stability.

The worst contingency among these three with respect to bus 36 is contingency LOSELINE30,only 15 MW can be injected before voltage collapse. LOSELINE30 will also be one of thecontingencies that contributes to voltage collapse for scenario A3 and A4, which are where thenumber of voltage collapses has increased from two to three in the PRA analysis for the originallocation, bus 38.

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In Table 16, there are five contingencies that are listed as worst contingencies but in the graphbelow there are only three contingencies, this is because two of the worst contingencies causevoltage collapse already form zero MW injected power.

Fig. 25. Effect on bus 36 during increased power injection at bus 38 during the most critical contingencies.

Figure 26, also shows the PV curves for injection of active power to bus 38, but now consideringbus 40 during the most critical contingencies. It is again LOOSLINE30 that set the limit for extraactive power but LOSELINE37 starts at a critically low voltage level, below 0,90 p.u.


2) PV curve analysis of transformer alternative location during worst contingencies: The sametype of PV curves will be drawn for increased injection of active power to the alternative locations,bus 61. Figure 27 shows the PV curves for the closest bus to the injection point, bus 47.

The PV curve is drawn with 65 MW power already at bus 61. From the PRA analysis of bus61 it is concluded that the system has n-1 redundancy for load of 65 MW and more; that is whythere are five instead of three worst contingencies in Figure 27 compared with Figure 25. Noneof the critical contingencies have a big impact on the amount of extra injected active power, it ispossible to inject about 65+135=200 which is approximately the same as when the PV curve forn-0 contingencies are drawn in Figure 24. Therefore, bus 47 can be excluded as a critical bus.

The same analysis is then done for bus 40 during injected power to bus 61 and consideringthe five worst contingencies, these curves are shown in Figure 28. In the PV curve with n-0contingencies it can be seen that bus 40 starts with a low voltage but there are two contingenciesthat cause the voltage at bus 40 to drop considerably. First LOSELINE 55, that starts at around

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0,96 p.u. and secondly LOSELINE37 that makes bus 40 start at critically low voltage level below0,90 p.u.


3) Voltage angle analysis: In this section the reasons for why the five most critical contingenciescause violations will be looked into. Figure 29 shows the map of Korsbarsdalen with voltageangles. The red colour represents high angle and blue represents low voltage angle. The top leftcorner is mostly red and the bottom right corner is mostly blue.

Furthermore, active power flows from a high voltage angle to low voltage angle, meaning thatthere is a lot of generation in the top left corner that needs to be transmitted to the load at thebottom right corner.

There are in total three parallel branches to transmit energy from the upper part to the bottompart and these are the branches where violations are seen. If one of these parallel branches failsthen the other two will be overloaded and result in voltage instabilities.

The grey lines in Figure 29, display the five most critical lines. The two contingencies or typesof faults that are causing voltage collapse at the original location and in the base case, are loss ofthe lines between bus 5 to bus 34 and from bus 33 to 34. The other lines drawn in grey only causevoltage and overload violations for the base case. However as the wind farm is increased fromscenario A1 to A4 all of the most critical contingencies cause voltage collapse for the originallocation.

Through the PV curve and PRA analysis, as well as in the contouring map in Figure 22, wecan see that the area around bus 40 originally has low voltage and has low voltage stability, thisexplains why there are voltage and overload violations when the wind farm at bus 38 is expanded.Increasing the generation at bus 38 results in the three parallel branches that are responsible for

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Fig. 29. Map of Korsbarsdalen with voltage angles, red is high angle and blue is low angle. The lines in grey representsthe five worst contingencies.

carrying the current from the top to bottom part of Korsbarsdalen, becoming even more burdened,especially during faults. Increasing the generation at the original location will also bring downthe already low voltage at bus 40 and result in further voltage instabilities in Korsbarsdalen.

E. Active power losses during n-0 contingencies

TABLE 17BRANCH LOSSES FOR INCREASED POWER INJECTION AT BUS 38

Senariolabel Total Losses [MW]

A1 21,02A2 21,42A3 21,64A4 22,1

If we consider the total active losses during n-0 contingencies, see Table 17, these are increasedby 5,15%, from scenario A1 to scenario A4. The explanation for this is that when the generation

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at the original location increases the grid has to transmit even more active power and consequentlythe losses increase.

Now, looking at bus 47, that has shown high voltage stability in both PV curve and PRAanalysis increasing the generation at the alternative location, bus 61, means that a higher share ofthe active power is generated closer to the load, hence, decrease the loading of the three parallelbranches connecting the upper and lower part of Korsbarsdalen. As we increase the generation atbus 61 from scenario B1 to B6 both the probability for overload and worst violation of over loaddecreased, see Table 14.

TABLE 18LINE LOSSES FOR INCREASED POWER INJECTION AT BUS 61

Senariolabel Total Losses [MW]

B1 21.02B2 19.47B3 17.61B4 17.30B5 17.14B6 17.40

Furthermore, the total losses during n-0 contingencies decreased with 17,22% form scenarioB1 to B6, due to that the active power does not have to be transmitted as far.

9. SUMMARY OF RESULTS AND DISCUSSION

To reach the objectives we required knowledge in two areas, namely in dynamic rating andpower system analysis. The objectives for dynamic rating is to build a DTR model and use itto calculate transformer behaviour during certain load and ambient temperature scenarios. Thepurpose of the DTR is also to investigate if the wind farm can be expanded without endangeringtransformer lifetime. Regarding power system analysis the objective is to test if the grid can receivethe extra generation that followed with DTR and an increased wind farm size. The objectives havesuccessfully been reached; the summary of the results are presented in this section.

The DTR algorithm is used to calculate how much the wind farm, connected at the transformerlow voltage side, can be expanded. Historical measurements of transformer loading and ambienttemperature are used as input. The result showed that the wind farm, for this specific time period,can be increased by 76% without breaching any of the temperature and load limits defined by IEC60076-7. An increase of the wind farm by 76% results in unity lifetime use, meaning that whenthe transformer has been used for ten months, also ten months of transformer lifetime have beenconsumed, compared with today when only 8,3 hours are consumed for the same ten months. Theinput was collected from February to December 2016. Ten months time period is too short to givean exact answer of how much the wind farm can be expanded, since the generated power canvary from year to year. Nevertheless, the result of 76% available transformer capacity indicatesthat the wind farm can be expanded, but in order to verify this a longer measurement period isrequired. It should also be mentioned that increasing the load will always result in faster insulationdegradation, if the load is increased by 76% the transformer can theoretically last for 17,13 years.It is always a trade-off between increased load and transformer lifetime, economical analysis tofind the loading that results in maximum profit have to be conducted to find the ultimate loadlevel.

The constructed DTR algorithm is used to calculate transformer behaviour for different loadlevels and ambient temperatures. The result show that especially during low ambient temperature,

54

the transformer could operate safely above fixed rated power. Simulations with an ambient temper-ature of 28◦C and a load level of one per unit result in a hot spot temperature of 110◦C, meaningthat as long as the ambient temperature is below 28◦C, the transformer could safely operate atname plate rating and the lifetime use will then exceed the designed lifetime. The highest ambientair temperature during the past five years at the transformer location is 28 degrees but most ofthe time much lower. It would therefore be possible to operate the transformer above name platerating for most part of the year.

The power system, Korsbarsdalen, does not have n-1 redundancy for the base case withoutextra injected active power. It should be mentioned that in real life this dose not cause a voltagecollapse. If one of the two critical lines is experiencing failure, the machines in Korsbersdalenwill decreased their load, hence, avoiding voltage collapse. Nevertheless, the system will benefitfrom more redundancy and higher voltage stability in some areas; especially the voltage level atbus 40, which is low. More reactive power in the area around bus 40 can therefore increase thevoltage stability of Korsbarsdalen. This could be done by investing in variable shunts that havethe ability to provide reactive power. Ellevio has, before the start of this master thesis, alreadyplanned to invest in redundancy for some of the lines that was identified as extra vulnerable, thesechanges are not accounted for in simulations in this study.

The original location for the transformer, at bus 38, shows poor response to increased injectionof power. The probability for both voltage and overload violation increases and the number ofvoltage collapses increases from two to eight when increasing the active power. The total amountof violations increased from 84,4 to 119 hours per year. If DTR is to be implemented in theoriginal location, the grid will have to be reinforced.

The probability of under voltage and overload when power is injected to bus 61 decreasesand the total amount of violation decreases from 84,4 to 55,8 hours per year. The grid benefitsfrom more active power at the alternative location which is located closer to the load, thereforeactive power does not need to be sent through the already loaded lines. This results in 17% lowerlosses in lines for scenario B6 during n-0 contingency. The two contingencies that caused voltagecollapse for the base case only cause violations when 65 MW or more wind power is installed atthe alternative location; the system gained n-1 redundancy.

Moreover, The fluctuating power generation that characterises wind farms can be seen in theload history diagram, Figure (18). To gain n-1 redundancy for Korsbarsdalen at least 65 MWneeds to be injected to the alternative location. This means that even if a wind power plant is builtat the alternative location, it will, during low wind speeds, produce less than 65 MW, hence thesystem will not have n-1 redundancy during low wind speed. To ensure n-1 redundancy a timeinvariant power supply will have to be built.

10. CONCLUSIONS

In this master thesis, a medium power transformer is dynamically rated. The result shows that,in many cases, the transformer can operate above its name plate rated power, especially if theambient temperature is low.

The DTR algorithm is used to calculate how much the wind farm, connected at the transformerlow voltage side, could be expanded. Historical measurements of transformer loading and ambienttemperature are used as input. The load history is increased in an iterative fashion until either unitylifetime loss is gained or any of the limits for long time overload of medium power transformerare reached, these limits are defined in the IEC std. 60076-7. Applying the above method to the

55

transformer in this study shows that the wind farm can be expanded without investing in a newtransformer.

DTR can be used both in the investment stage of a new transformer, to avoid over dimensioningand also to increase the capacity of already operating transformers; both of these scenarios canbenefit the environment and society. A smaller transformer or a more efficient use of operationaltransformers implies lower investment costs and therefore lower tariffs. When a smaller transformeris purchased or new investment is avoided, raw material is saved and benefits the environment,for example, the mining and processing of iron results in carbon dioxide emissions.

Moreover, through short term overloading, the grid operator can take advantage of the delayedchange in hot spot temperature after a load increase and the transformer can operate at a con-siderably higher load level compared with the name plate rating. It takes time for the hot spottemperature to adjust to a higher load level. This time is depending on the initial load level, wheninitial load is low, then also the hot spot temperature is low, hence, resulting in a longer time spanfor the hot spot temperature to adjust to the new higher load. When the load is decreased the hotspot temperature decreases without time delay.

Power system analysis are then carried out on the grid, with the objective to test how DTR andincreased wind power affects the grid performance. A procedure to perform system analysis forthe case of DTR and wind power is developed. The power system analysis procedure is designedin a manner so that it can be adapted for similar scenarios, hence it can be viewed as a manualto analyse grid performance of DTR, wind power or other similar changes.

The developed procedure includes voltage stability and probabilistic reliability assessment anal-ysis and provides a broad picture of system performance in regard to voltage stability, over loadand losses. The simulations are done in steady state; both voltage stability and reliability analysisare built upon power flow simulations in the power system tool PSS/E.

For reliability studies, a set of contingencies are defined including machines, branches andbusses. These contingencies were tested for different scenarios of increased wind farm size. Allpower components that are included in the contingency analysis are represented by a failure rateand a repair time. It can then be decided what type of faults that are causing most damage whenDTR was implemented and the change in probability for violations could be compared with andwithout DTR.

Through the process in this thesis it is possible to sort the contingencies and separate those thatdo not cause any severe violations from those that cause severe violation. This information canbe used for efficient reinforcement of the grid. The contingency and reliability analysis can thenwork as base to find the solutions that will decrease the probability for violations most efficiently.Furthermore, the developed procedure can also be used when expanding the grid and to determinewhich grid alternative that will be most reliable and most cost efficient in the long run.

DTR is mostly implemented to increase the capacity of already existing transformers, but canalso be used in the investment stage to avoid over dimensioning, as is described in the literaturereview. The scenario of using DTR in the investment stage is used to test an alternative location fora wind farm and a dynamically rated transformer; the alternative location dose initially not haveany wind power. The power system analysis for the alternative location shows a different result tothe original location, even though the same wind farm and transformer was used. The alternativelocation was in an area with strong voltage and therefore the response to increased power injectionwas better. An interesting result is also that it was a bus far away from the alternative locationthat caused problems. It is therefore important not only to focus on power components but also

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to have the wider system view, a change of one power component in the grid might affect thewhole system.

11. FUTURE WORK

The power system analysis performed in this study are done in steady state, for future workit would be interesting to investigate the effect of DTR and wind power during real time powerchanges, i.e. during transient conditions. Transient analysis is expected to show information ofhow the grid and transformer behaves during rapid load changes that are common for wind powerplants.

The result from the power system analysis of Korsbarsdalen shows that part of the grid hadvoltage instabilities, especially due to low voltages. If the voltage differs too much from one p.u.and especially if it is too low it can cause problems during faults, when the voltage normallydrops even further; this can in worst case result in a voltage collapse. Voltage stability problemscan be solved by increasing the amount of reactive power to these parts of the grid. As futurework, a method for maximising the benefit of extra reactive power can be designed. A populartopic in the same area is ancillary services which means that customers connected to the gridprovide a service that benefits the grid, such service can be to provide reactive power. Wind farmstoday tend to cause voltage instabilities because of their lack in feeding the grid with reactivepower. More studies of how ancillary services for wind power can benefit grid performance cantherefore be valuable.

The DTR algorithm that is used in this study is originally developed for testing transformers,for example in the performance of a heat run test. During these kinds of test the load is graduallyincreased over many hours. The power at wind farms often change rapidly, as can be seen in theload history diagram, Figure (18). Hence, adopting the DTR algorithm to a fast changing loadmight increase the accuracy of calculated top oil temperature . Such studies can be carried outby measuring the true hot spot temperature with means of optic fibre and compare the measuredhot spot temperature with calculated hot spot temperature.

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