Impact of transformer core size on thereactive power requirement of powertransformers due to GIC

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DEGREE PROJECT, IN , SECOND LEVEL STOCKHOLM, SWEDEN 2014

Impact of transformer core size on the

reactive power requirement of power

transformers due to GIC

CLAUDIA BERGSÅKER

KTH ROYAL INSTITUTE OF TECHNOLOGY

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Abstract

Geomagnetiskt inducerade strömmar (GIC) är ett naturfenomen som uppstår till följd av solstor- mar. Vid en solstorm kastas stora mängder magnetiserad plasma ut från solens yta, och när denna plasma når jorden uppstår uktuationer i det jordmagnetiska fältet. Detta kan leda till att DC- strömmar induceras i långa transmissionsledsningar. Dessa överströmmar påverkar kraftsystemet på era olika sätt, bland annat har de en stor påverkan på transformatorer. Då överströmmen

yter genom transformatorlindningarna ökar det reaktiva eektuttaget för transformatorn, vilket kan leda till spänningsinstabilitet i systemet. En fråga som legat till grund för detta projekt är hu- ruvida en ökning av transformatorkärnans storlek gör transformatorns reaktiva eektuttag mindre känsligt för GIC. För att undersöka detta har en ny transformatormodell använts; den såkallade hybridmodellen som kombinerar dualitetsprincipen med en matrisrepresentation av transformatorn.

Denna modell, som nyligen implementerats i simuleringsprogrammet PSCAD, har använts för att simulera GIC i transformatorer med kärnor av olika storlekar. Resultaten från dessa simuleringar indikerar att större transformatorkärna medför mindre förändring av det reaktiva eektuttaget när transformatorn utsätts för GIC. Det är även tydligt att det reaktiva eektuttaget som funktion av GIC är en icke-linjär funktion när hybridmodellen används. Denna funktion har tidigare ansetts vara linjär.

Geomagnetically induced currents (GIC) are a natural phenomenon which arises due to solar storms. During a solar storm, large amounts of magnetized plasma are ejected from the surface of the sun. When this plasma reaches earth, it causes uctuations in the geomagnetic eld. Such

uctuations may induce DC over-currents in long transmission lines. These currents aect the transmission system several dierent ways; In particular high voltage transformers are sensitive to GIC. When the over-current ows through the transformer windings the reactive power absorption of the transformer increases, which may lead to voltage instability in the power system. For this project, the main issue has been to determine whether or not an increase in the size of the transformer core leads to the reactive power absorption being less sensitive to GIC. In order to investigate this issue a recently developed transformer model has been used; the Hybrid transformer model.

This model combines the principle of duality with a matrix representation of the transformer. The Hybrid transformer model, which has recently been implemented in the power system simulations software PSCAD, has been used to simulate GIC events in transformers of varying core sizes. The results from these simulations indicate that a larger transformer core is associated with a smaller increase in reactive power absorption during a GIC event. It is also clear that the reactive power absorption as a function of GIC magnitude is a non-linear function when the Hybrid transformer model is applied. This function has previously been considered a linear function.

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Acknowledgments

First of all I would like to thank the Norwegian Transmission System Operator, Statnett, for funding this Master's Degree Project. In particular, I want to thank Jan-Ove Gjerde for giving me this great opportunity, and Trond M. Ohnstad who has been my supervisor during this project.

I would also like to thank Dr. Nicola Chiesa for answering the questions I had regarding the XFMR transformer model for GIC studies in PSCAD. Furthermore, I want to thank Prof. Göran Engdahl at KTH for showing me a great deal of patience and understanding. I would also like to thank my supervisor at KTH, Seyed-Ali Mousavi, for providing me with useful information and doing his best to help me despite the distance.

Finally I want to thank Dr. Luigi Vanfretti. Without your help and support this project could not have happened.

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1 Introduction

1.1 Background

Geomagnetically Induced Currents (GIC) are near-DC currents owing in transmission lines due to disturbances in the geomagnetic eld. These currents are a natural phenomenon which may pose a threat to the power system, and it arises as an eect of solar storms; eruptions of plasma and charged particles from surface of the sun. The solar activity follows an 11-year cycle, and the years 2012-2014 have been associated with a solar activity peak - meaning an enhanced probability of solar eruptions. For this reason, the interest in solar activity and the consequences it may have on society has been high during the last couple of years, with articles in e.g. National Geographic and IEEE Spectrum providing speculations regarding the potential dangers of solar storms and GIC. In the power system, the most vulnerable component to GIC impact is the power transformer. One of the eects of GIC on the power transformer is that reactive power absorption dramatically increases during a GIC event, which could lead to voltage instability and power outages. In order to make a scientic, reliable assessment of the risks associated with GIC, the behavior of power transformers when exposed to GIC must be studied.

1.2 Problem Denition

The key to studying GIC eects on the power system is transformer modeling. When simulating a GIC event in a transformer a complex model is required, a model which incorporates the non-linear characteristics of the transformer core. GIC can be described as a slow transient, for which reason an electromagnetic transient simulation software must be used. A transformer model suitable for GIC studies called the Hybrid Transformer Model has recently been developed. The purpose of this thesis is to use the Hybrid Transformer Model to study the increase of reactive power demand of large power transformers due to GIC. The modeling approach is presented in [1]. The focus of the thesis is core design impact on reactive power losses due to GIC. The main problems are

To determine how the increased reactive power demand depends on GIC magnitude according to the Hybrid Transformer Model

To determine if increased cross-sectional areaal area of the transformer core makes the transformer less sensitive to GIC

This thesis project is limited to the study of high voltage three-phase power transformers.

1.3 Objectives

The following objectives were set for the thesis:

Perform a literature review on GIC and transformer modeling in general and the Hybrid Transformer Model in particular

Learn how to use PSCAD for transient simulation

Use the implementation of the Hybrid Transformer Model in PSCAD to simulate GIC events and record reactive power absorption

Find a method for varying the transformer core cross-sectional area and record how the increase in reactive power demand depends on core cross-sectional area.

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1.4 Overview of the report

This report begins with a short introduction to the GIC phenomenon, and how power transformers are aected when subjected to GIC during solar storm events.

Section 3 describes transformer models for electromagnetic transients studies in general, and the XFMR transformer model in particular. In section 4 the GIC simulations carried out in this project are presented and discussed.

Finally, section 5 provides conclusions to be drawn from the results presented in section 4, and suggestions for further studies.

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2 The GIC Phenomenon

2.1 Geomagnetically Induced Currents

Geomagnetically induced currents (GIC) is a phenomenon related to solar activity. It arises due to so-called solar eruptions or solar ares in which the sun ejects plasma and radiation from its surface. An image of a solar are is shown in Fig. 1. Solar eruptions lead to solar storms, which are large streams of magnetized plasma traveling through interplanetary space. The magnetosphere surrounding our planet protects us from the major part of this plasma ow. However, charged particles can enter the magnetosphere in the polar regions, where the geomagnetic eld has a vertical direction, and reach the earth's atmosphere. These high-energy particles give rise to auroras, and cause uctuations in the geomagnetic eld. Disturbances in the geomagnetic eld cause changes in the currents in the ionosphere, which in turn may cause electric potential dierences at the earth's surface. Such potential dierences cause near-DC (0.01-0.001 Hz) currents to ow in the ground[14]. These currents ow through loops consisting of overhead-lines, power transformers, grounded neutrals and ground, and are known as Geomagnetically Induced Currents (GIC). GIC levels up to a few hundred amperes have been observed[14].

The transformer is considered the most vulnerable transmission system component primarily aected by GIC. The DC current owing in the transformer windings during a GIC event gives rise to an oset in the magnetization characteristic of the transformer core, which causes the transformer to saturate each half cycle of the system frequency. The transition from the unsaturated state to the saturated state is associated with a change in inductance of the transformer core by several orders of magnitude. As a result of the variation in core inductance the exciting current drawn from the supply is dramatically increased. Since the exciting current lags the system voltage by 90º, this leads to a rise in reactive power demand of the transformer. Unless there is sucient reactive power compensation in the system, this can lead to voltage instability, and in the worst case scenario voltage collapse.

Another eect of half-cycle saturation is increased harmonic content in exciting currents, which may lead to false relay tripping. Also, overheating of transformers as a consequence of saturation caused by GIC has been observed.

2.2 GIC impact on the power transformers

Frequently discussed risks associated with GIC events are overheating of transformers, false relay tripping caused by increased harmonic content of line currents, and voltage instability due to increased reactive power (var) absorption of the transformer. Previous work has mainly been focused on the rst two; temperature rise in transformers and false relay tripping. There have been wild speculations regarding the risks of transformers being damaged due to overheating as a consequence of GIC. The risk of overheating depends on the magnitude and duration of the GIC. Typically, a GIC event can be seen as high magnitude DC peaks of short duration (order of 10 minutes), separated by relatively low magnitude periods (order of 60 minutes). The duration of each peak is normally not great enough to increase the temperature of the transformer to a harmful level. In [12] two experiments on the eects of DC injection on temperature of windings and structural parts of power transformers are described, one performed by Hydro Quebec and the other by Fingrid. In these experiments, single and three-phase power transformers were injected at no load with high levels of DC; 75 A/phase up to one hour, and 200/3 A/phase for 20 minutes,

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Figure 1: Solar eruption on June 20, 2013. Image from NASA/SDO

respectively. The temperature rise in windings and structural parts were measured, and both experiments reported small temperature rise in windings and moderate rise in structural parts, compared to the IEEE Standard C57.91 temperature limits. It was concluded that at the GIC levels injected, no transformer damage would occur.[12]

False relay tripping due to GIC has been reported on various occasions. When the transformer is operating in the saturated state, the harmonic content of line currents increases. Relays may then react to the harmonics as to an over current, and trip falsely. The most severe incident took place in Quebec, Canada, in 1989.

Another concern is voltage instability due to increased var losses. The voltage stability depends on the operation point of the system. If the operation point is already close to a collapse, a GIC event could lead to voltage collapse. If a GIC event drives the system into a near collapse state, operators may be forced to disconnect load in order to avoid collapse. The stability of the power system depends on many dierent factors. Increased reactive power absorption in power transformers, combined with loss of reactive compensation equipment and failure to disconnect shunt inductances could lead to instability.

2.2.1 Reactive power losses due to GIC

When the geomagnetically induced DC-current ows through the transformer windings it generates a DC-ux in the transformer core. The DC-ux strength depends on the magnitude of the GIC, the number of transformer winding turns and the reluctance of the core. The DC-ux changes the operating point of the transformer on the hysteresis curve (the characteristics of the ferromagnetic core material). During normal conditions the transformer operates in the linear region of the hysteresis curve. The DC-ux generated by GIC causes an oset, so that the transformer reaches the saturated region of the hysteresis curve every half-period of the system frequency. Fig. 2 shows the shift in the operating point. The exciting current drawn from the supply is dramatically increased when the transformer operates in the saturated state. Also the harmonic content of the

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Figure 2: Oset in magnetic characteristics caused by DC excitation. The DC ux is added to the AC ux during one half-period, and substracted from the AC ux during the other half-period.

This leads to core ux densities in the saturated region. Figure from [3].

current is increased. The exciting current lags the system voltage by 90º, and is therefore associated with reactive (var) losses.

In [1] it is stated that only the fundamental lagging current components have a signicant impact on the system voltage prole. The fundamental component of the reactive power can be calculated as:

Q₍₁₎ = q

3 · V²I₍₁₎− P² (1)

where V is the line-to-line voltage, I(1) is the rms value of the fundamental component of the line current, and P is the active power consumed by the transformer. It is here assumed that the voltage has no harmonic distortion.[1]

In previous work [1, 12], it has been concluded that the reactive power absorbed by the transformer when subjected to GIC is directly proportional to the GIC level. The results presented in this thesis will suggest that the relationship between reactive power absorption and GIC level is non-linear.

2.2.2 The dierence between ve-limb and three-limb cores

The transformer core of a three-phase transformer has either ve or three limbs. In a ve-limb transformer, the outer limbs serve as return paths for the ux generated in the core legs. Fig. 3 shows a ve-limb transformer core. A three-limb transformer core, shown in Fig. 4, has no outer limbs and the DC-ux generated by by the DC current owing in the windings must close through the tank walls and air surrounding the core. Air and the non-magnetic tank material have orders of magnitude higher magnetic reluctance than the ferromagnetic core material. This means that in a three-limb transformer the ux must pass through a very high reluctance return path in order to close, which means that the change in ux due to GIC is smaller for a three-limb transformer.[3]

Three-limb transformers have proven to be less sensitive to GIC than ve-limb transformers [15]. In the Norwegian transmission system, ve-limb core transformers are common at high voltage levels.

Approximately 75% of the transformers at 400 kV are ve-limb. [8]

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Leg Leg Leg

Outer limb Outer limb

Figure 3: Core dimensions for a ve-limb transformer

Figure 4: Three limb transformer core

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2.3 Historical solar storms

The strongest solar storm ever recorded took place in 1859 and is known as the Carrington event

, after the British amateur astronomer Richard Carrington. Between August 28 and September 4, 1859, powerful auroras were observed around the world. This phenomenon which normally only takes place near the polar regions was observed in North- and South America, Europe, Asia and Australia. Auroras appeared as far south of the North Pole as Hawaii and the Caribbean, and as far north of the South Pole as Santiago, Chile. Geomagnetic irregularities were also observed;

magnetometer traces were driven o scale and the telegraph networks all over the world suered major disruptions.[13]

On September 1, Carrington observed, with his unaided eye, on the sun's surface two patches of intensely bright and white light [13] from a large group of sunspots (Sunspots are areas of lower temperature than the surroundings, for this reason they appear darker on the solar disc). This is the

rst recorded observation of the phenomenon now known as solar ares; eruptions of intensied radiation, plasma and charged particles from the sun. Although no connection between the solar

are and the peculiar magnetic disturbances were made at the time, the Carrington event would later contribute to the understanding of space weather and solar storms. In 1859, there was no power system to be aected by the powerful magnetic disturbances. One frequently discussed issue is what consequences a solar storm of the same proportions as the 1859 event would have on society today. Although it is unclear exactly how strong the 1859 solar storm was, it is agreed upon that it was stronger than any solar storm observed in modern time. Since there is only one known event of this proportion, it is dicult to estimate how often they occur. The most common estimation is that a solar storm of this strength appears once in 500 years.[15]

The most severe GIC event of modern time occurred in Quebec, Canada, in March 1989. It was caused by a coronal mass ejection occurring March 19, 1989. Two days later voltage variations in Hydro Quebec's transmission grid were detected. Early in the morning of March 13 ve 735 kV transmission lines were disconnected as a result of false relay tripping, which caused the system voltage to collapse. Nine hours later, 17% of the system load was still disconnected from the power grid [15]. The solar storm of March 1989 aected the power grid also in other parts of North America. In Manitoba, Canada, Manitoba Hydro observed a dramatic increase in reactive power consumed by synchronous capacitors at one of their substations. The total reactive power demand from the substation increased by 420 MVar within a few minutes time span. [8] In Virginia, U.S., at a substation in the Allegheny Power System a 350 MVA auto transformer was removed from service because of high levels of gas in the transformer oil (a byproduct of internal heating). The overheating was believed to be caused by GIC. [8]

As previously mentioned, wild speculations regarding the consequences of a strong solar storm have been seen in the last few years. In the February 2012 issue of IEEE Spectrum John Kap- penman concludes that it is reasonable to assume that a solar storm of the same proportions as the Carrington event, or even stronger, will happen again. Kappenman describes the consequences of such an event as a veritable doomsday scenario; It will lead to a massive planetary blackout, which in turn will cause severe damage on infrastructure, food and drinking water shortages, and healthcare failures. Kappenman states that the fatalities in case of such an event may reach millions of human lives. He concludes that a solar storm of such proportions would amount to one of the worst disasters in recorded history. It is however pointed out in [12] that articles such as these

do not oer a scientic and engineering analysis of the many complex issues that determine power system impacts.

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3 Transformer Modeling

There are numbers of dierent approaches for modeling and simulating electromagnetic transients in power system transformers. Typically, the choice of model depends on the character and frequency of the transient to be simulated. Very few transformer models can be applied to all power system transients for a complete frequency range. The frequency of the transient in question also determines which simplications are in order. A GIC event can be described as a low frequency transient.

One of the challenges when modeling the transformer for GIC studies is the modeling of the core non-linearity. For the ferromagnetic material of the core, the relationship between the magnetic

eld strength H, generated by the magnetizing (exciting) current of the windings, and the ux density B is non-linear and history-dependent, and follows the hysteresis loop. Magnetic saturation refers to a state where the ux density B reaches a maximum value, and an increase in magnetic

eld strength no longer produces an increased ux density. In the saturated state, the permeability of the iron core is lower than in normal operation which means that more ampere-turns will be required in order to produce the same amount of ux. In transformer models, the core non-linearity is generally represented by a non-linear inductance characterized by the relationship between ux linkage and current.

Another important parameter when modeling low frequency transients such as GIC events is leakage inductance. Leakage inductance represents magnetic ux owing outside the core, in air and inside and between the transformer windings.

The simplest transformer models for simulation of low-frequency transients consist of matrix representation of the branch impedances, where the elements of the matrices are found from short- circuit tests. This approach does not include the non-linear eects of the transformer core that are crucial to GIC studies. Non-linear elements representing the core may be attached externally to such a model. However, an externally added core is not necessarily topologically correct. [7, 9]

A topologically correct core representation can be achieved from duality-based transformer models. Such models are based on magnetic circuit theory. Magnetic circuit theory states that magnetic parameters can be transformed into electric parameters. Each component in a magnetic circuit has a corresponding electric circuit component. In a magnetic circuit, the ampere-turns drive a magnetic ux through a ux path characterized by a certain reluctance, in the same way that a voltage source drives a current through a conductor of a certain resistance. The node equations of the magnetic circuit are duals of the electrical equivalent node equations [7].

GIC impacts on transformers have previously been modeled using either FEM (the Finite Ele- ment Method) or magnetic circuit theory. For power system studies the latter is often preferred, due to the great computational burden of FEM analysis. [1]

A new transformer modeling approach, presented in [5], is the Hybrid Transformer Model. This model is based on a magnetic circuit representation of the transformer, which is transformed into its electric dual. The model is then separated into a core model and an inverse impedance matrix representation of the leakage uxes. The winding losses and coil capacitances are added at the transformer terminals. One of the main advantages of this model is that it includes a non-linear, topologically correct core model. The Hybrid Transformer Model is implemented in the software ATPDraw, and is there called XFMR. [5]

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3.1 The Hybrid Transformer Model

The Hybrid Transformer Model is based on a combination of two modeling approaches; a short- circuit model given by an admittance matrix representing leakage inductance, and a non-linear duality based core representation. The model incorporates frequency-dependent winding resistances and capacitive eects. A detailed description of the Hybrid Transformer Model can be found in [9, 10, 5]. Here, a brief summary will be given.

The core is modeled according to the following. A ctitious, innitely thin N+1th winding (where N is the number of physical windings) is assumed for the connection between the core equivalent and the short-circuit model. The N+1th winding is thought to be located at the surface of the core leg, between the innermost winding (normally low-voltage) and the core. Each leg and yoke of the core is represented by a core-loss resistance in parallel with a non-linear magnetizing inductance, as shown in Fig. 5. The behavior of the magnetizing inductance is modeled by the Frolich equation (2), which is an approximation of the B-H relationship of the core material. The magnetizing characteristic of the core is thus determined by the parameters a and b , which are specic to the core material. The magnetizing inductances of the legs and yokes are estimated individually based on the relative cross-sectional area and length of each part. [10]

B = H

a + b · |H| (2)

Equation (2) is reformulated into a relationship between ux linkage and current, Ψ − i , in the following manner [5]: the ux linkage is introduced as Ψ = B · A · N, and the current i = H · l/N.

Here, N is the number of turns of the innermost winding, A is the cross-sectional area, and l is the length of the core section in question. This gives:

Ψ = i · A · N²/l

a + b · |i| · N/l (3)

If the B-H characteristics, the absolute dimensions of the transformer core A and l, and the number of turns N are known, (3) and (2) can be used directly to nd Ψ − i pairs for each limb, which are used to describe the non-linear magnetizing inductance. However, these data are seldomly provided by transformer manufacturers. In order to use test report data to obtain Ψ − i pairs, (3) is re-written into:

Ψ = A_r· i

a⁰· lr+ b⁰· |i| (4)

where the substitutions

a⁰ = a · l_L/ N²· A_L (5)

and

b⁰= b/ (N · AL) (6)

have been made. Here, AL and lL are the absolute values of cross-sectional area and length of the core leg, and Ar and lr are the relative cross-sectional area and length of the core section to be modeled relative to the leg, i.e. Ar= ^A^section_A

L and lr= ^l^section_l

L . The absolute dimensions are thus eliminated, and only the relative dimensions of the core are required. The parameters a⁰and b⁰are found as functions of (VRM S, IRM S)pairs, available from factory test reports, which are converted

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Ry Rl

Ry

Rl Rl

L l L l

L l

L o L y L y Ro L o

Ro

Figure 5: Core model for a ve-leg transformer

into the corresponding Ψ−i pairs for each limb. A description of the parameter estimation method, which involves an optimization process, can be found in [10].

The core loss resistances consist of hysteresis losses, eddy-current losses and anomalous losses, which are lumped together into one core loss resistance for each limb [9]. The core losses are assumed to be proportional to the core volume, so that the outer leg and yoke resistances (Roand R_y) can be set as proportional to the leg resistance Rl. The total core loss is inversely proportional to the leg resistance, according to equation (7). K3/5is a constant whose value depends on the core geometry. [5]

Ploss=V² Rl

· K_3/5 (7)

The leakage ux of the transformer is modeled by a short-circuit admittance matrix, [A]. Leakage

ux refers to the part of the magnetic ux that leaks out of the core, and ows inside and between windings, and in the air surrounding the core. It may also ow through the transformer tank, or other metallic parts. Some leakage ux is always present, in all magnetic circuits, since the permeability is only 10³− 10⁴ times larger for ferromagnetic materials than for air.

The leakage ux can be investigated by means of short-circuit tests. In such tests one measures the voltage required to produce rated current in one of the windings (two in case of a three-winding transformer) while the other winding is short-circuited. The voltage drop over the examined winding will then consist of two components: one resistive component corresponding to load losses, and one reactive component corresponding to leakage ux. [6]

The admittance matrix used in the Hybrid Transformer Model has dimension (Nw+ 1) N_p , where Nw is the number of physical windings and Np is the number of phases. The (Nw+ 1) winding represents the ctitious core winding, as mentioned earlier. The admittance matrix is built according to the procedure presented in [2], section 6.5. For GIC analysis it is important to consider the air-path inductances, i.e. the transformed magnetic reluctance of the ux owing outside the core. This feature is not included in the Hybrid Model.

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ZTV

ZLV

Zg

Figure 6: System topology

3.2 Hybrid Transformer Model for GIC phenomena

In recent work by Sintef Energy Research, NTNU and Statnett, the Hybrid Transformer Model was implemented for GIC phenomena in PSCAD. The model was expanded to also include air-path inductances. The modeling approach used is presented in [1]. In this study, a 300 MVA ve-leg power transformer was used. The topology of the analyzed system is shown in Fig. 6. The GIC event is represented by a DC voltage source on the HV neutral point of the transformer, with the DC voltage applied as a ramp between 2 and 10 s. The magnitude of the GIC is determined by:

IGIC = VDC

Re {Zg} + R_W (8)

where VDC is the applied DC voltage, Zg is a resistive series source impedance and RW is the HV winding resistance. In this study the reactive power absorption is found to be a linear function of GIC magnitude.

The paper focuses on the impact of air-path inductances. These are calculated by 3D-FEM, and it is reported in the paper that neglecting air-path impedances leads to an underestimation of order 10-20% for the increase of reactive power demand due to GIC.

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4 Simulations

In order to investigate the relation between reactive power losses and GIC magnitude, two ve- limb and one three-limb power transformer have been used for simulation of GIC in PSCAD. The implementation of XFMR in PSCAD is the same as presented in [1]. The transformers most likely to be exposed to GIC are step-up/step-down transformers connected to long transmission lines, for which reason transformers with nominal voltage around 400 kV are of particular interest for GIC simulations. Also, for this project transformers with the ve-limb core conguration are the most relevant to use for simulations, since this conguration dominates at high voltage levels in the Norwegian power system.

As mentioned in the previous section there are two ways of obtaining the Ψ − i pairs describing the core non-linearity; either from transformer design data or factory test reports. The most straightforward way to study the core size dependence of reactive power losses would be to use design data as input, since the Ψ − i relation then directly depends on the absolute dimensions of the core. However, the implementation of the XFMR model uses test report data as input, since design data for transformer cores rarely are available. In the method for using test report data as input, the absolute size dependence has been eliminated, according to equation (4). In this project three dierent transformers in the Norwegian power grid have been used for GIC simulations. A list of simulated transformers is given in table 1. All transformers are three-phase, three-winding units with Y-connected primary and secondary windings, and delta-connected tertiary windings.

Transformers T1 is a ve-limb core transformer for which test report data was given, and T2 is newly produced ve-limb core transformer for which design data was available (but not test report data). Transformer T3 is a three-limb core transformer for which design data was available. The data of transformers T1-T3 are property of Statnett and cannot be presented in detail here.

In order to use transformers T2 and T3 to study the core size dependence of the relation between reactive power losses and GIC magnitude, a method for using transformer design data as input to the model had to be established. Also, a method for re-introducing the absolute dimensions dependence when using test report data is input had to be established, in order to use transformer T1 for the study.

Transformer Rated power Core type Available data T1 300/300/100 MVA Five-limb Test report T2 300/300/100 MVA Five-limb Complete design data T3 100/100/30 MVA Three-limb Complete design data

Table 1: Transformers

4.1 Simulation environment

The GIC simulations of this thesis project have been carried out using the power system simulation software PSCAD (version 4.5.1) where the XFMR model has been implemented for the purpose of relay testing. A base simulation model for GIC analysis was available for the project, and a stand-alone MATLAB application calculating the model parameters from test report data. The implementation of the XFMR model and the parameters calculations applications have been de-

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veloped by Sintef for Statnett, in accordance with [1]. The application requires the following input data:

Main transformer ratings and conguration

For calculating the impedance: transformer short-circuit test report data

For calculating the core characteristics (Ψ − i relation): Open circuit test report data and relative dimensions of the core

Transformer capacitances are not supported by the PSCAD model. The application calculates the transformer winding resistances and the admittance matrix based on short-circuit test report data, and generates the transformer core saturation curve expressed as ux-linkage as a function of current, based on positive sequence no-load test report data and relative dimensions of the core by calculating parameters a⁰ and b⁰ in equation (4). The application generates an optional number of

ux linkage - current pairs. The XFMR model in PSCAD allows for up to 10 − i pairs as input.

Only three-phase units are supported by the model, with two or three windings and a number of dierent winding congurations. The model supports ve-limb and three-limb transformer cores.

The main obstacle of the thesis project has been that neither the parameters calculation application or the XFMR model in PSCAD could be changed. They can be seen as two black boxes

whose content cannot be seen or manipulated. The parameters calculation application generates a data le containing the transformer parameters, which is used as an input to the XFMR model.

The data le containing the input for the transformer model is the only part where changes can be made. In order to study the core size dependence of the reactive power losses, the core characteristics must be calculated externally, for dierent core sizes, and then placed in the data le which is used as input to the XFMR model in PSCAD. The idea is shown in Fig. 7. The data le contains the following transformer parameters:

General settings; number of windings and core conguration

Non-linear core representation; Ψ − i pairs

Zero-sequence inductance and core loss resistance

The winding resistance in matrix form

The winding admittance in matrix form

All simulations have been carried out using the system topology shown in Fig. 6, with a duration of 90 s and a solution time step of 25 µs, which is the recommended time step for the model. Fig. 8 shows the network model in PSCAD, which is identical to the network model used in [1]. The GIC is represented as a DC voltage source at the HV neutral point, with the voltage applied as a ramp of 8 seconds from 0 V to the nal value. The DC voltage level corresponding to a certain GIC level is calculated from equation (8).

The voltage source in Fig. 8 is an ideal source, with zero internal impedance. The 0.02Ω resistance in series with the source represents a negligible resistive series source impedance. All line currents and voltages have been monitored, as well as the current owing through the high voltage neutral, core ux, air ux and core current. As mentioned above, capacitive eects have been neglected, which is reasonable since according to [9] such eects are negligible for low frequency transients.

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Figure 7: Process of changing the input method of the model

The fundamental component of the reactive power Q consumed by the transformer was calculated from equation (1). In the system shown in Fig. 8, Lload is small (0.1 mH), which means the reactive power drawn from the supply will be equal to the reactive power drawn from the transformer. I(1) was obtained by using Fast Fourier Transform on the primary side line current, and P was obtained by placing the Real Power Meter component in PSCAD at the primary side line. For a system where the transformer is loaded with a higher inductive or capacitive load, the reactive power drawn from the transformer must be calculated as QHV − (QLV + QT V).

4.2 Transformers

The transformers used for simulations in this project have been chosen on account of their voltage and power ratings, and congurations. As explained earlier ve-limb core transformers are of the highest relevance. However, one three-limb core transformer has been included in the study in order to to investigate if similar core size dependence on reactive power demand appears for the three-limb core conguration as for the ve-limb core. Since there are two dierent approaches to re-introduce the core size dependence, depending on the type of input data available, two ve-limb core transformers have been used, one for each approach.

In order to investigate how the reactive power absorption depends on the size (absolute dimensions) of the transformer core, the core saturation curve must be expressed as a function of absolute length and cross section of the core. If all design data, including B-H characteristics, absolute dimensions of the core and number of turns of the innermost winding are known, the saturation curve can be calculated by means of tting the B-H curve to the Frolich equation (2), obtaining parameters a and b, and calculating ux-linkage as a function of current from equation (4).

When only test report data is available, the core size impact can be studied by calculating a⁰ and b⁰ in equation (4) based on test report data, assuming values for length and cross-sectional area of the core and number of turns of the innermost winding, and then calculating a and b in equation (3). Then, equation (3) can be used in order to generate any number of ux linkage - current pairs, for dierent core sizes. Both methods will be presented below.

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Figure 8: System for GIC simulations with XFMR transformer model

4.2.1 Transformer T1

The transformer T1 is a 300 MVA ve-limb transformer. Short-circuit and no-load test report data were available, so the parameters calculation application could be used as intended to obtain the parameters a⁰ and b⁰ in equation (4) and generating a data le containing the parameters for the XFMR model. In order to vary the size of the transformer core, initial values of the absolute core dimensions had to be assumed. The relative core dimensions were known, and could be maintained.

The parameters a and b in (3) could be calculated by use of equations (5) and (6) using assumed values for lLand ALand an assumed value of N. For lLand AL, the length and cross-sectional area of a transformer with similar power rating as T1 was used. When assuming the number of turns of the innermost winding N, a rule of thumb is that each transformer winding turn corresponds to 300 V¹.

Next, nine Ψ−i pairs were calculated from equation (3) using MATLAB and put into a data le in order to be used as input to the XFMR model in PSCAD. This set of Ψ−i pairs is now approximately equal to the Ψ − i pairs originally calculated by the parameters calculation application. For the change in core size, the relative dimensions of the core were maintained, i.e. the ratios ^l_l^Y_L, ^l_l^O_L, ^A_A^Y_L,

AO

A_L were kept constant. Also the relation between the length of the leg lL and the cross-sectional area of the leg ALwas maintained. In this manner the change in core size can be expressed by the change in the length of the leg lL. How the length of the leg was measured is shown in Fig. 3. The lengths lL1= 1.00 · l_L, lL2= 1.05 · l_L, lL3= 1.10 · l_L and lL4= 1.20 · l_Lwere used. The length of the

1From correspondence with supervisor S. Mousavi

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0 2 4 6 8 150

200 250 300 350 400 450 500

current [A]

Flux linkage [Wbturns]

Figure 9: T1: Leg ux for four core sizes

core leg was thus increased by 5, 10 and 20%. These four core sizes will be referred to as 100, 105, 110 and 120%. For each core size, nine Ψ − i pairs were calculated and put into data les otherwise equal to the parameters le originally generated by the parameters calculation application. Only the Ψ − i pairs of each limb were changed. This is a simplication which means that the change in core size only aects the Ψ − i relation, and not the core loss resistance of the transformer. In reality increased core size leads to increased active core losses, according to (7). For this project, the dependence of core geometry on the constant K in (7) was unknown and therefore had to be omitted. Fig.9 shows Ψ(i) of the transformer leg for the dierent core sizes. Figs. 10 and 11 show Ψ(i)of the yoke and outer limb, respectively.

As can be seen in Figs. 9-11, increasing the core size gives a higher maximum ux linkage, i.e. moves the point of saturation upwards. This creates a margin for the DC-excited transformer to reach the saturated state. It is therefore expected that the larger core sizes will be associated with smaller reactive power demand compared to the smaller core size for the same GIC levels; i.e.

that the transformer with larger core will display less sensitivity to GIC in terms of reactive power absorption. Simulations in PSCAD were carried out as described in the previous section. For each core size (100, 105, 110 and 120% of the original size) the fundamental component of the reactive power drawn from the supply was calculated according to (1) for 12 dierent GIC levels between 0-525 A.

4.2.2 Transformers T2 and T3

The transformer T2 is a recently manufactured 300 MVA ve-limb power transformer. Complete design data for this transformer were available, including absolute core dimensions, number of turns of the innermost winding and the B-H characteristics. In order to obtain the Ψ − i relation for this transformer, the B-H data set was tted to the Frolich equation (2) in MATLAB and the parameters aand b were obtained. The original B-H curve of T2 and the Frolich t are shown in Fig. 12. Since the length and cross-sectional area of each core section were known, as well as the number of turns

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0 2 4 6 8 50

100 150 200 250 300

current [A]

Size1(100%) Size2(105%) Size3(110%) Size4(120%)

Figure 10: T1: Yoke ux for four core sizes

0 2 4 6 8

50 100 150 200 250 300

current [A]

Size1(100%) Size2(105%) Size3(110%) Size4(120%)

Figure 11: T1: Outer limb ux for four dierent core sizes

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0 100 200 300 400 500 600 700 0

0.5 1 1.5 2 2.5

H [A/m]

B [T]

Figure 12: T2: B-H curve (blue) and t to the Frolich equation (red)

of the innermost winding, the ux linkage - current relation could be obtained from (3) directly, from which nine Ψ−i pairs could be extracted. Four sets of Ψ−i pairs for dierent core sizes, (100, 105, 110 and 120%) could then be calculated by varying the limb lengths and cross-sectional areas in (3). The core was scaled in the same manner as transformer T1, described in the previous section.

Fig. 13 shows the Ψ − i relation of the core leg, for the four dierent sizes of the transformer core.

As can be seen in the gure an increase in core size is associated with a margin of the saturation curve. The yoke and outer limb uxes show very similar core size dependence as the leg ux. It can be noted that the maximum ux linkage level for T2 is much lower than that of T1. T2 is therefore expected to display an enhanced vulnerability to GIC in terms of reactive power increase compared to the transformer T1.

PSCAD simulations and calculations of the fundamental component of reactive power absorption were carried out in the same manner as described in the previous section. Simulations for four core sizes at GIC levels between 0-150 A were carried out. The reason for the dierence in GIC range simulated as compared to T1 is that T2 reaches the saturated state at much lower GIC levels than T1.

The transformer T3 is a recently manufactured three-limb transformer. Design data, including B-H curve and core dimensions were available. However, short-circuit losses and zero-sequence impedance were not available, for which reason they had to be assumed. These assumptions were made using test reports from transformers with similar rating as T3 as a reference. These assumptions will aect active and reactive power demand in steady state (when no GIC is present) as well as during a GIC event.

The same procedure as for transformer T2 was followed in order to obtain the Ψ−i characteristics of transformer T3. Fig. 4 shows the core dimensions The t of the B-H data to the Frolich equation (2) is shown in Fig. 14. The core size was again scaled into four sizes; 100, 105, 110 and 120%.

The Ψ − i relations for the leg and yoke of the transformer are shown in Fig.15. GIC levels between 0-500 A were simulated.

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0 20 40 60 80 100 10

20 30 40 50 60 70 80 90 100

current [A]

Figure 13: T2: Leg ux for four dierent core sizes

0 100 200 300 400

0 0.5 1 1.5 2 2.5

H [A/m]

B [T]

Figure 14: T3: B-H curve (solid) and t to Frolich (dotted)

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0 20 40 60 80 100 120 20

30 40 50 60 70 80

current [A]

Size 100%

Size 105%

Size 110%

Size 120%

Figure 15: T3: Leg ux for four dierent core sizes

4.3 Results

From each simulation of GIC events for transformer T1-T3, Q(1) was calculated from equation (1).

Q₍₁₎ as a function of IGIC for the three transformers, and for four dierent core sizes, are shown in Figs. 16-18. The function Q(IGIC) is apparently nonlinear for all three transformers. Q(1)

increases linearly with IGIC up to some certain level Qmax. The increase rate and the maximum level Qmaxare however dierent for the three dierent transformers.

From Figs. 16-18 it is clear that a larger transformer core leads to decreased reactive power absorption of the transformer during a GIC event.

4.4 Discussion

The results shown in Figs. 16, 17 and 18 indicate that the reactive power demand of a power transformer during a GIC event decreases with increased core size. For all three transformers the function Q(IGIC)is nonlinear, with a linear increase in a certain interval. The increase in Q then declines towards a maximum value Qmax. The core size impact seems to increase with GIC magnitude, i.e. a larger transformer core seems to be associated with a smaller slope in the linear region of Q(IGIC).This can be further investigated by calculating the ratio _Q^Q₁₀₀^x for dierent levels of GIC. Here, Qx is reactive power demand of core sizes 105, 110 and 120%, Q100 is the reactive power demand for the original core size. Figs. 19-21 show the ratio _Q^Q₁₀₀^x for transformers T1-T3.

As can be seen in the gures, the overall core size dependence seems to increase with increased GIC magnitude for all three transformers.

Transformers T1 and T2 are both ve-limb transformers, and have similar power ratings. They are therefore expected to display similar behavior when exposed to GIC. However, from Figs. 16 and 17 it is apparent that transformer T2 reaches much higher Q levels for lower GIC magnitude than T1, and that the maximum value Qmax,T 2is lower than Qmax,T 1, although initially T1 and T2 have almost identical reactive power demands. This dierence in behavior is due to the dierence in core

ux characteristics, shown in Figs.9 and 13. The ux characteristics of the original size are given by

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0 100 200 300 400 500 600 0

20 40 60 80 100 120

GIC, A

Q, MVar

size1(100%) size2(105%) size3(110%) size4(120%)

Figure 16: T1: Reactive power as a function of GIC for four dierent core sizes

0 50 100 150

20 40 60 80 100

GIC [A]

Q [MVar]

Figure 17: T2: Reactive power as a function of GIC for four dierent core sizes

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0 100 200 300 400 500 50

60 70 80 90 100 110 120

GIC [A]

Q [MVar]

Figure 18: T3: Reactive power demand as a function of GIC for four core sizes

equation (3) for transformer T2 and by equation (4) for transformer T1. The parameters a⁰ and b⁰ in (4) can dier between the two transformers due to a dierence in core cross-sectional area, core length and number of turns, as well as in the Frolich parameters a and b representing the magnetic properties of the core material. Since these parameters are unknown for T1 (only a⁰ and b⁰are known) it is not possible to determine wherein the dierence lays. However, one can use equation (3) to nd an indication of which parameters are most signicant for the ux characteristics. The parameters that were used for the Ψ − i characteristics of T1 and T2 are presented in table 2. Fig.

22 shows a simple comparison of the impact of the dierent parameters. As can be seen in the

gure, the dierence in the Frolich parameters a and b gives a relatively small deviation of Ψ(i).

The dierence in parameters l,A, and N have a greater impact on the deviation. In particular, it appears that the number of turns N causes the two Ψ(i) curves to dier.

As mentioned earlier, the assumed length, cross-sectional area and number of turns for T1 are based on the geometry of another transformer core, from a transformer with power and voltage ratings similar to T1, and the rule of thumb that each transformer winding corresponds to 300 volts, and the assumption that the innermost winding is the secondary winding. Since these parameter values dier from the parameters of T2, in particular with respect to number of turns N, they may not be realistic. However, the l, A and N dependence of the ux characteristics of T1 is included in the parameters a⁰ and b⁰ in (4). The reason that there is a dierence between T1 and T2 may be that

There is, in reality, a great dierence in the Frolich parameters a and b, i.e. the magnetic characteristics of the core material given by (2).

The methods for obtaining the Frolich parameters (optimization process from test report data vs tting the B-H data to the Frolich equation) give very dierent result, leading to a great dierence in a and b.

The two transformers are in fact very dierent in terms of core geometry and number of turns of the innermost winding.

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T1 T2 a 2.3460 7.5240 b 0.5210 0.4845 lleg[m] 3.119 2.621 A_leg[m²] 0.5041 0.8963

N 409 44

Table 2: Parameters of T1 and T2

Figure 19: Relative reactive power demand for transformer T1

The dierence in ux characteristics between T1 and T2 may of course also be due to a combination of the proposed explanations above.

As can be seen in Figs.16, 17 and 18, the reactive power as a function of GIC, Q(IGIC) , is non-linear for all three transformers simulated. This diers from what is reported in [1] and [12], where the reactive power absorption is given as a linear function of GIC magnitude. However, [4]

reports similar ndings. The study described in [4] has been carried out on a larger system, with several transformers. The non-linear saturation curve used for transformer characteristics in this study was based on eld test measurements. It is reported that that the relation between GIC magnitude and reactive power losses is non-linear. The relation between GIC and reactive power losses _I^∆Q_GIC is in [4] reported to vary between 0.32 and 0.50 MVAR/A. The corresponding ratios for the simulations of transformers T1-T3 above are as follows. For T1, _I^∆Q_GIC varies between 0.19 and 0.35 MVAR/A, for T2 between 0.19 and 0.66 MVAR/A, and for three-limb transformer T3 between 0.08 and 0.15 MVAR/A.

The results presented in the previous section give a clear indication that increased transformer core size makes the transformer less sensitive to GIC exposure in terms of reactive power losses.

One important simplication that has been made for the size dependence study is neglecting the change in active core losses when the core size is increased, as described in section 4.2.1. In reality, the active core losses (eddy current losses and hysteresis losses) are expected to increase when the

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0 20 40 60 80 0

200 400 600

I [A]

Psi [Wbturns]

0 20 40 60 80

0 200 400 600

I [A]

Psi [Wbturns]

0 20 40 60 80

0 200 400 600

I [A]

Psi [Wbturns]

0 20 40 60 80

0 200 400 600 800

I [A]

Psi [Wbturns]

Figure 22: Comparison of transformer parameters impact on ux-current relation. Upper left gure:

The original ux-current characteristics of T1 (blue, solid line) and T2 (red, dotted line). Upper right gure: Flux-current with the dierence in a and b maintained, l, A and N equal. Lower left

gure: Flux-current with the dierence in a, b, and N maintained, l and A equal. Lower right

gure: Flux-current with the dierence in a, b, l, and A maintained, N equal.

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core size is increased. This means that the reactive power losses are decreased. Taking the change in Plossinto account is therefore expected to further decrease the reactive power losses for enhanced core sizes.

Increasing the core size is associated with a dramatic increase in production cost, since the cost of the core material is proportional to the volume of the core. A scale wise core size increase of 20%

thus leads to a price increase of 73%, since the volume is proportional to l³. For the simulations above, the core length and cross-sectional area have been equally increased (not scale wise); an increase to core size 4 in the simulations above is thus associated with a volume increase of 44%.

Also the costs of transportation are increased if the transformer core size is increased. Therefore, one should not necessarily start manufacturing larger transformer cores in order to protect the power system from damage caused by GIC.

A number of other precautions for power system protection have been suggested. In [15] and [12]

the importance of space weather forecasts and the communication of such forecasts to transmission system operators is stressed. In [12] it is pointed out that monitoring and assessment procedures can prepare transmission system operators for responses in case of a GIC event. It is here recommended that, among other things, unusual swings in voltage or reactive power be monitored, as well as abnormal temperature rise in transformers. Also reactive power reserves should be monitored.

Operators must also be prepared for possible disruptions of telecommunications systems during a GIC event, which may cause false energy management system indications. In case of a severe GIC event operators must be prepared to remove transformers and transmission lines from service. It is however pointed out in [12] that removal of equipment from service may increase loading on other equipment, putting the system in a less secure state. Since operators may be required to evaluate trade-os such as these with very limited information at hand, the importance of carrying out studies ahead of time is emphasized.

In general, all investments in power system protection from GIC must of course be evaluated in relation to the expected frequency of these events, and the monetary losses associated with them. Since there is currently no consensus regarding either the risk of a strong solar storm (of the same proportions as the 1989 Quebec event described in section 2.3 or greater) or the expected consequences associated with such an event, this is not an easy task. Apart from the monetary losses suered during a large blackout, the opinion of the public must also be taken into consideration.

Large, long-lasting power outages are generally associated with great discontent among consumers directed towards operators, ocial agencies and politicians. Consequences such as these must of course also be taken into account when discussing potential threats to the power system, and investments in system protection.

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5 Conclusions and further studies

The results presented in the previous section indicate that increased transformer core cross-sectional area leads to smaller increase in reactive power demand during GIC events.

It is also noted that the the relation between GIC and reactive power demand is non-linear.

It is apparent that this relation depends on the B-H characteristics of the the core, which is a property of the core material. The reactive power - GIC relation therefore diers between dierent transformers, even if the power ratings are the same. Since the results presented in the previous section give a clear indication that a larger transformer core leads to smaller increase in reactive power drawn from the supply, it can be concluded that a transformer with a larger core is less sensitive to GIC disturbances, in terms of reactive power absorption. It can also be concluded that when using an advanced simulation model, incorporating non-linear elements, the relation between reactive power absorption and GIC magnitude is non-linear. Since the core size dependence of reactive power absorption diers greatly between transformer T1 and T2, no formulation of the function Q(IGIC)for ve-leg core transformers may be attempted based on the work presented in this thesis.

For future studies of the core size dependence of reactive power absorption increase due to GIC, simulations of GIC with design data as input method must be properly implemented in an electromagnetic transients software. The method that has been used in order to obtain the B-H characteristics of the transformer core based on design data in this thesis requires manual manipulation of a data le, which is time consuming and impractical. Also, as mentioned earlier, the impact of transformer core size on the active power absorption has been omitted for this project.

Future studies should include this property.

In this thesis project, the core size dependence of reactive power absorption as a function of GIC level for single phase transformers and auto transformers have not been investigated. Attempts to simulate GIC events in auto transformer have been made, but no satisfying adaptions of the XFMR model in PSCAD to auto transformers have been achieved. It is therefore suggested that future studies incorporate implementations of the XFMR model for single phase transformers and auto transformers. It is also clear that in order to draw conclusions of the impact of GIC events on the power system stability, simulations of larger networks including several power transformers must be performed.

When simulating a larger network, the XFMR transformer model used in this project should be combined with a ground conductivity model representing expected GIC level depending on geographic location of the transformer substation. Also, when studying large networks including several transformer substations, the results presented in [4] regarding the impact on geomagnetic storm orientation on the DC current levels owing in the transformer neutral should be taken into consideration. According to [4], the topology of the power system in relation to the orientation of the geomagnetic storm has a great impact on the DC current levels injected in the transformer neutral. In the simulations presented in [4] only substations in the extreme ends of the systems experience saturation due to GIC.

In this project, only transformers with small inductive load have been simulated. In further studies, simulations of transformer with larger inductive and capacitive loading should be performed, since no relation between loading and change in reactive power absorption of the transformer have been investigated here.

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References

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[2] H.W. Dommel. Electromagnetic Transients Program Theory Book. BPA, 1987.

[3] R. Girgis, K. Vedante, and K. Gramm. Eects of geomagnetically induced currents on power transformers and power systems. Technical report, Cigré, Paris, 2012.

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[10] B.A. Mork, D. Ishchenko, F. Gonzalez, and S.D. Cho. Parameter estimation methods for ve- limb magnetic core model. Power Delivery, IEEE Transactions on, 23(4):20252032, 2008.

[11] S. A. Mousavi. Electromagnetic modelling of power transformers with dc magnetization, 2012.

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[12] IEEE PES Technical Counsil Task Force on Geomagnetic Disturbances. Geomagnetic disturbances. IEEE Power and Energy Magazine, 11(4):7178, July 2013.

[13] Committee on the Societal and National Research Council Economic Impacts of Severe Space Weather Events: A Workshop. Severe Space Weather EventsUnderstanding Societal and Economic Impacts:A Workshop Report. The National Academies Press, 2008.

[14] P. R. Price. Geomagnetically induced current eects on transformers. Power Engineering Review, IEEE, 22(6):6262, June.

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TRITA TRITA XR-EE-ETK 2014:16

Impact of transformer core size on thereactive power requirement of powertransformers due to GIC