Master Level Thesis

Allowing more solar power connected to the grid, using

thermal and ageing models of distribution transformers.

Master thesis 30 credits, 2021 Solar Energy Engineering

Author: Amena Khatun

Supervisors: Fatemeh Hajeforosh and Math Bollen

Examiner: Ewa Wäckelgård

Course Code: EG4001

Examination date: 2021-05-27

Dalarna University

Solar Energy Engineering

European Solar Engineering School

No. 279, June 2021

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Abstract Increasing amounts of solar power connected to the low-voltage network will adversely affect the performance of the network. The two impacts that will most often set the limit are overvoltage with the customers and overloading the distribution transformer. In this work, alternative methods have been studied for determining when a transformer is overloaded, to allow more solar power to be connected to the low-voltage network, i.e., increasing the hosting capacity for solar power.

A limit-based method on the highest temperature inside the transformer (the hotspot temperature) and a method based on the loss-of-life of the transformer insulation due to hotspot temperatures above the design temperature are those alternative methods in this study. These methods are known as "dynamic transformer rating", a technology proposed in the literature but with very little practical experience in distribution networks.

Two models were developed and implemented in MATLAB: a thermal model of the transformer calculating the hotspot temperature for a given time series of loading and ambient temperature; and a model for the loss-of-life of the winding insulation for given time series of the hotspot temperature. These models have been applied to existing distribution networks: measured consumption patterns with high time resolution (10-minute time step) for nine different distribution transformers for 1.5 years (network operator); measured ambient temperature (SMHI); and solar-power production calculated from satellite measurements (Renewables Ninja).

For these nine distribution transformers, the time series of the hotspot temperature and the loss-of-life over the 1.5 years have been calculated for different values of the solar power installed capacity on the low-voltage side of the distribution transformer. The resulting time series are used to estimate the hosting capacity for solar power of a 200 kVA transformer.

Using the existing design methods, the hosting capacity is 200 kW. Once that value is reached, the further connection of solar power should be stopped until a larger transformer is available.

According to IEC design methods, the hosting capacity is about 270 kW using a limit to the hotspot temperature. This value somewhat depends on the loading patterns of the transformer before the connection of solar power. Once that value is reached, the further connection should again be stopped.

Even for installed capacity exceeding 270 kW, the loss of life of the transformer insulation is still small and acceptable. This allows for further connection of PV without the immediate need to replace the transformer. Even values up to 350 or 400 kW may be acceptable, but a limit based on loss-of-life will require a detailed risk analysis as the pre-solar loading of the transformer is shown to play an important role.

This work has shown that dynamic transformer rating allows more solar power to be connected to a distribution network than using classical rating methods without unacceptable risk for transformer loss-of-life.

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Acknowledgement I would like to express gratitude to my internal thesis supervisor, Professor Math Bollen of Luleå University of Technology, and my thesis supervisor, PhD student Fatemeh Hajeforosh of Luleå University of Technology, who supported my effort and assisted me to get results of better quality.

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Contents 1 Introduction ................................................................................................................................... 1

Background ............................................................................................................................. 1 Aims ......................................................................................................................................... 2 1.2.1. Scope ............................................................................................................................... 2 1.2.2. Objectives ....................................................................................................................... 2 Method .................................................................................................................................... 3 Previous work ......................................................................................................................... 5 1.4.1. Overview of hosting capacity ...................................................................................... 6 1.4.2. Dynamic rating benefits and determination approaches ......................................... 7 1.4.3. Comparison of the various thermal models .............................................................. 8 1.4.4. Summary of literature ................................................................................................... 9

2 Basic definitions ........................................................................................................................... 10 Simulation engine ................................................................................................................. 10 Normal cyclical loading ....................................................................................................... 10 Limits of overloading .......................................................................................................... 10 Insulation degradation ......................................................................................................... 10 Transformer loading ............................................................................................................ 11

3 IEC model implementation ....................................................................................................... 12 Differential equation ........................................................................................................... 12 Conversion to the difference equation ............................................................................. 13 Transformer specification ................................................................................................... 14 Boundary conditions ........................................................................................................... 14 3.4.1. Assumptions ................................................................................................................ 14 3.4.2. Simplification ............................................................................................................... 15 3.4.3. Limitation ..................................................................................................................... 15 Detailed steps to analyse the case study. .......................................................................... 16

4 Results ........................................................................................................................................... 17 Case 1: Fixed transformer rating study without the solar PV production .................. 17 Case 2: DTR application without the PV production .................................................... 18 Case 3: Dynamic transformer rating including solar PV production. .......................... 21 Parametric analysis ............................................................................................................... 23

5 Further analysis ............................................................................................................................ 26 Hosting capacity ................................................................................................................... 26 Transformer size .................................................................................................................. 27

6 Discussion .................................................................................................................................... 29

7 Conclusion .................................................................................................................................... 30

8 Future work .................................................................................................................................. 31

9 References .................................................................................................................................... 32

Appendix A Check-list before submitting your first draft ................................................. 34

Appendix B Distribution Transformer Specification from Hitachi ABB ....................... 36

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Abbreviations Abbreviation Description DR Dynamic rating DTR Dynamic thermal rating HC Hosting capacity HST Hot spot temperature LV Low voltage LOL Loss of life MV Medium voltage ONAN Oil natural air natural ONAF Oil natural air forced p.u. Per unit value PV Photovoltaic TOT Top oil temperature

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Nomenclature Symbol Description Unit

D Difference operator, in difference equations Dt Time step 𝑘𝑘11 Thermal constant - 𝑘𝑘21 Thermal constant - 𝑘𝑘22 Thermal constant - L Total ageing over the time period considered days n Number of each time interval R Ratio of load losses at rated current to no-load losses - s Laplace operator t Time variable V Relative ageing rate 𝑉𝑉𝑛𝑛 Relative ageing rate during interval n x Oil exponent - y Winding exponent - 𝜏𝜏𝑜𝑜 The oil time constant min 𝜏𝜏𝑤𝑤 Winding time constant min 𝜃𝜃𝑎𝑎. Ambient temperature °C ∆𝜃𝜃ℎ𝑟𝑟 Hotspot to top oil gradient at rated current, K ∆𝜃𝜃𝑜𝑜𝑟𝑟 Top oil temperature rises in steady state at rated losses

(no-load losses + load losses) K

∆𝜃𝜃ℎ Hotspot to top oil gradient at the load considered K 𝜃𝜃ℎ Hotspot temperature °C 𝜃𝜃𝑜𝑜 Top-oil temperature (in the tank) at the load considered °C

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1 Introduction Background

With an increase in electricity demand, there was a concern about carbon dioxide emissions contributing to the global warming. In the last few years, European new regulations and laws have started motivating people to use more renewable energy sources to restrict carbon dioxide emissions [1]. Nuclear power, wind power and hydropower are common sources of electricity supply in Sweden. Nevertheless, these three sources impact the environment differently, although neither of them contributes to CO2 emission. Apart from wind power, in recent years, the market for grid-connected Photovoltaic (PV) systems has grown rapidly in Sweden [2]. The key reasons for such growth are the lower cost of a PV installation, tax reduction and economic incentives. However, PV production varies with time, and the production capacity cannot be predicted and controlled. Moreover, both large and small production unit integration impact transmission and distribution system operation, among others, due to the variation in production [3]. PV system utilises solar energy to convert this solar radiation into electricity. A PV system is almost always connected to the distribution system; roof-top and other small installations are connected to the low-voltage (LV) network; larger installations are connected through a dedicated transformer directly to the medium-voltage (MV) network. There is, however, a limit to how much PV production can be associated with the power system for a safe, reliable and high-quality operation, known as a hosting capacity (HC). The distribution grid is usually dimensioned in such a way that it can accept a certain amount of renewable energy production, in this case, solar PV. With larger amounts of solar PV, unacceptable levels of overvoltage, overload and possibly other unwanted phenomena will occur [4]. The limits for overvoltage due to solar PV are among others studied in [5]. One of the consequences of large amounts of solar PV or other types of distributed generation is an increased risk of component overloading and reducing components' lifespan. The distribution transformer will be the first power system component that gets overloaded with large penetration of roof-top solar PV [6]. Overloading can be mitigated by adding higher rating transformers or local battery storage, but both solutions require additional investment in the grid. For many distribution transformers in Sweden, the highest loading occurs during winter, when electric heating loading dominates. High penetration of PV generation will result in high loading of the distribution transformer during a different season. The nameplate rating of a transformer gives the static rating of the transformer, calculated using a worst-case scenario to ensure a safe transformer operation during all weather conditions. However, the worst-case scenario does not often occur, as it is based on constant ambient temperature during low as well as high loading of the transformer. The ambient temperature in northern Sweden shows a strong seasonal variation. As there are strong seasonal variations in consumption and solar-power production, the constant-ambient-temperature model can incorrectly estimate the actual overloading limit. Dynamic rating (DR) limits the risk of overloading a component but without the high risk of over dimensioning that can occur with static rating. DR is especially effective when loading shows a high seasonal component, as is the case with distribution transformers. It is helpful for intermittent production and for more efficient utilisation of components capacity. It can be explained for a transformer as follows: "The maximum loading which the transformer may acceptably sustain under time-varying load and/or environmental conditions [7]". Dynamic thermal rating (DTR) of the transformer varies with time and is related to variations in ambient conditions, load variations and changes in cooling operation [8]. Nowadays, grid operators are facing challenges with maintaining an efficient but reliable power supply due to intermittent sources of production. Hence, the implementation of DTR has significant benefits to grid operators. Network operators can save money by not having

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to replace components, and they can still ensure a reliable power supply. It is also essential for grid owners to obtain insight into how the distribution transformers get affected by a rising number of residential-scale PV units. This insight allows corresponding reinforcement to be planned accordingly. In this thesis, the potential for temporary thermal overloading of transformers is studied. To quantify the impact of solar PV and estimate the HC, the thermal model and ageing model is used for transformer overheating analysis with specific application to the oil-immersed transformer. The IEC thermal model and ageing model of distribution transformer are reviewed and applied to understand and quantify the impact of PV penetration on the risk of thermal overloading in the distribution transformer.

Aims The project is part of research activities within the Electric Power Engineering group at Luleå University of Technology, with the aim of increasing the HC of the electricity grid for solar power. Understanding thermal model and ageing model of power transformers.

Quantify the potential of increasing the HC by temporary loading distribution

transformers beyond their nameplate rating.

1.2.1. Scope Simulations have been performed using actual consumption data from 9 distribution transformers in northern Sweden. Moreover, using the Renewables Ninja calculation engine, hourly solar production is calculated for a location close to the 9 LV networks [9]. The going study evaluates the potentiality of connecting more solar power in existing LV transformers when thermal and ageing models are used for the distribution transformer.

1.2.2. Objectives The objectives of this project are: Modelling the thermal behaviour of the distribution transformer and implementing

DTR.

Studying the maximum loading capacity of a transformer depending on thermal limitations as a function of weather conditions and loading conditions without affecting the projected lifetime.

Analysing how DTR strategy allows extending the potential size of PV depending on the HST, rate of insulation degradation and transformer LOL.

Providing an overview of the hosting capacity for the LV network and how the stakeholders benefit by using DTR for connecting solar power production.

Finding how much PV can be added to the distribution transformer going beyond the HST limits using ONAN cooling.

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Method The thesis work is based on MATLAB simulations. From selecting parameters for coding to getting results and analysis, the work follows a heuristic approach. The overall methodology is presented in Figure 1.1.

Figure 1.1 The overview of the adapted methodology for the thesis work.

The project consists of the following activities:

Literature review: A comprehensive literature review is performed after recommended thermal models of distribution transformers. In Section 2.1, the results of a literature study are presented regarding DTR and HC. Then, the acquired knowledge is used to create a simple but sufficiently detailed thermal model and ageing models of the insulation. These models are next implemented in MATLAB.

Verification of coding: In the initial step, the verification of code is done comparing with the reference case in the IEC standard. In IEC standard 60076-7, the example is given for 2 hours of ambient temperatures and transformer loading. The parameters are selected so that the rated HST is equal to 110 °C at 30 °C ambient temperature with 3 minutes interval [10]. The final output obtained from the model implemented in MATLAB shows that the validity of the algorithm in Figure 1.2. It is similar to the IEC standard example [10]. Therefore, it can be believed that with a good approximation the implemented algorithm is correct.

Literature review

Verification of coding

Identify boundary conditions

Programming tool development

Sensitivity analysis

Result and discussion

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Boundaries conditions: Based on the literature findings and previous studies, some boundary conditions are established for the final simulation. Primary data for the study are collected from Hitachi ABB power grids and IEC standard. Moreover, the project supervisors provide the secondary required inputs such as consumption pattern, ambient temperature, and solar-power production patterns for further assessment. Then, some of the designated parameters have been verified after executing several simulations. The preliminary aim was to conduct the analysis with one transformer loading pattern, nine others consumption patterns have been studied in less detailed.

Programming tools development: In order to analyse the DTR of a distribution transformer, MATLAB programming is used considering boundary conditions with existing methods thermal and ageing models of a 200 kVA distribution transformer have been built. The next step is divided into two parts. In the first part, the capacity of the transformer beyond its rating has been analysed without adding solar PV as well as using existing methods to avoid overloading. After that, solar power production is integrated into the model to analysed HC and avoid transformer overloading. Figure 1.3 illustrates the flow chart of transformer thermal limit with solar power production after implemented DTR.

Sensitivity analysis: A sensitivity assessment is performed to augment the alternative boundary conditions, thermal limit with and without solar PV production This is used to demonstrate the advantage of using DTR instead of static rating. Transformer loading and ambient temperature are the primary input constraints that affect the overloading capacity. Therefore, it is important to identify the impact of increasing transformer loading and ambient temperature on the HST and LOL, which are important measures in transformer asset management. Furthermore, the system reliability depends on the transformer capability to withstand any severe

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Figure 1.2: The redrawn result that is given as an example in IEC 60076-7: 2005 standard using thermal characteristics for medium and large power transformer with ONAF cooling [10].

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shortcomings [11]. Therefore, the parametric analysis has been done with regards to ambient temperature, load factor and PV installed capacity.

Result and Discussion: The study concludes with a review of the results and formulates recommendations to network operators. The validation of the outputs has been analysed by comparing them with previous studies. Future work is also presented, along with an uncertainty analysis.

Figure 1.3: Workflow diagram to determine the maximum solar installed capacity applying DTR beyond transformer nameplate rating.

Previous work

This section describes different concepts that are interconnected with this thesis work, for instance, significant issues with HC, static rating of transformer, thermal characteristic of a transformer, dynamic thermal rating, and its benefits.

Run IEC thermal and ageing model for DTR.

Obtain HST, TOT and total ageing of the transformer.

Determine the allowable solar installed capacity.

End

Start

Acquire inputs data (transformer loading, ambient temperature, and solar production).

Adjust some inputs data applying interpolation method.

Estimate missing data.

Collect transformer specification from manufacture and make assumption following IEC standard.

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Perf

orm

ance

inde

x

Amount of solar production

Range of hosting capacity

A transformer is a critical and expensive element in a distribution system. The power quality and reliability of the distribution network are affected by the loading of the distribution transformer. Too much local PV production changes the power flow direction through a transformer, and with excessive back-feed, the transformer gets overloaded. Distribution transformer operational limits are defined by the winding hot spot temperature in an oil-immersed transformer. Overloading results in accelerated ageing of the winding insulation, the general outcomes of overloading a transformer are given below [10]. The temperatures of winding, insulation and oil will rise and may cross the tolerance

levels. The moisture and gas content in the insulation and oil will vary as the temperature

changes. Eddy current losses increase in metallic parts of a transformer. Increasing pressure on the bushing, tap changer, cable end connection and current

transformer will result in extreme dielectric failure.

1.4.1. Overview of hosting capacity Sweden is moving forward to green electrification with a high share of renewable energy sources. About 78 % of electricity is produced from nuclear and hydropower, 18 % of the generation comes from wind power, 4 % from combined heat and power plants and 0.3 % from solar [12]. The solar industry is expanding faster than predicted in Sweden. The power system industry is facing a significant challenge to incorporate a vast amount of renewable energy production. The electricity production from solar and wind power varies with time in a volatile way. Additionally, consumption and solar PV production are not correlated during a year. For example, in the morning and evening, the demand is highest, whereas the amount of solar PV production is highest around noon [3]. The distribution grid has a limit to how much new production can be connected without affecting the reliability of the grid or the power quality. This term is known as HC, and it is also a helpful term for the study of new consumption, especially electric vehicles. The HC varies with different geographical locations, type of distributed generation and installed capacity. For example, the ambient temperature in northern Sweden is lower than in the southern part, so that the grid may accept more production without any additional investment. It is essential to define performance indicators such as overvoltage, overloading or harmonics to evaluate hosting capacity. Then, the limit of performance indices must be determined and calculated as a function of new production or consumption [13]. In our case, the performance indicator is maximum current through a transformer for every 10 minutes. The HC approach has also several uncertainties a side from performance index and limit. With PV system, the production varies a lot with time, location, type of installation and size of generation units that results the voltage variation. The HC for PV production could be a wide range of values as in Figure 1.4 instead of one value for the HC [3]. HC1 is worst capacity value free of uncertainties and HC2 is the usual hosting capacity. Figure 1.4 Range of hosting capacity values for uncertainties [3]

HC1 HC2

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A small quantity of production may improve the power system's performance because the power flow is reduced through the transformer. If more production has added, then it might be possible that the solar production is getting higher than the consumption, so that the power flow changes its direction through the transformer, which is known as a back feed. A transformer can be overloaded with too much solar production [3]. Due to overloading, network users may experience an interruption (when the overload protection is activated), or power system equipment will damage (when the overload protection is not activated).

1.4.2. Dynamic rating benefits and determination approaches Before jumping into a DR, it is essential to discuss the static rating. The thermal properties determine transformer rating, and it depends on the ambient temperature, wind speed and loading factor. Increased transformer loading causes high winding temperature, oil temperature and losses in the core. Winding temperature rise must typically not exceed the permissible design limit. Otherwise, the electric insulation can break down as transformer life is a function of the winding insulation that degrade with the temperature. IEEE [14] and IEC [10] transformer loading guides suggest a loading limit based on the size of the transformer, cooling system, ambient temperature, and other relevant factors. In general, transformer rating considers worst-case environment conditions that mean the static thermal rating allows overloading a transformer (10 to 20) % beyond the nameplate rating without risk of any damage [15]. Many transformers rarely deal with their temperature limits, consequence the transformer lifespan increases. So, using the dynamic rating, network operators can utilise the capacity of existing components. DR is a technique to use the maximum capacity of the transformer considering the ambient temperature and loading condition. The current is limited by the maximum design temperature of the transformer. The ambient temperature is much lower in winter, so the maximum allowed current through the transformer will be higher without reaching critical design conditions. For lower ambient temperature and the same current, insulation degrades slower. Several authors [16], [17], [18] have studied the potential of dynamic rating (DR) in Sweden. These and other studies concluded that DR has both technical, environmental, and economic benefits. It can play an important role to develop bidirectional grid communication. It also helps to design the transformer more efficiently in the transformer designing phase and limit the additional investment cost in the power system. Moreover, fewer reinforcement expenses can offer lower tariff cost and reduce environmental impact in the raw materials extraction phase. The authors of [19] also identified some issues regarding the DR application of transformers, such as collecting and handling data, correctly modelling the hot spot temperature, and performing performance analysis with the wind power integration system. The permitted load of the transformer can be affected by top oil temperature and winding hot spot temperature. The hot spot temperature is a significant parameter in dynamic transformer rating, although it is challenging to calculate this variable. Direct and indirect methods are discussed in different research papers. The direct monitoring approach requires additional investment cost due to direct measurement by fibre optics and temperature sensors. Therefore, an indirect method has been used in this study based on weather data and different load conditions [20]. There are several models to calculate the thermal behaviour of the transformer. IEEE [14] and IEC [10] standards are well established to analyse the transformer heat balance. IEEE and IEC standard suggests the highest permissible hot spot temperature to be 110 °C [14]. The HST depends on ambient temperature and loading condition so that the HST limit cannot directly be translated into a current limit. In IEEE standard C57.12, the average and maximum ambient temperature are mentioned as 30 °C and 40 °C. Transformer power rating is defined for four conditions which are a) rated frequency, b) rated voltage c) ambient temperature ( 𝜃𝜃𝑎𝑎= 30 °C) and d) rise of winding HST.

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In [21], the study was done for a three-phase distribution transformer with every 15 min field data. Four scenarios were studied, unbalanced operating conditions with solar input and without solar input and balanced operating conditions with solar inputs and without solar inputs. They revealed that PV generation would increase the transformer lifetime even through high loading conditions, which was helpful in this study.

1.4.3. Comparison of the various thermal models IEEE and IEC thermal models both evaluate the thermal rating of the transformer based on HST and top oil temperature. The implementation of thermal models depends on the assumptions and available information of the transformer. Table 1.1 presents some benefits and drawbacks of the different thermal models. IEEE Guide for loading mineral-oil-immersed transformers standard [14] suggests two thermal models, which are given below: IEEE top oil rise model or Clause 7 model. IEEE bottom oil model or Annex G model.

IEC 60076-7 standards [10] presents two thermal models, The exponential method. The differential method.

The IEC differential model and IEEE bottom oil model results are widely accepted in terms of performance. The IEEE Annex G model shows an accurate response in terms of the hot spot temperature, but it requires additional information [20]. According to [22], the modified thermal model has exhibited improved response without external cooling and zigzag cooling. The IEC differential model output is similar to the IEEE bottom oil temperature model, and fewer inputs data are required. So, the IEC differential model is considered in this study to investigate the distribution transformer's thermal rating.

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Table 1.1 Comparison of different transformer thermal models [23]

The IEC exponential method and differential method output are the same because of using the same set of differential heat transfer equations. The differential equation method is applicable for time-varying loading and ambient temperature.

1.4.4. Summary of literature The literature reveals the benefits of DTR to increase the hosting capacity for solar production. However, there are just a few papers investigating [21] the dynamic transformer rating for distribution transformers, including high PV penetration. The IEC differential equation model is selected in this study for studying dynamic transformer rating. The external cooling system is not considered here, and IEC 60076-7 standard thermal constants for a distribution transformer are used. Precise ambient temperature is required for calculating accurate hot spot temperature. The ambient temperatures in this study are measured within 10 minutes limit, affecting the accuracy of calculated top oil temperature and loss of transformer life calculations. Important findings from literature studies are given below. Static rating limits efficient utilisation of power equipment, whereas DTR allows

taking advantage of the hidden capacity of power components. The limit of hosting capacity dependent on the selected performance indices. The loss of insulation life is the function of increasing the transformer load ability. The maximum hotspot temperature is 110 °C for a thermally upgraded transformer,

and for normal cyclic loading, the maximum HST is 120 °C at 30 °C and full loading condition.

A small amount of PV penetration could reduce HST in the summer and increase the distribution transformer lifespan [21]. However, higher PV penetration will result in the reverse flow of power from the LV to MV network. However, back-feed is not a problem for distribution transformer unless it gets overloaded [25].

Advantages Disadvantages IEEE top oil rise model or Clause 7 model

Simple model

It leads to unpredicted ageing of insulation paper [24].

Poor performance.

The variation in load and the ambient temperature does not consider.

IEEE bottom oil model or Annex G model

Transient loading has good performance.

Valid for silicon and

HTHC as well [24].

More complex compared to the previous method.

Additional monitoring data requires, such as bottom oil temperature.

The exponential method

Separate equations are used based on load increase or load decrease.

Only accepts the loading curves as the step function.

The differential method

Suitable for arbitrarily time-varying load factor and time-varying ambient temperature [10].

Load shape is not restricted.

It is used the thermal constants depending on transformer size

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2 Basic definitions In the following sub sections, the key descriptions for this study are defined.

Simulation engine The project is based on the MATLAB simulation software and Microsoft excel. The tools are used to analyse the system performance based on the inputs. Each software is accessible with Dalarna University studentship. It is beneficial to research, development, and design. The advantages and disadvantages of using MATLAB are given below: It is easy to implement the algorithm. It has predefined functions to do technical programming. Data can import and read by calling MATLAB commands xlsread and readtable

directly. It is easy to work with big datasets compare to Excel. It is less user friendly, and it takes a long time to learn.

Normal cyclical loading

Normal cycle loading implies a cyclical load at a normal constant ambient temperature of 30 °C with a continuous HST of 110 °C for thermally upgraded paper [10]. Besides, it is allowed to operate the transformer beyond this HST limit. However, maximum allowable hotspot and top oil temperatures cannot be exceeded.

Limits of overloading The recommended limits from the IEC standard for normal cyclic loading over the nameplate rating of the distribution transformer are presented in the table. Table 2.1 Current and temperature limits applicable to loading beyond nameplate rating for normal cyclic loading

Types of loading Distribution transformer Current (p.u.) 1.5 Winding hotspot temperature and metallic parts in contact with cellulosic insulation material °C)

120

Other metallic hotspot temperature (in contact with oil, aramid paper, glass fibre materials) (°C)

140

Top-oil temperature (°C) 105

Insulation degradation There are two types of paper insulation, thermally upgraded insulation papers and non-thermally upgraded insulation paper. Deterioration of insulation is a time function of temperature, moisture content, oxygen content and acid content [10]. However, IEC-60076 is established on the insulation temperature as the controlling parameters. In this case, the relative ageing rate 𝑉𝑉 is expressed according to thermally upgraded paper in Equation 2.1.

𝑉𝑉 = 𝑒𝑒�15000

110+273 − 15000𝜃𝜃ℎ +273�

Equation 2.1

where 15000 is selected for the ageing rate constant and the reference hot spot is 110 °C. Table 2.2 is showing the relative ageing rates at different hotspot temperature. The relative ageing rate is equal to 1 for 110 °C. It increases for any higher hotspot temperature than 110 °C, and the relative ageing rate decreases when HST gets below the reference temperature value.

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Table 2.2 Relative ageing rates for thermally upgraded insulation papers due to hotspot temperature.

𝜽𝜽𝒉𝒉 (˚𝐶𝐶) 80 86 92 98 104 110 116 122 128 134 140 𝑉𝑉 0.036 0.073 0.145 0.282 0.536 1 1.83 3.29 5.8 10.1 17.2

So, loss of life, L over a certain period, is calculated using Equation 2.2. 𝐿𝐿 = ∫ 𝑉𝑉 𝑑𝑑𝑑𝑑𝑡𝑡2

𝑡𝑡1 Equation 2.2

Transformer loading

The transformer loading data is provided by the supervisor. It is part of the data obtained of the total consumption of 32 LV distribution networks for every 10 minutes interval [25] and used in IEC model implementation. The minimum downscaled load is 0.08 p.u, and the maximum is 1.01 p.u. Figure 2.1 shows that the load frequency distribution is around 38 % of the total load time are less than 0.3 p.u. Therefore, the percentage of having higher loading than 1 p.u. is only 1 %. However, a higher load increases the losses as well as the pressure on the electrical and mechanical part of a transformer. Hence, the winding temperature and LOL increase, resulting in the highest HST. Therefore, transformer loading is an important input data for estimating the HST.

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Figure 2.1 Transformer loading frequency distribution in per unit which is downscaled for 200 kVA distribution transformer from 2017-01-01 to 2018-09-28.

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3 IEC model implementation The IEC standard 60076-7 has two thermal models to calculate TOT and HST at varying ambient temperature and load conditions: a) exponential equations solution and b) difference equations solution. These methods describe the hotspot temperature as a time for varying load current and ambient temperature [10]. In the following subsection, the differential equation method will be further explained.

Differential equation Differential equations are applicable for randomly time-varying load factor, K and ambient temperature, 𝜃𝜃𝑎𝑎. The first objective is to find the hot spot temperature and ageing of insulation life for a distribution transformer. In Figure 3.1, the block diagram of differential equations is presented. All symbols for variables and parameters are explained in the Nomenclature section.

Figure 3.1 The redrawn block diagram representation of the IEC differential equations model [10]. (the equations are the function in terms of the Laplace variable s). If the measured top-oil temperature (last line) is accessible, it is added to the calculated hotspot temperature (first line); otherwise, the blocks in the second line are executed to calculate top-oil temperature rise and then added to measured ambient temperature third line, to calculate the top-oil temperature.

The top oil temperature equation (inputs K and 𝜃𝜃𝑎𝑎, output 𝜃𝜃𝑜𝑜 ) is.

(∆𝜃𝜃𝑜𝑜𝑜𝑜) ⋅ �1+ 𝐾𝐾2𝑅𝑅1+𝑅𝑅

�𝑥𝑥

= 𝑘𝑘11𝜏𝜏𝑜𝑜 ⋅ 𝑑𝑑𝜃𝜃𝑜𝑜 𝑑𝑑𝑑𝑑� + [𝜃𝜃𝑜𝑜 − 𝜃𝜃𝑎𝑎] Equation 3.1

The differential equation for hotspot temperature rise is combined with two differential equations. ∆𝜃𝜃ℎ = ∆𝜃𝜃ℎ1 − ∆𝜃𝜃ℎ2 Equation 3.2

where ∆𝜃𝜃ℎ1 and ∆𝜃𝜃ℎ2 are derived from the differential equations for hotspot temperature rise.

𝑘𝑘21 ⋅ 𝐾𝐾𝑦𝑦 ⋅ (∆𝜃𝜃ℎ𝑜𝑜) = 𝑘𝑘22 ⋅ 𝜏𝜏𝑤𝑤 ⋅ 𝑑𝑑∆𝜃𝜃ℎ1 𝑑𝑑𝑑𝑑� + ∆𝜃𝜃ℎ1 Equation 3.3

and

13

(𝑘𝑘21 − 1) ⋅ 𝐾𝐾𝑦𝑦 ⋅ (∆𝜃𝜃ℎ𝑜𝑜) = (𝜏𝜏𝑜𝑜/𝑘𝑘22 ) ⋅ 𝑑𝑑∆𝜃𝜃ℎ2

𝑑𝑑𝑑𝑑� + ∆𝜃𝜃ℎ2 Equation 3.4

The solutions of Equation 3.3 and Equation 3.4 are combined in Equation 3.2. The hotspot temperature equation is. 𝜃𝜃ℎ = 𝜃𝜃𝑜𝑜 + ∆𝜃𝜃ℎ Equation 3.5

The complexity is to account that the oil cooling medium has mechanical inertia and thermal inertia regarding Equation 3.2 to Equation 3.4. That effect is more prominent for a natural cooling medium as regards power transformer. However, it is not very important for distribution transformer [10].

Conversion to the difference equation The differential equations can be solved if they are transformed into difference equations. First, the difference operator D implies a difference in the associated variable that corresponds to each time step Dt. The time step should not be greater than half of the shortest time constant to get an accurate temperature prediction. This method is discussed thoroughly in IEC standard [10]. The equations from Equation 3.6 to Equation 3.11 describe the difference equations used in MATLAB coding.

𝐷𝐷𝜃𝜃𝑜𝑜 = 𝐷𝐷𝑑𝑑

(𝑘𝑘11 ⋅ 𝜏𝜏𝑜𝑜)⋅ [ �

1 + 𝐾𝐾2𝑅𝑅1 + 𝑅𝑅 �

𝑥𝑥

⋅ (∆𝜃𝜃𝑜𝑜𝑜𝑜) − (𝜃𝜃𝑜𝑜 − 𝜃𝜃𝑎𝑎)] Equation 3.6

𝜃𝜃𝑜𝑜(𝑛𝑛) = 𝜃𝜃𝑜𝑜(𝑛𝑛 − 1) + 𝐷𝐷𝜃𝜃𝑜𝑜(𝑛𝑛) Equation 3.7

𝐷𝐷∆𝜃𝜃ℎ1 = 𝐷𝐷𝑑𝑑 (𝑘𝑘22 ⋅ 𝜏𝜏𝑤𝑤)� [𝑘𝑘21 ⋅ 𝐾𝐾𝑦𝑦 ⋅ (∆𝜃𝜃ℎ𝑜𝑜) − ∆𝜃𝜃ℎ1] Equation 3.8

𝐷𝐷∆𝜃𝜃ℎ2 = 𝐷𝐷𝑑𝑑 (1/𝑘𝑘22)⋅𝜏𝜏𝑜𝑜� [(𝑘𝑘21 − 1) ⋅ 𝐾𝐾𝑦𝑦 ⋅ (∆𝜃𝜃ℎ𝑜𝑜) − ∆𝜃𝜃ℎ2] Equation 3.9

∆𝜃𝜃ℎ(𝑛𝑛) = ∆𝜃𝜃ℎ1(𝑛𝑛) − ∆𝜃𝜃ℎ2(𝑛𝑛) Equation 3.10 Finally, the hotspot temperature at the nth time step, 𝜃𝜃ℎ(𝑛𝑛) = 𝜃𝜃𝑜𝑜(𝑛𝑛) + ∆𝜃𝜃ℎ(𝑛𝑛) Equation 3.11

Transformer insulation life is the total time between the initial state when insulation is new and the final state due to thermal ageing, dielectric stress, short-circuit stress, or mechanical movement that could occur in transformer standard service. Moreover, relative thermal ageing is the rate at which transformer insulation ageing is reduced or accelerated compared with the ageing rate for a given HST. The loss of cellulose insulation differential equations can be converted to difference equations [10]. The fundamental differential equation is. 𝑑𝑑𝑑𝑑

𝑑𝑑𝑑𝑑� = 𝑉𝑉 Equation 3.12

The equivalent ageing in hours is obtained by multiplying the relative ageing rate with the number of hours.

14

𝐷𝐷𝑑𝑑(𝑛𝑛) = 𝑉𝑉(𝑛𝑛) ⋅ 𝐷𝐷𝑑𝑑 Equation 3.13

and 𝑑𝑑𝑛𝑛 = 𝑑𝑑(𝑛𝑛−1) + 𝐷𝐷𝑑𝑑(𝑛𝑛) Equation 3.14

Transformer specification

IEC difference equation model is implemented with a 200 kVA distribution transformer. The transformer specifications are shown in Table 3.1, which are collected from the manufacture. Table 3.1 200 kVA distribution transformer specification

Parameters Value Rated Power 200 kVA Primary voltage 11 kV Secondary voltage 420 V Rated HV current 10.5 A Rated LV current 274.9 A Cooling operation ONAN Load losses 1920 W No-load losses 214 W Max. / min. ambient temperature 40 / - 40 ˚C

Boundary conditions

The following assumptions and simplification are made for the analysis and used as inputs for the dynamic thermal model study.

3.4.1. Assumptions The oil temperature increases linearly from bottom to top. Design hotspot temperature and ambient temperature are respectively 110 °C and

30 °C. The oil viscosity is invariable in this case. In general, the transformer oil has high

viscosity at low temperature and vice versa; moreover, this phenomenon has a significant impact during short term overloading. This analysis is focused only on normal cyclic loading so that it would not have any significant impact.

∆𝜃𝜃ℎ𝑜𝑜 and ∆𝜃𝜃𝑜𝑜𝑜𝑜 are same for different sizes of transformers. Winding and oil time constants are static. The winding insulation ageing is considered as an influencing factor for calculating

LOL. Only the ONAN cooling method is analysed for the distribution transformer. The effect of harmonics on transformer LOL and HST have not been considered

for the distribution transformer. However, the large power transformer has significant leakage flux effects, so it is needed to study.

15

The Table 3.2 shows the summary of the various boundary conditions used for the analysis. Table 3.2 Boundary condition used for the simulation.

Parameters Value Location Northern Sweden Transformer power rating 200 kVA Oil exponent 0.8 Winding exponent 1.6 Loss ratio 8.97 The oil time constant 180 min Winding time constant 10 min Thermal constant 1 Thermal constant 1 Thermal constant 2 Hotspot to top oil gradient at rated current 35 K Top oil temperature rise 45 K

3.4.2. Simplification For every 10 minutes, the solar input production and ambient temperature data are

interpolated. Few transformer loading data were missing, so the average value has been taken for

these missing values. The ratio of losses can be determined as a function of the tap position [10].

Overloading of a transformer can be determined precisely if the effect of a tap changer is considered. No-load losses and load losses are collected from the manufacture. So, the tap changer effect does not include in this case study. However, it is mentioned in [26], the effect of the tap changer is notable for the large transformer.

3.4.3. Limitation The accuracy of calculated hot spot temperature and loss of life depends on many factors. In this thesis, a distribution transformer is loaded by combining measured consumption with simulated solar PV production connected at the LV side of the transformer. As a result, consumption is available with a 10-minute time resolution. Solar PV production is interpolated to obtain 10-minute values that could have a small impact on HST, LOL and allowable hosting capacity. Time step should be selected as small as possible and should not go beyond one-half of the shortest time constant in the equations. However, it does not have a significant impact on outputs. The technical parameters of the transformer are the main limitation of this study. Transformer thermal capacity and hosting capacity vary with the technical specifications of the transformer, such as thermal constants, the hot spot to top oil gradient at rated current and top oil rises in a steady-state condition. These values are generally achieved from manufactures during heat run test. However, manufacturers have not provided these values for this study, so the recommended values are used from the IEC standard for distribution transformer with ONAN cooling class. There are calculation techniques to get thermal constants that are explained in [10]. Though, it requires additional data from temperature tests during specific transformer loading.

16

Ambient temperature error has a significant impact on the accuracy of the dynamic rating. Therefore, accurate ambient temperature monitoring is essential. Power system reliability analysis has not been performed due to the lack of time, and it is out of the scope of this thesis work.

Detailed steps to analyse the case study. The following steps are performed to get DTR outputs in this case study. Per unit is a common term to express transformer loading. The per-unit load is defined as the ratio of actual current (I) and rated current (𝐼𝐼𝑜𝑜𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟). It can be increasing by increasing actual load, decreasing rated load, or decreasing transformer size. Before the assessment, the input parameters were checked for any missing data, and Microsoft Excel was used to assess this initial information. Establish the transformer parameters: Initially, the parameters are established for

a 200 kVA distribution transformer. Then, some parameters are collected from the manufacture, and several are chosen from the IEC standard.

Establish the input data: The initially selected transformer loading is given for the 1000 kVA transformer. Therefore, it has been downscaled to match with the selected 200 kVA transformer. During the winter months (November to April), the loading is high due to heating equipment and low during the summer months (May to October). The load factor (K) can be calculated using the following equation for a balanced three-phase transformer.

𝐼𝐼𝑜𝑜𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑆𝑆𝑜𝑜𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟√3 ⋅ 𝑉𝑉

Equation 3.16

where 𝑆𝑆𝑜𝑜𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟 is the transformer rated power and.𝐼𝐼𝑎𝑎𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎𝑎𝑎 is the highest RMS loading current among three phases and V is a secondary voltage, and it is equal to 415 V for selected 200 kVA rated transformer. Then, obtained load factor is multiplied by the ratio of the selected rated transformer divided by the maximum transformer loading (200 kVA / 1000 kVA = 0.2) to obtain the downscaled per unit load factor. Next, the measured solar PV production is in kW and divided by the power factor 0.8 to convert the solar production into kVA. The power factor is a ratio of real power to apparent power. Then the kVA value of solar PV production is divided by 200 kVA to get the per-unit value for solar production. Calculated the initial conditions: The initial conditions are calculated by setting

the time derivatives equal to zero and assumed that the LOL is zero at the initial condition.

Solve the differential equations: After that, the simulations are performed for parametric studies in MATLAB.

𝐾𝐾 = 3 ⋅ 𝐼𝐼𝑎𝑎𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎𝑎𝑎 𝐼𝐼𝑜𝑜𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟

Equation 3.15

17

4 Results This section includes results from the simulation and data analysis followed by discussion. First, based on IEC standard, hotspot temperature, top-oil temperature, and LOL have been estimated for various rated transformer using MATLAB. The primary aim of this study is to establish a DTR model using the IEC differential equation and analyse the ageing of the transformer during normal cyclic loading. Then, based on the new transformer rating capability derived from DTR, the approximate amount of solar PV production has been estimated. This is the maximum production in the region under study, based on the input data, without endangering the transformer's lifespan.

Case 1: Fixed transformer rating study without the solar PV production

Calculated hotspot temperatures are shown for various transformer loading at the steady-state condition in Figure 4.1. Moreover, the per-unit value is utilised to express transformer loading that describes the percentage of the rated voltage required to produce a full load current. The range of ambient temperature from - 30 °C to 30 °C is used here. In the same figure, the HST gets 110 °C when the ambient temperature is equal to 30 °C, and transformer loading is 1 p.u. Thus, it is satisfied the IEC standard design criteria since modern transformer's insulation is made with thermally upgraded paper with the rated HST of 110 °C. Loss of life accelerates faster if the HST exceeds 110 °C thresholds value at 30 °C.

Figure 4.1 Hotspot temperature under steady-state load for 200 kVA ONAN distribution transformer at various loading value and ambient temperature.

Ageing of insulation is a function of temperature, oxygen content, moisture content and acid content. IEC 60076 standard model is based on the insulation temperature as the controlling parameter. In this study, the standard life value has been considered as 180000 hours or 20.55 years at a rated hotspot temperature of 110 °C [10]. Figure 4.2 illustrates that a loss of life is increasing with ambient temperature from -30 °C to 30 °C under static loading factor. LOL is estimated by integrating the relative ageing rate (𝑉𝑉𝑛𝑛) over a specific time. The designed lifetime of a transformer will be maintained if the hotspot temperature is equal to 110 °C with a relative ageing rate of 1 for thermally upgraded insulation paper. As it has been discussed in Section 2.3, the relative ageing rate will be doubled for every 7 °C increase of HST above 110 °C. After one year of operation, the LOL has dropped to 3 days/year of

1030507090

110130150170190

0.8 1 1.2 1.4 1.6

Hot

spot

tem

pera

ture

(°C

)

Transformer loading (per unit)

(-30 ℃) (- 20 ℃) (-10 ℃) (0 ℃)(10 ℃) (20 ℃) (30 ℃)

18

its expected lifetime at 30 °C ambient temperature and full load (1 p.u), as shown in Figure 4.2. The relative ageing rate is also 0.0082 for one year of full operation. The relation between the rate of LOL and transformer loading is exponential. During 1.1 p.u loading conditions, the HST is 122 °C at 30 °C ambient temperature, and LOL also increases from 3 days/year to 6 days/year. The rate of relative ageing is 0.016 for every 12 °C increase in the HST in this case study.

Figure 4.2 Deterioration of insulation under steady-state load for 200 kVA distribution transformer with ONAN cooling system.

Case 2: DTR application without the PV production

The IEC model is employed to calculate the total loss of life, hotspot temperature and top-oil temperature. In this study, distribution transformer performance has been observed using dynamic loading and ambient temperature data. The inputs data are applied from January 2017 to September 2018 for a city in northern Sweden. The initial load is considered 0.29 p.u. and ambient temperature is -1.18 °C on 2017-01-01 00:00:00. The total simulation time is 15248 hours, and simulation has been performed for normal cyclic loading. In Figure 4.3, it can be seen that the maximum HST is discovered around 57 °C on January 11, 2018, at full load condition (load factor 1) and continued in a few hours. This happened because the transformer loading was equal to 1 p.u. As a result, HST with DTR is lower compared to static rating case at full load condition.

0

20

40

60

80

100

120

140

160

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Loss

of

life

(day

s/ye

ar)

Transformer loading ( per unit)

(-30 ˚C) (- 20 ˚C) (-10 ˚C) (0 ˚C)(10 ˚C) (20 ˚C) (30 ˚C)

19

Figure 4.3 Dynamic rating results, [up] hotspot temperature at full load condition without adding solar power production from 2017-01-01 00:00:00 to 2018-09-28 08:00:00 and [down] highest hotspot temperature is found on January 11, 2018.

The transformer hotspot temperature is primarily dependent on the loading condition. During the winter, the loading current is higher than in the summer, so the HST rise is more significant during winter, as shown in Figure 4.4. The inertia of the HST relies on the top oil time constant, and it takes time to reduce HST.

Figure 4.4 Transformer loading effect on hot spot temperature during winter (up) and summer (down) in 2017.

Top oil temperature depends on ambient temperature and transformer loading. According to the standard, the difference equation is suitable for variable ambient temperature and load compared to the exponential equation. In IEC standard, oil exponent, x and winding exponent, y depend on the cooling setting of the transformer. As the selected transformer has an ONAN cooling system, the oil circulation will vary with the top-oil temperature. It also depends on the load and load losses. Thus, top oil rise does not follow the load factor, K, linearly [10]. Figure 4.5 shows that the TOT is high in summer, and there are some negative values due to low ambient temperature. The negative TOT also discussed in [26]

20

and [27]. However, the negative value is not significant since the transformer oil pour point needs to be lower than -25 °C to reach the dielectric breakdown voltage [28].

Figure 4.5 Top oil temperature rise with respect to ambient temperature at full load condition (1 p.u.) without adding PV production.

The HST to top oil temperature rise is dependent on the transformer loading. The initial load mainly determines the distribution transformer dynamic capacity. Figure 4.6 shows that for a higher load factor close to 1, the temperature rise is higher, and for a low load factor, it could be a small temperature rise just close to zero.

Figure 4.6 The hotspot temperature to top oil temperature rises as a function of transformer loading.

21

Figure 4.7 LOL after applying DTR and differential model in IEC standard. Note the factor 10-3 with the right-hand vertical axis.

The loss of life corresponding to the computed hotspot temperature for a thermally upgraded distribution transformer under various loading are shown in Figure 4.7. The highest hotspot temperature is about 57 °C, and the accumulated loss of life at the end of the period is about 0.0064 days. This is a very small value, and it can be concluded that the LOL is negligible after implementing DTR.

Case 3: Dynamic transformer rating including solar PV production.

It has been shown in Figure 4.8 that the installed capacity should not be more than 288 kW or 1.44 per unit for thermally upgraded insulation paper, assuming that the maximum permissible HST for this insulation paper is 110 °C. In this case, the transformer would not be overloaded until 1.44 per unit installed capacity. The accumulated loss of life is 1 day/year at 110 °C hotspot temperature, which is still a very small value and will not significantly reduced the transformer life. Table 4.1 shows four different lifetimes for thermally upgraded paper in IEC standard. The normal insulation life of the distribution transformer is 180 000 hours or 20.55 years, then the transformer's life will be maintained during the whole operation period under or equal to 110 °C of hotspot temperature.

22

Table 4.1 Normal insulation life of well dried, oxygen-free thermally upgraded insulation system at the reference temperature of 110 °C [10].

Basis Normal insulation life Hours Years

50 % retained tensile strength of insulation 65000 7.4 25 % retained tensile strength of insulation 135000 15.4 200 retained degree of polymerised in insulation 150000 17.1 Interpretation of distribution transformer functional life test data

180000 20.6

In normal cyclic loading operation, the maximum HST is 120 °C, the top oil temperature is 105 °C, and transformer loading is 1.5 per unit according to IEC standards. When installed solar PV is about 306 kW in the LV side, the highest HST is observed to be 120 °C, and the top oil temperature is 71 °C. The corresponding loss of life is equal to 3 days/year, satisfying the increasing factor of 2.71 for each degree increase in the hot spot temperature. Since the plotted time is 1 year or 365 days and the relative loss of life during this overload period is 0.0082, (3/365), times of the normal cyclic load. This value is negligible.

Figure 4.8 Dynamic transformer rating results after adding solar production.

With DTR more solar PV would be connected at the distribution level without any overloading in transformers. Analysis shows that transformer can be loaded up to around 1.5 times of the full load condition with no considerable increase in LOL or HST.

0.00

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100.00

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200.00

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300.00

350.00

400.00

450.00

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40.00

60.00

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100.00

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140.00

160.00

180.00

200.00

0 50 100 150 200 250 300 350 400 450

Loss

of

life

(day

s/ye

ar)

Tem

pera

ture

(˚C

)

Installed capacity of PV power (kW)

HST_max (˚C) TOT_max (˚C) LOL (days/year)

23

Table 4.2 Hosting capacity as a function of highest hotspot temperature for 200 kVA distribution transformer. The ambient temperature is used northern part of Sweden.

HST (°C) Hosting capacity (kW) 110 288 117 300 120 306 140 340 180 400

The Table 4.2 indicates that depending on the acceptable HST, that is mainly between 120 °C and 140 °C, one can increase solar PV production from 306 kW up to 340 kW, that is around 1.7 times of the full load normal condition.

Parametric analysis The parametric analysis is performed to determine certain assumptions in the solar installed capacity, particularly HST and LOL. In general, the back-feed is not a problem for the transformer as the transformer can cope with power flow in both directions [3] . However, all transformers encountered back-feed power flow during the summer, although it did not overload the transformers until 1.44 per unit load factor except the transformer number 2 (T_2) in the given location. Moreover, the transformer overloading limit using DTR can vary from place to place. Table 4.3 shows the maximum load in per unit for eight distribution transformers with same specification but different loading profiles. The base case transformer is 200 kVA, so T_1 is rated 9.5 times the base transformer with maximum load. Table 4.3 Transformers highest actual loading per unit.

Unit T_1 T_2 T_3 T_4 T_5 T_6 T_7 T_8 Maximum load (p.u.)

9.5 1.0 1.7 7.7 5.0 8.5 8.2 5.5

24

Figure 4.9 HST for various loaded transformer with solar power production

Considering the worst case, it can be seen until 100 kW installed capacity, HST is distinct among the transformer due to different loading. As the peak load is scaled for 200 kW and solar PV is dominated during summer months, therefore, the HST differences are not so noticeable among the transformer above 240 kW. But still, it has a small difference because some of the transformers have higher summer loads. In Figure 4.9, it is shown that the 300 kW installed capacity of solar PV can be connected to a 200 kVA transformer without exceeding the normal cyclic loading limit. However, due to thermally upgraded transformer limitation, only up to a 288 kW installed capacity can be added. In that case, an exception happened for T_2, where the maximum installed capacity is 280 kW considering normal cyclic loading because the transformer's size is smaller than others. Since in the region under study during summer the consumption is lower, we could expect higher solar PV capacity. Simulation shows that there would be no significant impact on the hotspot temperature rise until 150 kW installed solar PV capacity. If the installed capacity of solar PV is getting increased from 150 kW to 200 kW; the HST is drastically increased from 51 °C to 71 °C for T_2 due to the back-fed effect. Beyond 200 kW, for every 20 kW increased in installed solar PV capacity, the LOL also increases 2.7 times for every 10 degrees increase in HST. Results are presented in Table 4.4.

0

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60

80

100

120

140

160

50 100 150 200 250 300 350

Hot

-spo

t tem

pera

ture

(˚C

)

Solar installed capacity (kW)

T_1 T_2 T_3 T_4 T_5 T_6 T_7 T_8

25

Table 4.4 Hotspot temperature and loss of life for T_2 with PV power production.

Solar installed capacity (kW)

HST (℃)

LOL (days/year)

50 39 0.0 100 40 0.0 150 51 0.0 200 71 0.0 220 80 0.1 240 89 0.2 260 99 0.5 280 110 1.3 288 114 2.1 300 121 3.9 306 125 5.5 320 133 11.7

Maintaining the guidelines, the hosting capacity will be roughly 280 kW for a 200 kVA distribution transformer without a risk for network operators for the meteorological conditions in northern Sweden.

Figure 4.10 Ageing factor after implementing DTR for various loaded transformer with solar power production.

Figure 4.10 illustrates that the loss of life is very small for installed capacity below 260 kW. For 320 kW installed capacity loss of life would still be less than 12 days per year that is an acceptable value showing 1 year loss for each 30 years of the transformer’s life. It should be noted that the loss of life is a unique value for different transformers depending on the loading profiles and the geographical location.

0.00

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50 100 150 200 250 300 350

Loss

of

life

(day

s/ye

ar)

Solar installed capacity (kW)

T_1 T_2 T_3 T_4 T_5 T_6 T_7 T_8

26

5 Further analysis In this section, the accuracy of the analysis and parametric study has been performed.

Hosting capacity This study is divided into three cases that are summarised as follows: Case 1 has been accomplished for static rating analysis. It was found that the transformer cannot be overloaded more than 1 per unit. At 1.1 p.u loading condition, the hotspot temperature rises from 110 °C to 120 °C at 30 °C ambient temperature in Table 5.1, and the relative ageing rate is 0.016 for every 12 °C increase of HST. The hosting capacity can be determined based on various temperature limits and transformer insulation properties. Table 5.1The results summary of the static rating analysis

HST limit Allowable installed PV capacity 110 °C 200 kW 120 °C 220 kW 140 °C 240 kW

In the static rating, standards suggest not to overheat the transformer beyond 110 °C for a thermally insulated transformer. Therefore, the hosting capacity will be less than 200 kW for this case study. Case 2 has been performed for dynamic transformer rating without having PV power illustrated in Figure 5.1. The highest hotspot temperature is about 57 °C, and the accumulated loss of life at the end of the period is about 0.0064 days at 1 per unit load. Thus, DTR increases transformer rating capacity. Using DTR without PV, the transformer can be overloaded until 1.5 per unit according to the guideline's restriction. The HST is around 110 ℃ and the accumulated loss of life 0.3 days during the whole time period, so for the year 2017, it is around 0.2 days. Furthermore, the relative ageing factor is 0.0004 (0.15 /365) times normal operation ageing.

Figure 5.1 Dynamic transformer rating results without solar production

05101520253035404550

020406080

100120140160180200

1 1.2 1 .4 1 .6 1 .8 2

Loss

of

life

for w

hole

per

iod

of ti

me

(day

s)

Tem

pera

ture

(°C

)

Transformer loading (p.u.)

HST TOT LOL

27

Case 3 has been performed for dynamic transformer rating with solar PV capacity that is illustrated in Figure 4.8. As it is discussed in Section 4.3, the installed capacity of PV will increase up to 340 kW. Furthermore, the loss of life will play an important role to make a decision for the maximum hosting capacity. If we accept maximum 3 days/year LOL, then the maximum HC would be 306 kW. In Table 5.2, LOL is around 19 days/year for 340 kW installed capacity or almost 1.5 years for each 30 years operation that is considerable in that case. The hosting capacity would be 340 kW considering certain LOL because the highest HST appears only for one day at a specific time. However, it is not recommended to go beyond this installed capacity; otherwise, the loss of life will become unacceptable. Table 5.2 Installed capacity as a function of loss of life for the 200 kVA transformer.

Installed capacity (kW) Loss of life (days/year) 288 1 300 2 306 3 320 7 340 19 360 54 380 153 400 424

Transformer size

In this part, the HST and ageing analysis have been done considering solar PV production to investigate the benefits of applying DTR in the planning and designing stage for 50 kVA, 100 kVA, 200 kVA and 315 kVA. The transformers specification is shown in Table 5.3. All the transformers have the exact specification except the ratio of load loss to no-load losses. The HST and the LOL are higher with higher no-load losses condition, and with lower no-load losses, the transformer will face lower HST and ageing. Actual transformer loading is upscaled for 50 kVA, 100 kVA, 200 kVA and 315 kVA and implemented the IEC thermal and ageing model with solar PV production. The consequence of the ratio of load losses to no-load losses has minor impacts on ageing and HST. Table 5.3 Transformer specification for 50 kVA, 100 kVA, 200 kVA and 315 kVA.

50 kVA 100 kVA 200 kVA 315 kVA Rated HV current (A)

2.6 5.2 10.5 16.5

Rated LV current (A)

68.7 137.5 274.9 433

No load losses 77 123 214 308 Load losses 714 1190 1920 2666 The ratio of load losses to no-load losses (R)

9.3 9.7 9.0 8.7

28

Table 5.4 Transformer loss of life estimation for different size of transformer with solar power production

Loading T_50 T_100 T_200 T_315

HST LOL HST LOL HST LOL HST LOL 1 74 0.1 74 0.1 74 0.1 74 0.1 1.1 84 0.1 84 0.1 84 0.1 84 0.1

1.2 93 0.3 93 0.3 93 0.3 93 0.3

1.3 104 1.0 104 1.0 104 1 104 1

1.4 115 2.8 115 2.8 115 2.8 115 2.8

1.5 126 8.0 126 8.1 126 8.1 126 8.1

From Table 5.4, it is found that the HST and LOL have not been impacted by the size of the transformer considerably, and it is possible to increase loading up to 1.4 times the current loading without any constraints from the transformer for the northern part of Sweden. The result shows the possibility of providing a smaller transformer considering DTR with a certain level of additional solar PV production.

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6 Discussion The case study is based on the weather data from a region in northern Sweden with a 200 kVA transformer as a base model. Therefore, the outcomes can also be suitable for the Nordic region to decide how much PV can be connected without overloading a distribution transformer or when network operators need to install a new transformer. Furthermore, DTR implementation shows that LV networks (with or without PV units) can use the extra capability of the distribution transformer without damaging the transformer. Due to various simplifications and assumptions introduced, the analysis is subjected to uncertainties that may impact results. For the current analysis, the sources of uncertainties can be categorised as followed: Load: The load is an important input data for the simulation. A few loading data

was missing; however, the sensitivity analysis shows that the percentage of such uncertainty for the loading profile is negligible in the study.

Dynamic parameters: Solar PV production is calculated in [9] for a location close to 9 low-voltage networks for every 1-hour interval. Renewable Ninja calculates hourly production for a hypothetical solar-power installation from satellite data and a model of the panel. The interpolation was performed to generate every 10 minutes interval to match the transformer loading. After performing interpolation, some level of uncertain production has been generated. As solar production is a key parameter for calculating the hosting capacity, some simplification is applied to get the same accurate solar production every 10 minutes. However, the variation is not significant in this analysis.

Constant parameters for transformer: The effect of transformer parameters is also of importance. In general, the suggested value by the standard result is an overestimation of ageing. This gives more security and reduces the operational potential of the transformer. Ideally, all the parameters should be available for a transformer. In this case, some assumptions are made. The recommended values for oil time constant ( 𝜏𝜏𝑜𝑜) is a good approach and will not affect ageing considerably. For the study, winding time constant (𝜏𝜏𝑤𝑤) does not have significant effects, but a shorter time span must be used to analyse better. For R, the most conservative approach would take a value of 4. A value of 6 is suggested for a less conservative approach. A suggested top oil temperature rises in steady state (∆𝜃𝜃𝑜𝑜𝑜𝑜) of 45 K results in lower ageing; a higher value should be used for a conservative approach.

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7 Conclusion The high penetration of solar PV at the distribution grid will result in overloading multiple components, mainly transformers. In this master thesis, overloading a distribution transformer beyond its nameplate rating has been analysed which is known as DTR. DTR is a possible solution to the need for rapid network connections without investing in additional infrastructure. It offers a great opportunity to use the PV units in a more efficient way while getting a greater benefit from the same investment. The results show that the transformer can be loaded beyond the normal operational limits to expand the capacity of existing solar PV without affecting the transformer LOL considerably. The IEC differential thermal model is applied to calculate the HST and LOL of the transformer and to estimate the amount of solar PV that can be connected to the distribution transformer through DTR. Some of the other findings, together with the discussion, are presented below. The loading limit can be increased above 1.5 per unit, considering a specific loss of

life. As it is shown in Figure 4.3, the highest hotspot temperature was observed on January 11, 2018. The simulation is carried out until the maximum installed capacity 400 kW, then 340 kW PV production is the limit based on HST and LOL.

There is a relation between the increment in HST and loading profile, meaning that during the light loaded hours, transformers have a lower HST. However, due to the lower time constant, it takes a longer time for HST to follow the increment in the load. Therefore, it could also be advantageous for the grid operator to decide how much PV they will connect to the LV network along with when and where the extra investment requires a new transformer or how the battery storage system reduces the LOL [29].

The same methodology is applied to eight transformers with the same specification but different loadings, which shows that the load profile does not impact the conclusion considerably.

The hosting capacity can be varied depending on HST and LOL limits; therefore, the safe range of the hosting capacity is from 280 kW to 300 kW for this case study.

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8 Future work Several assumptions have been made during the study presented in this thesis. Hosting capacity depends on the different performance index to vary with different ambient temperature and loading patterns. Some of the future work that remains to be covered is summarised below. The work in this thesis is based on one set of time series loading and ambient

temperature. The work should be extended to use randomly generated time series, using methods like Monte Carlo [30]. These methods can be used to generate time series for PV production and different time series of loading profiles.

As the balanced three-phase transformer has been analysed for residential load, it still has a certain safety margin level. In reality, the phases are not identically loaded, and unbalance between the phases will cause different hotspot temperature and LOL in each leg of the transformer. A study should be performed with unbalanced phases for residential, office, and commercial loads.

The analysis in this work is based on one transformer’s specification; however, it is worth applying the same methodology to other sizes of transformers and to investigate the maximum level of solar PV production with respect to loading of transformer and insulation life.

In this thesis, the impact of DTR on maximum solar PV production (hosting capacity) had been investigated. However, the same analysis can be performed for different geographical locations (in Sweden and elsewhere) to analyse the scope of DTR application with PV. The meteorological parameters and loading profiles are different from one place to another, which is likely to affect the hosting capacity for PV.

The proposed methodology can be used for a medium-sized power transformer where the variations in the cooling modes need to be considered. Furthermore, switching the cooling method from ONAN to ONAF can increase hosting capacity since the cooling mode's heat run test parameters are affected.

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9 References [1] F. R. Segundo Sevilla, V. Knazkins, P. Korba and F. Kienzle., "Limiting Transformer

Overload on Distribution Systems with High Penetration of PV Using Energy Storage Systems," International Journal of Emerging Technology and Advanced Engineering, vol. 6(1), no. January , pp. 294 - 303, 2016.

[2] Swedish Energy Agency, "National Survey Report of PV Power Applications in Sweden, 2019.," 2019.

[3] M. Bollen and F. Hassan., Integration of Distributed Generation in the Power system, A John Wiley & Sons, Inc., Publication, 2011.

[4] E. Mulenga, M. H. Bollen and a. N. Etherden, "A review of hosting capacity quantification methods for photovoltaics in low-voltage distribution grids.," International Journal of Electrical Power & Energy Systems 115, vol. 105445., 2020.

[5] N. Etherden and a. M. H. Bollen, "Increasing the hosting capacity of distribution networks by curtailment of renewable energy resources.," IEEE Trondheim PowerTech, IEEE, pp. 1-7, 2011.

[6] E. Mulenga, N. Etherden and M. H. Bollen, "Likelihood of Overload due to connected Solar PV," CIRED, 2021.

[7] M. F. Lachman, P. J. Griffin, W. Walter and A. Wilson, "Real-Time Dynamic Loading and Thermal Diagnosticof Power Transformers," IEEE transactions on power delievry, vol. 18, no. 1, pp. 142-148, 2003.

[8] H. Wan, J. D. McCalley and V. Vittal, "Increasing thermal rating by risk analysis," IEEE Transactions on Power Systems, vol. 14, no. 3, pp. 815-828, 1999.

[9] S. Pfenninger and I. and Staffell, "Long-term patterns of European PV output using 30 years of validated hourly reanalysis and satellite data.," Renewable ninja. (https://www.renewables.ninja/), vol. 114, pp. 1251-1265, 2016.

[10] "IEC 60076-7:2005 Power transformers - part 7: Loading guide for oil-immersed power transformers," IEC, 2005.

[11] M. Wang, A. Vandermaar and a. K. D. Srivastava., "Review of condition assessment of power transformers in service," IEEE Electrical Insulation Magazine, vol. 18, no. 6, p. 12–25, 2002.

[12] Svenska kraftnät, "Svenska kraftnät," 2020. [Online]. Available: www.svk.se. [Accessed May 2021].

[13] N. Etherden, M. Bollen, O. L. Ackeby and &. Susanne, "The transparant hosting capacity approache- overview, applications and developments," 23rd International Conference on Electricity Distribution(CIRED), June 2015.

[14] "IEEE guide for loading mineral-oil-immersed transformers and step-voltage regulators .," IEEE Power & Energy Society, March 2012 .

[15] M. Kuisis, Transformer Management Systems – Uprating with Safety, South Africa: Martec division of Hendev (Pty) Ltd.

[16] C. J. Wallnerström, P. Hilber, P. Söderström, Hansson., R. Saers and O. Hansson, "Potential of dynamic rating in Sweden," IEEE Swedish Centre for Smart Grids and Energy Storage (SweGRIDS), 2014.

[17] N. Etherden, "Increasing the hosting capacity of distributed energy resources using storage and communication," PhD, Luleå, 2012.

[18] F. Hajeforosh and M. Bollen, "Dynamisk belastningsförmåga av luftledningar," 2020. [19] R. Karlsson, "Power system performance when implementing dynamic rating on a

wind farm connected transformer," KTH Royal Institute of Technology, ISBN: 978-91-7729-554-9, Stockholm, Sweden , 2017.

[20] T. Zarei, "Analysis of reliability improvements of transformers after application of dynamic rating," KTH Royal Institute of Technology, Sweden, June 2017.

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[21] H. Pezeshki, P. J. Wolfs and a. G. Ledwich., "Impact of high PV penetration on distribution transformer insulation life," IEEE Transaction on Power Delivery, 2013.

[22] M. Lehtonen and D. Susa, "Dynamic thermal modelling of power transformers: further development-Part I," IEEE Trans. on Power Delivery, vol. 21, no. 4, Oct 2006..

[23] B. Das, T. S. Jalal and F. J. S. McFadden, "Comparison and Extension of IEC Thermal Models for Dynamic Rating of Distribution Transformers," IEEE, 2016.

[24] B. C. Lesieutre and W. H. H. a. J. Kirtley., "An improved transformer top oil temperature model for use in an on-line monitoring and diagnostic system," IEEE Transactions on Power Delivery, vol. 12, no. 1, pp. 249-256, 1997..

[25] M. H. Bollen, "Risk of negative net consumption during backup-generator operation of LV distribution networks with solar PV," CIRED , June 2021.

[26] N. Rashid, "Short-time overloading of power transformers," KTH Royal Institute of Technology , Stockholm, Sweden, June, 2011.

[27] C. U. Engin Yigit, "Investigation of IEC Thermal Models of Power Transformers," 10th International Conference on Electrical and Electronics Engineering (ELECO), 2017.

[28] Wikipedia, "Transformer oil," 18 May 2020. [Online]. Available: https://en.wikipedia.org/wiki/Transformer_oil. [Accessed 2021].

[29] S. Talpur, T. T. Lie, R. Zamora and B. P. Das., "Maximum Utilization of Dynamic Rating Operated Distribution Transformer (DRoDT) with Battery Energy Storage System: Analysis on Impact from Battery Electric Vehicles Charging," Energies , vol. 13, no. 13, 2020.

[30] S. Hajeforosh and M. Bollen, "Uncertainty analysis of stochastic dynamic line rating.," Electric power systems research, vol. 194, 2021.

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Appendix A Check-list before submitting your first draft Please go through this check-list before you submit your first draft to your supervisor. To show that you have done it; mark the done parts by clicking on the check box☒. If the instructions in this document are not followed, your supervisor can refuse to read your thesis. You will remove the checklist from the appendix after you have received grade and the comments from the examiner. ☒ Use the given thesis template and do not change the style. Note the page breaks

after each section were taken away to make the document shorter. Please add them where it is necessary. Each section should always start on a new page.

☒ Always use the spell check in the text editor before you hand in a report to avoid

misspellings. Set the language before you start writing in the document. You can use US or UK English but you must be consistent with the one style all the way through the thesis

☒ Use the check-list in [7] for the SI rules and style conventions. ☒ The Abstract should include the important parts of introduction, method, results

and conclusion with focus on method and conclusions. ☒ The Abstract should stand alone from the report, thus no references or cross-

reference to figures or tables should be made. ☒ All abbreviations have to be listed in alphabetical order in the Abbreviation section

and have to be introduced the first time they are used in the text; same for the nomenclature list.

☒ Do not include a list of figures to the thesis. ☒ Does the Introduction give a good background to the research question and is it put

into perspective and do you describe why it is relevant to make this investigation? ☒ Does the Method section clearly describe the procedure of the study and performed

experiments and are the main simplifications and limitations of the method discussed.

☒ Preferably the used method should be motivated in relation to the aim of the study

and other possible methods. ☒ Are the results clearly presented and easy to understand for the reader? ☒ Have you really looked at the results with critical eyes and tried to find contradictory

data and unexplainable results or trends? ☒ Have you critically evaluated the results and critically discussed simplifications and

uncertainties in the method and possible implications for the results due to these imperfections?

35

☒ Have you critically evaluated the results and critically discussed simplifications and uncertainties in the method and possible implications for the results due to these imperfections?

☒ Are your results put in relation to the results from other similar studies? ☒ Excluding or avoiding the presentation of data which does not fit what you expect is

strictly forbidden. Just if you know that there was a specific mistake in the measurement or the methodology for that particular data point, then the data could be excluded and the criteria to exclude data should be given in the Method section.

☒ Recommendation for further work should be included in the thesis. ☒ Are all figures, tables, equations, references and appendices referred to in the text?

Use the Word cross-reference function. ☒ A report is usually a formal text where personal words such as "I", "we", "us", "our"

etc. are seldom or never used. Therefore, formulate without using these words, i.e. the passive form, e.g.: Do not write: I will investigate the effect of climate on xxxx. Instead: The effect of climate on xxxx will be investigated.

☒ Original figures (copy/paste) used from other sources should be referred in the

figure text and permission need to be requested from the author. In that case the figure text will include "[ref] with permission from (the publisher/copyright owner)" This should be only done if it is really necessary to understand the context. Otherwise avoid it.

☒ Redrawn figures used from other sources should be referred in the figure text. In

that case the figure text is "Reprinted from [ref]". ☒ All statements and conclusions presented must be backed up with either a reference,

a logical discussion, which explains the point of view, or it should be concluded from your own results.

☒ If you use labels in equations or figures they must be explained the first time they

appear and then shown in a nomenclature list (with units) placed before the reference section.

☒ Use consistent terminology if you talk about the same thing: e.g. do not use once

"solar radiation" and somewhere else "sunlight".

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Appendix B Distribution Transformer Specification from Hitachi ABB Overview data- Eco design series T2

Primary voltage Secondary voltage

11.00 ± 2 × 2.5 % V 420 V

Power (*) kVA 50 100 200 315 Rated current primarily. (at full 100% rated power)

A 2.6 5.2 10.5 16.5

Rated current secondary (at full 100% rated power)

A 68.7 137.5 274.9 433.0

Connection Dyn11 Dyn11 Dyn11 Dyn11 Frequency Hz 50 50 50 50 No-load losses, 𝑃𝑃𝑜𝑜 W 77 123 214 308 Load losses, 𝑃𝑃𝑘𝑘 at 75 ℃ W 714 1190 1920 2666 Short circuit impedance, 𝑈𝑈𝑘𝑘 at 75 ℃

% 4 4 4 4

Cooling mode ONAN ONAN ONAN ONAN Temperature rises of oil/winding

K 60/65 60/65 60/65 60/65

Total weight kg 524 712 1056 1409 Oil weight kg 116 149 193 237

(*) Load capacity according to IEC 60076-7 Loading guide