August 16, 2017 | Author: Jorge Carrion Gonzalez | Category: Transformer, Finite Element Method, Temperature, Heat, Electricity
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Effect of Power System Harmonics on Transformer Loading Capability and Hot Spot Temperature Shamsodin Taheri a, Hamed Taheri b, Issouf Fofana a, Hossein Hemmatjou a and Ahmad Gholami c a

Département des sciences appliquées, Université du Québec à Chicoutimi (UQAC), G7H 2B1, Chicoutimi, Canada b Département de génie électrique, École de technologie supérieure (ETS), Université du Québec, H3C 1K3, Montréal, Canada c Faculty of Electrical Engineering, Iran University of Science & Technology, IUST, Tehran, Iran Email: [email protected], [email protected] ABSTRACT

Under harmonic conditions, caused by nonlinear loads, losses and temperature inside the power transformer increase. The hot spot temperature is one of the major limiting factors that affect the transformer life time and its loading capability considerably. This paper presents the determination of field distribution on the transformer components as well as its losses using finite element method (FEM). The hot spot and top oil temperature are computed under harmonic conditions according to two techniques, i.e. the dynamic thermal model and IEEE guide. The effect of harmonics on the useful life of transformer is then analyzed. Finally, an algorithm is proposed to determine the loading capability of transformer under harmonic conditions. Index Terms— Transformer, Hot spot, HarmonicsLosses, Finite element method, Loading capability, Life time. 1.


Power transformers represent the largest portion of capital investment in transmission and distribution substations and their correct functions are vital for system operations. The widespread use of nonlinear loads has increased the level of harmonics intensively. The increase of the transformer power losses and consequently its temperature rises are the primary concerns of the harmonic impacts. The hottest spot temperature (HST) which is increased due to harmonic current causes rapid thermal degradation of insulation and subsequent thermal breakdown. To predict the limits of loading capability and useful life of a transformer, it is necessary to estimate the HST of transformer winding. To determine the hot spot and top oil temperatures under sinusoidal conditions, many methods have been proposed to date. A transformer thermal modeling approach in the form of an equivalent

circuit based on fundamentals of heat transfer theory has been suggested [1]. Full simulation and renewal process approaches have been presented to evaluate the time to failure of the insulation. The estimations of some relevant reliability parameters such as life, time-to-reach design life, and probability of failure at a given time are also presented [2]. Analytical methods for estimating the temperature and its distribution at different points of the transformer are presented based on a closed-form mathematical technique using generalized heat conduction (GHC) model [3]. However, there are few methods to assess the hot spot temperature under harmonic conditions. A model similar to traditional transformer equivalent circuit is used to predict the hot spot temperature and transformer life time [4]. Moreover, a model including a potential difference defined as the second derivative of the load current representing eddy current losses in windings and the other stray losses represented by a resistor in series with the leakage inductance and dc resistance is presented [5]. Recently, the authors presented a method to determine the field distribution on the transformer components using finite element method (FEM) and the calculations of hot spot and top oil temperature under harmonic conditions [6]. The lack of thermal models for forecasting the hot spot temperature and loading capability of transformer under harmonic conditions has motivated the present study, which aims at developing reliable dynamic models to analyze the transformer performance. This paper deals with the analysis of the magnetic field distribution and losses by 3D FEM and uses two methods, namely the IEEE guide and a dynamic thermal model, to determine the hot spot temperature. The effect of harmonic on transformer life using the aging acceleration factor will be discussed. Finally, Transformer loading under nonlinear load will be determined using the proposed algorithm.

2012 25th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) 978-1-4673-1433-6/12/$31.00 ©2012 IEEE


in Fig. 2, the flux density in the transformer components is shown in Fig. 3.


Transformer losses (PTL) are generally classified into no load (PNL) or core losses and load losses (PLL) as follow: (1)


where PNL is the losses due to the voltage excitation of the core and also PLL is expressed as [7]:



Fig. 1. The mesh model of transformer

where PΩ is the losses due to load current and dc winding resistance, PEC introduces Winding eddy losses and POSL refers to other stray losses in clamps and tanks. Current harmonics are supposed as significant barriers that affect on transformer performance nowadays. These harmonic current components cause additional losses in the windings and other structural parts. The eddy current losses due to any non-sinusoidal load current can be expressed as [8]:


h = hmax


h =1

Ih 2 2 ) h IR

Fig. 2. Daily load cycle


where PEC-R, Ih and IR are rated eddy current losses, current at harmonic order h and rated current respectively. Although the heating due to other stray losses is generally not considered for dry-type transformers, it can have a substantial effect on liquid-filled transformers. The other stray losses due to non-sinusoidal load current can be expressed as [8]: hmax

POSL = POSL − R ∑ I h2 h 0.8

Fig. 3. Transformer field solution


h =1

where POSL-R denotes the rated other stray losses. 3.


Transformer winding turns usually consist of copper conductors in the shape of small rectangular strands. These strands are immersed in an alternating magnetic field. The losses are found from a magneto-static solution. A finite element method is adapted to estimate the losses in each turn/disc to determine the hot spot temperature. Analysis of the field by 3D FEM would be more accurate. However complexity would increase. Fig. 1 shows the model of a 250 MVA, 118/230 kV transformer that is meshed using Maxwell software which divides the transformer components. Regarding the load cycle shown

In order to calculate the transformer losses, two methods including FEM and mathematical equations are introduced in this study. The results calculated from standard equations (Eq. (3) and Eq. (4)), as well as the calculated values from FEM, are presented in table 1. From the results, it may be observed that there is satisfactory agreement between the standard equations and finite element analysis. The maximum calculated error is about 6%. Table 1. Transformer losses calculations under harmonic conditions





Standard method FEM









The hot spot temperature plays an important role in determination of useful transformer life. To determine the hot spot and top oil temperature, two methods, namely the IEEE guide and the dynamic thermal model are used in this work. The commonly used model for top oil and hot spot temperature calculations is described in Clause 7 of the IEEE Guide [7]. In order to analyze the temperature conditions inside a transformer, the analogy between thermal and electrical processes is used which is named dynamic thermal model. After some simplifications, the differential equation used to calculate the hot spot temperature is [8, 9]:

⎡ ⎤ P I 2 ⎢ K θ + EC − R ⎥ Kθ ⎦ 1 1 dθ ⎣ .[Δθ H − R ] m = τ H . H + [θ H − θ o ] m 1 + PEC − R dt


where θH is the hot spot temperature, Kθ-R is the resistance correction due to temperature change, ΔθH-R is the rated hot spot rise, τH is the hot spot time constant and m is exponent which defines nonlinearity. Fig. 4 shows the hot spot temperature for the same harmonic loads supplied to the transformer. The THD of 22% gives a temperature rise 30°C than where there are no harmonics for the hot spot temperatures. The simulation results verify that the thermal model and IEEE model can properly calculate the top oil and hot spot temperature under harmonic conditions.

the hot spot temperature and aging acceleration factor is given by [7, 10]: (6) ⎛ ⎞

15000 15000 ⎟⎟ − Faa = exp⎜⎜ 383 + 273 θ h ⎝ ⎠

To estimate insulation heating effect, the loss of life factor is integrated over a given period of time (T) as:


∫ Faa dt

t =0


Fig. 5 shows loss of life factor of transformer at daily load cycles. As shown in Fig. 5, under heavy harmonic conditions, the transformer life factor is increased four times thenormal life that means the transformer life is (15) life of declined significantly by one fourth of normal transformer.

Fig. 5. Transformer Loss of life factor


Fig. 4. Predicted hot spot temperature



The hot spot temperature is considered to be the most important parameter in determining the insulation loss of life and the potential risk of releasing gas bubbles during a severe overload conditions. The relationship between


t =T


As simulation result has shown, the presence of harmonic loads increases transformer loss of life dramatically. Hence, transformer loading is needed to be derated according to level of network harmonics. Power transformer model tests indicate that the normal life expectancy at a continuous hottest spot temperature of 110°C is 180 000 hours (1 per unit). Thus, if transformer maintains its loss of life factor at the end of operation cycle equal to one, it works on its normal life (180,000 hours) [10]. In order to determine the loading capability of transformer, a suggested flowchart is shown in Fig. 6. It shows a simplified flowchart of the self-consistent timedependent mathematical model. After correction action of the loss of life factor at the end of load cycle, the new loss of life is one per unit shown in Fig. 7. Therefore, the transformer is capable to maintain its normal life.

current increases the hot spot and top oil temperature, and declines its useful life intensively. To maintain the transformer life in normal limitation, a new loading is applied. Furthermore to determine the new loading, a flowchart was proposed.

8. [1]




Fig. 6. Flow chart to determine loss of life [5]


Fig. 7. Transformer Loss of life factor under new load

[7] [8]



Since the transformer is driving harmonic loads, it may be subjected to additional losses and heating, leading to the reduction of its expected life time. To estimate the transformer loss of life properly, it is necessary to take into account the harmonic current spectrum, the electrical characteristics, the thermal behavior, the realistic load and ambient temperature profiles. In this study an electromagnetic analysis was used to determine the total loss in various parts of the transformer. Then, two methods including thermal and IEEE models were used to calculate the winding hot spot temperature. Finally, the effect of harmonics on the transformer loss of life was analyzed. The simulation results show that the harmonic




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