IEEE PES PowerAfrica 2007 Conference and Exposition Johannesburg, South Africa, 16-20 July 2007

A new apparatus for mitigating the hot spot problem in large power transformers using Ants algorithm Kourosh Mousavi Takami

Jafar Mahmoudi

IST dep., Mälardalen University, Box 883, SE 721 23, Västerås, Sweden Phone: +46 73 672 9496; Fax: +46 21 101370; [email protected]; [email protected] Abstract –Hot spot temperature (HST) is the most important parameter in the operation of power transformers. The HST has to be held under a prescribed limit. HST has a considerable effect on the insulation aging. Therefore detecting, monitoring and removing the HST could be a very important and necessary action for Utilities. A new design of oil spraying and its effect, along with a thermal management in a transformer cooling system has been studied in this paper. The effect of oil fluid flow on the HST problem has been considered in this paper; and the calculations and simulation have been performed by Ants algorithm. The simulation results have been validated based on a 230/63/20 kV, 250MVA transformer at the Sari substation in Iran, and the results indicate that the new design could mitigate the limitations of transformer loading due to the HST problem. The Ants algorithm have been proposed and applied for accomplishing this task and to give an improved level of accuracy.

I.INTRODUCTION Transformers are one of the main components in the electric power systems. The losses in the transformer core and the windings of high efficiency transformers cause an increase in the operating temperature of the transformer. This increase in the temperature can affect the insulating material used in its windings. Therefore, the Hot spot point could affect life of transformer. It is important to accurately calculate and identify the hot spot point because after it is located, various methods can be used to cool down its temperature. Currently, manufacturers do not use any devices for removing the hot spot point. Rather, they compensate for it by decreasing the loading level, increasing the fan speed and the speed of oil circulation. [1] which might lead to shutting down the transformer or a black out in the network. Assunçlo et al. [2] proposed estimating the top-oil temperature by using a method based on Least Squares Support Vector Machines approach. This estimated top-oil temperature is then compared with the measured data of a power transformer in operation. In their approach they have only found a model, but have not introduced a device for cooling. teNyenhuis et al. [3] presented an accurate calculation of the value of the core hot-spot temperature. At the design

stage, it is very critical to ensure that hydrogen generation, which can be caused by oil-film degradation at core hot-spot temperatures of as low as 110–120oC, is limited. K. Eckholz et al. [5] calculated the heat transfer coefficients at the winding surface using heat run test results of various ON- and OD-cooled winding types. Two different general approaches were proposed for ON- and OD-cooled windings. The characteristics of the heat transfer coefficients were calculated for each type of the winding. Further temperature rise experiments with an ON-cooled disc winding operated with variable heat flux densities were performed in order to investigate the influence of the heat flux density on the cooling efficiency of the boundary layer [6]. However, the above approaches have only found methods for calculating of heat transfer coefficient. Instead, the utilities mainly need a device for removing the hot spot problem. Usage of oil spraying systems can decrease the HST and finally could increase the allowable temperature rise in a transformer by more than 65 oC, because the HST is one of major obstacle of transformers for loading. With calculation the flow rate, speed and temperature of oil that would be threw to hot spot, could find the best nozzle cross section, oil pump speed and so with oil spraying it has been shown in this paper that could decrease or remove the hot spot temperature. The volume of the spray mix applied per area by a sprayer depends on: • Nozzle flow rate • Width sprayed • Travel speed of the sprayer. Before finding a sprayer, proper nozzles must be selected. Nozzles should be matched and replaced as a set except under unusual circumstances. The following study intends to provides a framework for the calculations necessary for nozzle selection and sprayer calibration. I. EXPERIMENTAL DATA The experimental data are gathered from a 230/63/20KV Sari substation in Iran, on a 230/63/0.4KV transformer. For a one month period, in July 2006, the temperatures of the oil, the three windings, and the ambient have been measured throughout each day (Fig. 1).

It can be seen that the low voltage winding has the highest temperature. This is due to the fact that it carries the highest current magnitudes.

Table I: transformer data from IEEE guide 1995[7] Description

Value

No Load (W)

78,100

Pdc losses (W)

411,786

Eddy losse (W)s

41,200

Nominal Voltage

118 kv

variation of temperature in TR. (july) 66 temperature in oc

64

therid w inding temp.

62 60

low voltage w inding temp

58

high voltage w inding temp

56 54 52

oil temp.

50 1 3

Variations of ambient temprature 40

Temp. (oc)

35 30 25 20 15 10 5 0 1

Pdc at HST location

467

527

Eddy current losses at HST

309(0.65pu)

157(0.3pu)

p.u. height to winding HST

1

1

Temperature Rise ºC

5 7 9 11 13 15 17 19 21 23 Hours

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 Hours

Fig.1. Variation of temperature in transformer and ambient for three winding 250MVA, 230/63/0.4KV transformer on July 2006 in SARI 230/63/20KV substation – Iran

As another example we used the data for a 250 MVA power transformer, obtained from the IEEE loading guide published in 1995 (Table I). II. HIGH PRESSURE NOZZLE DEFINITION The purpose of this section is to simulate the operation of a nozzle. A nozzle is perhaps the most important and basic piece of engineering hardware associated with the high-speed flow of oils for cooling the hot spot. The usual configuration for a nozzle is shown in the figure2 .The oil flows through the nozzle from a region of high pressure (usually referred to as the chamber or Tank) to one with low pressure (referred to as the hot spot area). The Tank is usually big enough so that flow velocities in it are negligible. The pressure in the tank is denoted by the symbol pc. Oil flows from the chamber into the converging portion of the nozzle, past the throat, through the diverging portion and then shoots into the hot spot point. The pressure of the HST point is referred to as the “back pressure” and is given the symbol pb. In order to understand the concept and behavior of the fluid pressure, we have to remember only few basic rules: • When the flow accelerates, the pressure drops, • The pressure rises instantaneously across a shock, • The pressure falls across an expansion wave.

230kv

Rated top oil rise

38.3

Rated top duct oil rise

38.8

Rated hot spot rise

58.6

50.8

Rated average winding rise

41.7

39.7

Rated bottom oil rise

16

Initial top oil

38.3

Initial top oil duct

38.3

Initial average winding

33.2

Initial bottom oil

28

Initial hot spot

38.3

Transformer components weights (kg) Mass of core and oil 172,200 assembly Mass of tank 39,700 Mass of oil

37,887

Note that the temperature distribution qualitatively like the pressure distribution.

behaves

A. Selecting the sprayer application rate A recommended range of sprayer application rates, in liter/mm2, is calculated on base of the nominal power of transformer and distance of tank body with core surface. From that range, could choose the rate that is compatible with spraying equipment. B. Selecting the field speed A 10% reduction in the oil speed will result in a reasonable heat transfer coefficient; it is shown in figure7. Where speed must be reduced for a short period at the end of cooling period, when get the over 70% of HST cooling or in other situations, (for a 30% of all spraying time) [23], a small reduction in pump speed is preferable to selecting a lower cooling. Reducing the cooling speed causes the nozzle flow rate as well as the travel speed to decrease, although not proportionately. If it is necessary to reduce the speed frequently, calibrate the sprayer for the slower speed.

C. Determining the width sprayed by each nozzle The width sprayed by each nozzle on a broadcast spray boom is equal to the distance between the nozzles. If a sprayer has nozzles spaced every 40 inches on the boom, the width sprayed by each nozzle would be 40 inches. If a sprayer has several nozzles that will be used to spray each row, such as sprayers used to apply insecticides to row crops, then the width sprayed by each nozzle is equal to the distance between the rows divided by the number of nozzles used to spray each row. If the sprayer is a band sprayer and the labeled rate applies to the actual area sprayed, the width is equal to the width of the band. If the sprayer is a band sprayer and the labeled rate applies to the total area covered, the width is equal to the spacing between the rows. However, since an intelligent system based on fuzzy logic is been used in this paper, the nozzle can rotate and have many degrees of freedom. This allows us to reduce the number of nozzles to half or less.

V =

D × 60 T

(2) Where V = travel speed (mm/s) D = distance (mm) T = travel time (seconds) 60 = a constant (seconds per minute) E. High Viscosity Problem for nozzle The high viscosity of the oil prevents the nozzles from forming the equivalent spray patterns, at equivalent temperature and pressure settings. The first and most obvious solution is to increase the working pressure of the system. The drawbacks to this solution are higher cost in the higher pressure rated pumps, motors, and delivery lines to the nozzles. This also increases the safety concerns in the event of ruptured lines in the building. A booster pump on the outlet of this system can be a solution. A second solution is to employ local area pumps. And finally, the third option to be considered is to use some sort of rotating nozzles, which would spray the oil in a rotating type fashion. III. TEMPERATURE CALCULATION

a

b

A. Heat transfer conventional equations In most of the heat and mass transfers the heat equation [17] can be seen. In this paper, convection and conduction is considered for all the calculations. The following are the assumptions considered for simulation: • Oil and air are initially in steady state. • Oil is a Newtonian and incompressible fluid. • Fluid flow is laminar, unsteady and twodimensional. Continuity equation: ∂ρ ∂t

+

∂ ∂ (ρ u ) + (ρ v) = 0 ∂x ∂y

(3) Linear momentum equation in the x direction Fig. 2. a-nozzle b-schematically cut of power transformer with oil spraying system [23].

D. Determining the nozzle flow rate The nozzle flow rate can be calculated: GPM = GPA x V x W x k (1) Where k a constant for conversion of units GPM nozzle flow rate (liter/s) GPA sprayer application rate (litre/mm2), W width sprayed by each nozzle (mm). And the travel speed is given by:

∂(ρu) ∂ ∂ +u (ρu) + v (ρu) = ∂t ∂x ∂y ∂p ∂ ∂u ∂ ∂u − + (µ )+ (µ ) ∂x ∂x ∂x ∂y ∂y

(4) Linear momentum equation in the y direction ∂(ρv) ∂ ∂ +u (ρv) + v (ρv) = ∂t ∂x ∂y ∂p ∂ ∂v ∂ ∂v − + (µ )+ (µ ) − g ( ρ − ρ ref ) ∂y ∂x ∂x ∂y ∂y

(5)

Energy equation ∂ ( ρC p T )

∂ ∂ ( ρC pT ) + v ( ρC p T ) = ∂x ∂y ∂ ∂T ∂ ∂T (k )+ (k ) + A ( t ) q ′′′ ∂x ∂x ∂y ∂y (6) ∂t

+u

∂u 1 ∂σ i ∂T = − ∂y µ ∂T ∂x

With 0 for fluids   −4  A (t ) =  − 1 .37 × 10 − 9 × t 2 + 0 .805 × 10 × t + 0 .1358  for the compunents of the active unit   

Where τ is the thermal process time constant (TC); ∆t is the time difference; ρ is the density and µ is the dynamic viscosity.

The initial conditions are (7) At t=0, u=v=o, T0 =Tf =24 o C The boundary conditions considering natural convection, with the transference coefficient h as a function of the wall temperature and radiation are [20]: x = 0, y = y , t = t , u = v = 0

∂T w T = h yl ( −Tf ) x = 0 ∂x T + εσ .(( + 273 ) 4 − (T f + 273 ) 4 ) x = 0 (8) x = lx , y = y, t = t, u = v = 0

− kw

− kw

∂Tw T = h yr ( −Tf ) ∂x x = lx

y = 0, x = x, t = t , u = v = 0

∂T w T = h yb ( −Tf ) ∂y y =0 T + εσ .(( + 273 ) 4 − (T f + 273 ) 4 ) y = 0 (10)

y = l y , x = x, t = t, u = v = 0 − kw

T + 273 ) 4 − (T f + 273 ) 4 ) y = ly

ε = 0 . 2 , σ = 5 . 67 × 10

−8

k

(11)

m k Where The convective coefficients included in the boundary conditions are determined using the approach proposed by Montsinger [7], which permit to determine the convective heat losses by unit area on the tank wall in terms of the air friction factor f, the barometric pressure Pb, and the wall and surrounding temperatures Tw and Tf, respectively. It is given by W c = 2 . 17 . f . p b ( T w − T f ) 1 . 25 (12) Where f = 1 for flat walls. In another way, in accordance with the Newton’s Law, the convective heat transfer on the tank walls is given by: q ′′ = h .( T w − T f ) (13) So, from (12) and (13), it is obtained that:

h ( x , y ) = 2 . 17 .( T

− T

)

0 . 25

2

4

(14) At the interface oil-air, the boundary condition is the one used by Ramaswamy and Jue [8]: w

f

To derive the equation system (magnetic field) solves, start with Ampère’s law, (16) ∇ × H = J + ∂∂Dt = σ E + σ V × B + J e + ∂∂Dt Now assume time-harmonic fields and use the definitions of the potentials, B = ∇ × A , E = −∇ V − ∂∂At , and combine them with the constitutive relationships B = µ 0 ( H + M ) and D = ε 0 E + P to rewrite Ampère’s law as ( j ωσ

− ω 2ε 0 ) A + ∇ × ( µ

−1 0 0

(17)

∇ × A − M ) −

)∇ V = J

In the 2D in-plane case there are no variations in the zdirection, and the electric field is parallel to the z-axis. Therefore you can write ∇ V as −∆V/L where ∆V is the potential difference over the distance L. Now simplify these equations to − M y  2 − ∇ .( µ 0− 1 ∇ A z −   ) + σ V .∇ A z + ( j ωσ − ω ε 0 ) A z (18)  M x  = σ ∇LV + J ϕe + j ω Pϕ

Where: σ is the electrical conductivity, Vloop is the loop e

∂T w T = h yt ( −Tf ) ∂y y = ly + εσ .((

B. AC power electromagnetic fields

σ V × ( ∇ × A ) + ( σ + j ωε

T + εσ .(( + 273 ) 4 − (T f + 273 ) 4 ) x = lx (9)

− kw

(15)

potential, J ϕ is the external current density, P ϕ is the electric polarization, A z is the magnetic potential z component and v is velocity. The Ants algorithm using finite element mode performs this transformation to avoid singularities on the symmetry axis. The relevant interface condition is n 2 × ( H 1 − H 2 ) = J ϕ The natural boundary condition fulfills this equation if the surface current vanishes. We can transform the Neumann condition of this PDE into: − M y  − M y  ) 1 − ( µ 0− 1 ∇ A z −  − n .[( µ 0− 1 ∇ A z −  ) 2   M x   M x  (19) = − n × ( µ 0− 1 ∇ × A − M ) 1 − ( µ 0− 1 ∇ × A − M ) 2

[

]

= −n × (H 1 − H 2 ) = 0

C. Solution procedure The Ants algorithm has been used for the solution of these set equations. A set of m artificial ants construct solutions from elements of a finite set of available solution components C = { c ij } , i = 1,..., n , j = 1,..., D i . A solution construction starts with an empty partial solution S p = φ . Then, at each construction step, the current partial

solution S p is extended by adding a feasible solution component from the set of feasible neighbors N ( s p ) ⊆ C . The process of constructing solutions can be regarded as a path on the construction graph GC(V,E). The allowed paths in GC are implicitly defined by the solution construction mechanism that defines the set N ( s p ) with respect to a partial solution S p . The best known rule is the one of ant system (AS) :

p(cij s p ) =

τ ijα .ηijβ

∑τpilα .ηilβ

, ∀cij ∈ N ( s p ),

(20)

cij ∈N ( s )

whiere τ ij and η ij are the pheromone value and the heuristic value associated with the Furthermore, α and β are component c ij respectively. positive real nodes in solution matrix whose values determine the relative importance of pheromone versus heuristic information. Solution components cij are the edges of the graph, and the

IV. RESULTS AND DISCUSSION A. Magnetic field solution Fig 2.2b shows the magnetic field solution of transformer. The leakage flux in the windings flows axially up through the coils and then bends radially across the windings. From Fig 2.2b it can be seen that the component of the leakage flux has its greatest concentration at the interface between the two windings and then decreases progressing away from the gap between the windings. The inner LV winding typically has a higher attraction of the leakage flux due to the high permeance of the core. The leakage flux in the HV winding is divided between the core and the core clamps and other structural parts [8]. In the upper end of the windings, the conductors are exposed to an inclined magnetic field with two components, an axial component and a radial component. The eddy current loss is the contribution of these two components.

pheromone update for τ ij , that is, for the pheromone associated to the edge joining parameters i and j , is m

performed as follows: τ ← (1 − ρ ).τ + τ k ∑ ij ij ij k =1

where ρ ∈ ( 0 , 1] is the evaporation rate, m is the number of ants, and ∆τ ijk is the quantity of pheromone laid on edge ( i , j ) by

the 1 Lk

∆τ ijk = {0

otherwise ,

k -th

ant: Fig.2.1: Transformer

if ant k used edge (i, j ) in its tour ,

where Lk is the tour length of the k -th ant. When constructing the solutions, the ants in AS traverse the construction graph and make a probabilistic decision at each vertex. The transition probability p (cij s p ) of the k -th ant moving from i parameter to parameter j is given by (20). η ij = 1 d , where dij is the length of component cij (i.e., of ij

edge ( i , j ) ). In this work a transformer model was adapted using the FEM analysis software FEMLAB [7]. The solution has been successfully converged around 765 iterations. The FEM analysis was carried out on different industrial transformers to estimate the winding eddy current losses. Circulating current losses in continuously transposed conductors (CTC) or properly transposed windings is small and their contribution to the eddy current loss was considered negligible.

a.

b.

Fig. 2.2 a- Transformer essential parts b-Transformer field solution in FEM environment Hot spot and thermal simulations

We wrote a program by PDE operator in MATLAB software environment based on genetic algorithm, as an MATLAB file. The assessment was done in the steady state

TABLE II. Calculated COEFFICIENTS c and N

S/So

C

n

100%

9.1

0.41

30%

1.65

0.61

20%

0.495

0.685

10%

0.83

0.66

evaluation of temperature profile with ONAN and oil spraying to %91 of core height 90 100

temprature in oc

mode. We equal the second part of the equation (5) to zero and solve it. We have obtained and calculated these behaviours of oil and temperatures, with and without oil spraying, and finally have modeled the transformer oil flow in order to obtain the flow pattern. Although the velocity and temperature distributions will be simulated by fluent software. For the maximum internal temperature above the surrounding oil, we found T (0, 0) - Toil=25°C. The surface temperature rise in the top of oil is approximately T (top)-T (oil)=17.8 °C and bottom oil is T (bottom) –T (oil) =12.2 °C This modeling shows that the hot spot point is located in 91% of the core and winding height from the bottom. With oil spray to top of winding (in 91% height of core), in the top of oil we could see that, without oil forced, oil temperature will decrease. For the maximum internal temperature we found that above the surrounding oil we have T (0, 0)-Toil= -35.8°C. But there is a problem in the power transformer for oil spraying and that is electrical and magnetic field problem. While spraying oil, non-homogeneous field might occur, and this causes a break down before the manufacturer determinations may occur, and for this problem we have to assess and calculate field effects.

80

80

70

60

60

40 50 20 1

40 1 0.5

30

0.5

radius of core and winding in per unit

0

0

per unit of core and winding height

Fig. 4. : Evaluation of temperature profile with OFAF and oil spraying to %91 of core height (location of hot spot). With nozzle cross section of 2826mm2 and oil speed 1m/s 125

Temprature in oc

125 120

120

115 110

115

105 100 1

110

0.5 radius of core and winding in pu.

0.6

0

0

0.2

0.8

0.4 Height of core and winding in pu.

1

flow diameter in verticall direction in decimeter

130

3 2 1 0 -1 -2 -3

flow diameter in horizental direction in decimeter

2

10 0

5

-2 0

distance between nozzle and winding in decimeter

105

Fig. 3. evaluation of temperature profile with OFAF

B. Simulation of nozzle in shooting of oil Flow of sprayed oil, which is passing through the oil in the tank, is calculated using MATLAB environment; these are illustrated in figures 3 and 4. It is shown that oil pressure form nozzle to the HST point will decrease, but it has not created too much disturbance, therefore the produced turbulence is negligible. In figures 5 and 6, the colours red, yellow, light blue and dark blue create a flow rate from high to low ranges. A load of computations shows that the contribution of variation of Re and Nu numbers are very limited, therefore for sake of complicity the laminar flow has been chosen.

Fig . 5. Flow pattern that emission from nozzle to HST

For heat transfer coefficient (HTC) calculations in this section a simplified approach is used: h (G ) = C . G n (21) Coefficients C and n depend on the geometry and are evaluated from measured HTC using a least square method. The values of the coefficients in equation (21) are calculated to C and n that are shown in table 2. The experiments were made on an ON-cooled disc winding with oil guiding elements and radial cooling ducts. The cross section of the investigated winding is natural convective cooling (ON) and forced directed cooling (OD), and the winding equipped with a number of PT100 sensors in order to measure local temperatures.

temperature diffrerence between oil and winding(Twinding-Toil)

diameter of oil flow from nozzle center

we propose usage of oil spraying devices, that spray oil on hot spot points. 2 1 0 -1 -2 2 0

diameter of oil flow -2 from center

1

2

3

4

5

8

7

6

9

distancce from nozzle to core and winding in decimeter

Fig. 6. Flow pattern in slice form by 30-degree rotation form nozzle

In figure 7 variations of heat transfer coefficients with heat flux density are evaluated in 4 kind’s cross section of nozzle. It is assumed that S0=2826mm2 and oil velocity due to pumping and nozzle action is 1m/s. In figure 8 it is shown that with changing the heat flux density in some cross sections of nozzle, differential of temperature in winding with oil is considerable. It means that with higher cross sections, removing heat from the winding is more efficient. In Table III the values of the coefficients C and n, stated in equation (14), for all four oil entrance cross sections are given. 1400 S/So=100%

Heat transfer cofficent(w/k.m2)

1200

1000 S/So=30%

800

600

S/So=20%

400

200

0

50

100

150

200 q(w/m2)

250

300

350

40

S/So=15%

S/So=40%

35

S/So=70%

30 S/So=100%

25

20

15

10 50

100

150

200 250 heat flux density(w/m2)

300

350

400

Fig. 8. differential of winding and oil temperature versus heat flux density in much nozzle cross-section.

Oil sprays provide many times the cooling rate for removing of hot spot. By changing the geometric parameters of the spraying apparatus and the physical parameters of the oil one can substantially vary the cooling rate in any temperature range. The other way is installation a number of oil-spraying nozzles in which would be automatically activated when the temperature exceed HST. Further, the nozzles could be adjusted to move at any angle until it can spray oil to hot spot point or area. See figure 4. In this method, the solution has been convergence with maximum 765 iterations; of course it can be reduced to lower by choosing a best initiation data. The control system can be designed using genetic algorithm, neural networks, fuzzy logic…, that could be chosen for spraying applications. Worth to mention that all spraying equipment including nozzles will be done located inside tank. REFERENCES

S/So=10% 0

45

400

Fig. 7. heat transfer coefficient versus heat flux density on much cross section of nozzle

V. CONCLUSIONS The main objective of this study is to find the temperature distribution and hot spot temperature value and location by which it is possible to determine the life of the transformer and to remove or mitigate its side effects by oil spraying. With increase of ambient temperature or loading level, the temperature will increase, which creates hot spot. In order to solve this problem, considering effect of the magnetic field,

1.

2.

3.

4. 5.

Kourosh mousavi Takami, A FFT technique for discrimination between faults and magnetizing inrush currents in power transformers, KAHROBA scientific magazine specialized in power electric engineering, Mazandaran, Iran T. C. B. N. Assunçlo, J. L. Silvino, and P. Resende, Transformer TopOil Temperature Modeling and Simulation, transactions on engineering, computing and technology volume 15 October 2006 ISSN 1305-5313 Ed G. teNyenhuis, Ramsis S. Girgis, Günther F. Mechler, and Gang Zhou, Calculation of Core Hot-Spot Temperature in Power and Distribution Transformers, IEEE transactions on power delivery, Vol.17, NO. 4, October 2002 T. V. Oommen, R. A. Ronnau, and R. S. Girgis, “New mechanism of moderate hydrogen generation in oil-filled transformers,” in Proc.CIGRE Conf., Paris, France, Aug.–Sept. 1998, Paper 12-206. “Hydrogen generation for some oil-immersed cores of large power transformers,” in Proc. DOBLE Conf., Mar.–Apr. 1998. K. Eckholz*, W. Knorr, M. Schäfer, K. Feser, E. Cardillo, new development in transformer cooling calculations.

6. 7. 8.

9. 10. 11. 12. 13. 14. 15. 16.

17. 18.

19. 20. 21.

22. 23.

24.

IEEE Loading Guide for Mineral Oil Immersed Transformer, C57.91, pp. 18–19, 46–53, 1995. FEMLAB V2.3, Electromagnetics Module. Comsol, 2002. A. Elmoudi, M. Lehtonen, “Eddy losses calculation in transformer windings using FEM,” The 44th International Scientific Conference of Riga Technical University, Riga, Latvia, October 9-11, 2003, Series 4, Vol. 10, pp. 46-51. K. Haymer and R. Belmans, Numerical Modelling and Design of Electric Machines and Devices, WIT-Press, 1999. M. David and Others, Finite Element Method Magnetic FEMM. A. Konard, “Inegrodifferential Finite Element Formulation of TwoDimensional Steady-State Skin Effect Problems,” IEEE Trans. on Magnetics, vol. MAG-18, no.1, Jan 1982, pp.284-292. J. Weiss and Z. J. Csendes “A One Step Finite Element Method for Multiconductor Skin Effect Problems,” IEEE Trans. on Power Apparatus and Systems, vol. PAS-101, no.10, Oct. 1982, pp.3796-3800. A. Konard, M. V. K. Chari, and Z. J. Csendes “New Finite Element Techniques for Skin Effect Problems,” IEEE Trans. on Magnetics, vol. MAG-18, no.2, Mar. 1982, pp.450-455. Lates L. V., Electromagnetic calculation of Transformers and Reactors: Moscow ENERGY, 1981 (In Russian), p.313. D. Pavlik, D. C. Johnson, and R. S. Girgis, “Calculation and reduction of stray and eddy losses in core form transformers using a highly accurate finite element modelling technique,” IEEE Trans Power Delivery, vol. 8, no. 1 Jan. 1993, pp.239-245. Kourosh Mousavi Takami, Evaluation of oil in over 20 year’s old oil immersed power transformer, Mazandaran University, May 2001. Kourosh Mousavi Takami, Advanced Transformer Monitoring & Diagnostic Systems and thermal assessment with robust software's, research presentation, Water and power University, March 2007, Tehran, Iran Kourosh Mousavi Takami, Hot Spot identification and find a best thermal model for large scale power transformers, April 2006, KTH University, Stockholm, Sweden. M. K. Pradhan and T. S. Ramu, `` Prediction of Hottest Spot Temperature (HST) in Power and Station Transformers``, IEEE Transaction on power delivery,vol.18, NO.4,October2003 Kourosh Mousavi Takami, Hassan Gholinejad, Jafar Mahmoudi, Thermal and hot spot evaluations on oil immersed power Transformers by FEMLAB and MATLAB software’s, IEEE Conference, Int. Conf. on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2007, London, 17 April 2007, pp 529-534. Kourosh Mousavi Takami, Jafar Mahmoudi, Evaluation of Large Power Transformer Losses for green house gas and final cost reductions, 3rd IGEC conference, Sweden, June 18, 2007. Kourosh Mousavi Takami, Jafar Mahmoudi, A novel device (oil spraying system) for local cooling of hot spot and high temperature areas in power transformers, 3rd IGEC conference, Sweden, June 19, 2007. Kourosh Mousavi Takami, Jafar Mahmoudi, Thermal evaluation and energy saving with loss reduction in core and winding of power transformers, 3rd IGEC conference, Sweden, June 19, 2007.

Kourosh Mousavi Takami was born in Sari, Mazandaran,Iran . He received the B.S.c. degree in electric power engineering from the Iran University of Science and Technology (IUST) Tehran, Iran, Oct1995 and the M.Sc. degree in electric power engineering from the Engineering Faculty of Mazandaran University, Iran in 2002. Currently, he is PhD student at Mälardalen University in Sweden since 2005. He has so over ten years experience in power system design and installations. His research interests include Optimization and simulation of heat generation and transfer in the core and winding of power transformers; diagnostic

testing and condition monitoring of power equipments, and application of fuzzy and Ants algorithm to condition monitoring of power equipments. Jafar Mahmoudi was born in Tehran, Iran. He received the B.Sc., M.Sc. Degree in Sharif University and PhD degrees from KTH University, Stockholm, Sweden. Currently, he is a Professor with the Department of Public Technology Engineering in MdH University, Västerås, and Sweden. His major research focus is development of new technology and methods for industrial energy optimization with special focus on heat and mass transfer. He has years of theoretical & experimental- experience on this. He also has a broad technical background encompassing thermodynamic, numerical methods and modelling (CFD computation) as well as materials science. This in combination with his industrial experience has served as a solid basis to build upon in expanding his research activities and focusing on relevant and current industrial issues. Over the last 10 years his focus has been on the practical and industrial application of the above mentioned methods, an effort conducted in a large number of industrial projects. In this, his teaching experience has proved invaluable.