International Journal of Emerging Electric Power Systems Volume 9, Issue 2

2008

Article 7

Numerical Modelling of Heat Generation and Distribution in the Core and Winding of Power Transformers Kourosh Mousavi Takami∗

∗ †

Jafar Mahmoudi†

Malardalen University, [email protected] Malardalen University, [email protected]

c Copyright 2008 The Berkeley Electronic Press. All rights reserved.

Numerical Modelling of Heat Generation and Distribution in the Core and Winding of Power Transformers Kourosh Mousavi Takami and Jafar Mahmoudi

Abstract The power transformer is a complex and critical component of the power transmission and distribution system. System abnormalities, loading, switching and ambient condition normally contribute to accelerated aging and sudden failure. In the absence of critical components monitoring, the failure risk is always high. For early fault detection and real time condition assessment, an online monitoring system in accordance with the age and conditions of the asset would be an important tool. Power loss, heat generation and heat distribution evaluations in a large-scale oil immersed power transformer are presented here, along with the details of computer implementation and experimental verification. Core power losses are approximately constant with temperature variation or may decrease with that. Over the temperature range of 20 to 100◦ C the change in hysteresis loss Ph with temperature was negligible. Since the total core loss PT decreased with increasing temperature over this range, almost all the loss reduction was due to a reduction in the eddy current loss component Pe that was inversely proportional to the resistivity. Winding and oil temperature will increase with the load increasing and may create a hot spot. This is caused by degradation insulation and the loss of life in the power transformer. Hottest spot temperature and temperature profiles in radial and height coordinates were found using three different methods in this paper. The finite element method (FEM), finite difference method (FDM) and discrete furrier transform methods (DFT) are used to analyze algorithms in this paper. Computational results based on theoretical considerations and using the DFT method are shown to be in good agreement with FDM and FEM. Two mathematical formulae are proposed for temperature distribution in both radial and horizontal axes of core and windings. COMSOL for FEM, GEMINI for FDM and MATLAB for DFT are used. KEYWORDS: hot spot temperature, losses, ONAN, simulation, FDM, DFT, FEM

Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

I. INTRODUCTION Since large electric power transformers belong to the most valuable assets in electrical power networks, it is suitable to pay higher attention to these operating devices. Thermal impact leads not only to long-term oil/paper-insulation degradation; it is also a limiting factor for the transformer operation. Therefore, the knowledge of the temperature, especially the hot-spot temperature (HST), is of high interest. Power transformer is exposed to the worst injures because if we draw an over load from the network, surely it would be damaged, or would cause loss of life insulations and other parts of power. Because in this facts, we have to analyze all the parts, that may have a temperature rise. Thermo vision photo, cooling system in schematic form and active part of transformer for get a finer imagination are illustrated in figure3. Instance with on line monitoring we can see the temperature of all the parts in oil, winding and cores. Then decide which fan should start working or which ones should rotate in twice RPM. In power transformer fans have two modes of turning. Originally, heat generations in power transformers are resistance losses, eddy current and hysteresis losses that the two recent items varies less than resistance losses with load or temperature. Any way in transient analyses, we have to note all of losses. This paper focus on the source of heat generation and distribution and using of MATLAB and COMSOL software’s will analyze the losses and temperatures. Analyzing have been done using FEM, FDM and DFT methods. There are two main categories of losses, no load losses and load losses. No load losses are basically core losses associated with energizing the transformer and driving flux through the core. Load losses are further subdivided into RI2 losses and stray losses. Stray losses are the result of the stray flux from the winding or lead impinging on metal parts such as the tank walls , the clamps , and even the winding themselves , resulting in induced eddy currents. Recently, the efficiency of power transformer is improved as well as the size is becoming smaller. Therefore, it is very important that thermal characteristics of power transformer should be estimated and predicted precisely [1]. When power transformer is operated, the generated heat causes temperature rise inside the transformer tank including the windings and insulation. For many years, empirical method has been used to predict average temperature in windings but that could not give detailed temperature distribution of power transformer [2]. Our algorithms decide the number of coolers that are required to dissipate the calculated losses. Our designed program decides which coolers must be activated on data based in the actual and/or predicted load and ambient conditions.

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

The cooling fans are under control and each permutated to run according to the number of hours in operation. This results in longer bearing life and reduced costs. II. DISCRETE FOURIER TRANSFROM (DFT) ALOGRITHM The Discrete Fourier Transform is a simply a method of laying out the computation, which is much faster for large values of N, where N is the number of samples in the sequence. The idea behind the FFT is the divide and conquer approach, to break up the original N point sample into two (N / 2) sequences. This is because a series of smaller problems is easier to solve than one large one. The DFT requires (N-1)2 complex multiplications and N(N-1) complex additions as opposed to the FFT's approach of breaking it down into a series of 2 point samples which only require 1 multiplication and 2 additions and the recombination of the points which is minimal. x(0), x(1), … , x(N-1), N=2m

N −1

X (k ) =

∑

N / 2−1

x(n)W N nk

=

n =0

∑ n =0

let m = n-N/2 (n = N/2+m) N / 2 −1

⇒ X (k ) =

∑

x(n)WN nk +

n=0

N / 2 −1

=

∑ x(n)W

N

nk

=

∑ x(n)W

N

nk

Where;

n= N / 2

N / 2 −1

∑ x( N / 2 + m)W

N

+

WN = (e − j 2π / N )

(1)

( N / 2 + m) k

m=0

∑ x( N / 2 + m)W

N

mk

(2)

N WN 2 k

m=0 N

WN 2 = −1 ⇒ W N 2 k = (−1) k ⇒ X (k ) = N / 2 −1

N −1

n = N/2 => m = N/2-N/2 = 0 n = N-1 => m = N-1-N/2 = N/2-1

N / 2 −1

n =0 N

x(n)W N nk +

∑[ x(n) + (−1)

k

N / 2 −1

N / 2 −1

n =0

m=0

∑

x(n)W N nk +

∑ (−1)

k

x( N / 2 + m)W N mk

x( N / 2 + n)]WN nk

n =0

N / 2 −1

k : even ( k = 2r ) ⇒ X (k ) = X (2r ) = WN

2 rn

= (e

∑[ x(n) + x( N / 2 + n)]W

n =0 − j 2π / N 2 rn

)

N

2 rn

= (e − j 2π /( N / 2) )rn = WN / 2rn

N / 2 −1

⇒ X ( k ) = X ( 2r ) =

∑[1x(n4) 4+4x2( N4/ 24+43n)]W n =0

N / 2 −1

N/2 point DFT ⇒ Y ( r ) =

∑ y(n)W

N /2

N /2

(3)

rn

y (n)

rn

n =0

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution k : odd ⇒ k = 2r + 1 N / 2 −1

⇒ X (k ) = X (2r + 1) = Z (r ) =

∑[ x(n) − x( N / 2 + n)]W

N

n ( 2r +1)

(4)

n =0

N / 2−1

=

∑ n =0

N / 2 −1

Z (r ) =

∑ z(n)W n=0

N /2

rn

[ x(n) − x( N / 2 + n)]WN nWN 2rn = 14444244443

←

z ( n)

N po int 2

DFT

of

z (0), L, z (

N / 2−1

∑

z (n)WN 2rn =

n =0

N / 2−1

∑ z(n)W

N /2

rn

n =0

N − 1) 2

X(k) : N-point DFT of x(0), …, x(N) Î two N/2 point DFT

Figure 1: The initial decomposition of a length-8 DFT into the terms using even- and odd-indexed inputs marks the first phase of developing the FFT algorithm. When these half-length transforms are successively decomposed, we are left with the diagram shown in the bottom panel that depicts the length-8 FFT computation.

Length-2 transforms (see the bottom part of Figure 1), pairs of these transforms are combined by adding one to the other multiplied by a complex

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

exponential. Each pair requires 4 additions and 4 multiplications, giving a total number of computations equalling 8. This number of computations does not change from stage to stage. Because the number of stages, the number of times the length can be divided by two, equals log2N, the complexity of the FFT is O(Nlog2N) . III. FINTIE DIFFERENCE METHOD The finite element method is the best known approach for solving of differential equations. The numerical method approximates the equation of interest, usually by approximating the derivatives or integrals in the equation. The approximating equation has a solution at a discrete set of points, and this solution approximates that of the original equation. Such numerical procedures are often called finite difference methods. Most initial value problems for ordinary differential equations and partial differential equations are solved in this way. Numerical methods for solving differential and integral equations often involve both approximation theory and the solution of quite large linear and nonlinear systems of equations. Z-dir n+1 n+1/2 n-1/2

n n-1 m-1/2 m+1/2 r-dir m-1

m

m+1

Figure 2: Introduce of necessary parameters for finite differential method

m and n are the points of temperature in r and z directions. In FDM method, equation can solve in a defined method, these schematic illustration is shown in figure 2. We used general Fourier equation in this analysing. The summarized equations are:

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

kr

∂ r∂r

1 ∂T ∂ 2T ⎛ ∂T ⎞ +G = ~ ⎜⎜ r ⎟⎟ + k z 2 ∂ r α ⎝ ⎠ ∂z d ∂t

(5)

∂ ⎛ ∂T ⎞ ∂ 2 T k r ∂T kr + ⎜r ⎟ = kr r∂r ⎝ ∂r ⎠ r ∂r ∂r 2 ∂ 2T ∂r 2 ∂ 2T

(

=

=

∂T ∂r

∂T ( ∂z

− m+ 1

2

− n+ 1

2

∂T ∂r

∂T ∂z

Δr

∂T , ∂r

Δx

∂T , ∂z

) m− 1

2

) n− 1

2

m+ 1

1

=

Tm +1 −Tm Δr

2

=

Tn +1 −Tn Δz

,

,

∂T ∂r

m− 1

∂T ∂z

1

=

Tm −1 −Tm Δr

2

=

Tn −1 −Tn Δz

n+ n− ∂z 2 2 2 Tm +1,n .(2r + 1) − 2Tm,n + Tm −1,n ( 2rm,n − 1) Tm,n +1 − 2Tm,n + Tm,n −1 1 ∂T kr + kz +G = ~ 2 2 α d ∂t Δz 2rm,n Δr

(6) For boundary conditions and in the last layer that immerged with tank oil, equation is: h(Toil − Tm,n ) + k r

Tm−1,n − Tm,n + 0.5Δr.G = 0 Δr 2Δr.h

Δr 2 .G

2Δr.h

Then: 2Tm−1,n − (2 + k ).Tm,n + k + k Toil = 0 r r r This equation only used for last point.

(7) (8)

IV. CALCULATING OF CORE LOSSES (EDDY CURRENT AND HYSTERESIS LOSSES) Cores in power transformers are generally made of stacks of electrical steel laminations. These are usually in the range of 0.23- 0.46 mm (and for large scale power transformer may be up to 0.5 mm )in thickness and up to 1 meter wide or as much wide as it can be accommodated by the rolling mill. The losses of a ferrite core or core set Pv is proportional to the area of the hysteresis loop in question. It consists of three components: Pv=Pv,basic+Pv,hysteresis+Pv, eddy current owing to the high specific resistance of ferrite materials, the eddy current losses in the common frequency range today (50Hz - 2 MHz) may be practically disregarded except in the case of core shapes having a large cross-sectional area. In principle, the following applies: (9) Pv = U ..I . cos(ϕ ) The power loss PV is a function of the temperature T, the frequency f, the flux density B and is of course dependent on ferrite material and core shape. The temperature dependence can generally be approximated by means of a third-order polynomial, while equation 10 applies for the frequency dependence. Equation 11 is for the flux density dependence. Published by The Berkeley Electronic Press, 2008

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7 (1+ x )

0〈 x 〈1

(10)

Pv ( B ) ∝ B (1+ y )

0〈 y 〈1

(11)

Pv ( f ) ∝ f

The coefficients x and y are dependent on core shape and material, and there is a mutual dependence between the coefficients of the defining quantity (e.g. T) and the relevant parameter set (e.g. f, B). A transformation program is available for EFD and ETD cores as a design tool that allows core losses to be converted to different operating conditions (specific to core shape / material). General relationship between B and H: (12) B = μ0 ⋅ μr (H ) ⋅ H -6 μ0= 1.257 * 10 And total loss relation is: Wi = [ k h .B 1.6 . f + k f .t.B 2 . f 2 ]vol (13) Figure 6 shown the magnetic flux in LVand HV winding and bushing. These flux are the source of magnetic losses, hysteresis and eddy losses. Simulation shown that, with the increase in temperature from 25°C to 50°C hysteresis loss will decrease. After that from 50°C to 75°C it will raise as the same way (it decreased before), and from 75°C until 100°C it will increase but with less slope; and finally after 100°C slope will approximately decrease but like the last case.

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

(c) (d) Figure3: a) Active part of transformer with tap changer and its diverters b) oil directed oil flow improves cooling (OWAF) it lowers the hot spot temperature and reduce the thermal aging of insulation c) thermo vision photo, d) core and winding

For all simulations, PT decreased linearly with increasing of temperature. The Ph values tended to be constant or increased slightly between room temperature and 75- 100°C and then decreased slightly from 100°C to 120°C. The eddy current component of loss Pe that was defined as PT - Ph, followed dependence with increasing temperature. (See figure 4). Hysteresis loops shows in Figures5 and 6, for the temperature rang of 25 °C to 100 °C. Table 1 shows how power loss varies with temperature rise in the core. Table 1: Constant total loss for f constant P (w/m3) B=50 B=100 B=200 B=300 25 11.62 56.43 251.23 609.69 30 10.73 52.66 237.05 581.8 40 9.04 45.29 209.51 527.97 50 7.49 38.33 183.76 478.01 60 6.1 31.94 160.64 433.49 70 4.9 26.33 140.98 395.97 80 3.91 21.67 125.62 367.01 90 3.15 18.14 115.4 348.17 100 2.64 15.95 111.14 341.01 110 2.4 15.26 113.68 347.09 120 2.45 16.28 123.86 367.97

T °c

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

Power loss versus of T

1000

B=50

Pl[W/m³]

100

B=100 B=200

10

B=300

1

0

50

100

150

T[°C]

Figure4: core power loss total for f constant

hysteresis loss at T=25 c 500 400 300

B[mT]

200 100 0 -100 -200 -300 -400 -500 -298.0 -238.4 -178.8 -119.2 -59.6

0.0

59.6 119.2 178.8 238.4 298.0

H[A/m]

Figure5: hysteresis loss at T=25 c

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

hysteresis loss at T=100 c 500 400 300 200

B[mT]

100 0 -100 -200 -300 -400 -500 -300

-240

-180

-120

-60

0

60

120

180

240

300

H[A/m]

Figure6: hysteresis loss at T=100 °c

a)

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

b) Figure 7: a) flux in bushing b) flux in windings

V. TEMPERATURE CALCULATION The following equation can be used in the most of heat and mass transfers. Oil is mass and heat can create by losses. In this paper, convection and conduction consider for all the calculations. The following are the assumptions considered for simulation: • Oil and air initially are in steady state. • Oil is a Newtonian and incompressible fluid. • Fluid flow is laminar, unsteady and two-dimensional. • There is internal heat generation. • Data base used from appendix 1 The thickness of the copper-insulation layers, as shown in Fig. 2(a), can be calculated from the design data of the winding that is seen in factory information’s and catalogue: log kr = (

log

r0 r1

+

log

r3 r2

rn r1

+ ... +

log

rn rn −1

)

(14) Similarly, the thermal conductivity of a disc or layer of windings in zdirection can be calculated as in (7) [Fig. 2(b)]. kz =

kr1

kr 2

kr1

k cu k kp k pb (t cu + t kp + t pb )

k cu t kp k pb + t cu k kp k pb + k cu k kp t pb

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

The calculated effective thermal conductivity of a high voltage power transformer Windings in axial and radial direction has been given in Table 1. These values have been used in the computation of HST at next sections. Table 1: values of k for winding kr

kz

K

w / moc

w / moc

w / m oc

Windin g type

Transformer rating(MVA)

2.5

4.4

3.32

Hv disc

250

7.2

4.46

5.67

Lv disc

250

7.35

4.46

5.72

Lv disc

250

It is obvious that the winding is a thermally inhomogeneous structure for this; the thermal conductivity should be discussed as a tensor. The thermal conductivity takes the following form: k ten =

k rr

k rz

k zr

k zz

Where, k rr ....k zz are conductivity Coefficients. Considering in the transformer winding, the insulation structure closely satisfies the orthotropic structure in the orthogonal coordinate system and the above equation will substituted by the following arraies: k rr

0

k ten =

= 0

k zz

kr 0

0 kz

=

k1 = k 2 0

0 k3 = k 4

The terms k r and k z are the principal thermal conductivity. These were classified to z and r directions. VI. HEAT FLOW EQUATIONS With the determined thermal conductivity, the system of no homogeneous HCE under a no homogeneous boundary condition in cylindrical coordinate system are written as the following equations: kr

∂ ⎛ ∂T ⎞ ∂ 2T 1 ∂ 2T 1 ∂T + kϕ +G = ~ ⎜r ⎟+ kz 2 2 2 r∂r ⎝ ∂r ⎠ α d ∂t ∂z r ∂ϕ

This equation is In the regions of:

a≤r≤b

(16) ,0 ≤ z ≤ l

l≥0

.

At the inner cylindrical surface and in the region of (r = a, t f 0) , boundary condition is: Published by The Berkeley Electronic Press, 2008

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7 ∂T + h1T = h1Ta ∂r

(17)

∂T + h2 T = h2 Tb ∂r

(18)

− k1

At the outer cylindrical surface of windings and in the region of (r = b, t f 0) are: k2

At the bottom flat surface and in the region of ( z = 0, t f 0) , this is ∂T + h3T = h3Tbottom ∂z

(19)

∂T + h4T = h4Ttop ∂z

(20)

− k3

At the top flat surface ( z = l , t f 0) k4

(21) In the region, a ≤ r ≤ b ,0 ≤ z ≤ l , and t = 0 T = F (r , z ) , ( T = T (r , z, t ) ) The term G is the heat source function, and has been modified here to take care of variation of resistivity of copper with temperature. The heat source term G can be of the form: G = g 0 (1 + ρ t (T − T0 )) = g 0 − g 0 ρ t T0 + g 0 ρ t T = G0 + g 0 ρ t T (22) Where; g0= 3*RhvIhv2+3*RlvIlv2+Wh+We, ρ t is the temperature coefficient o −1 of electrical resistance of copper wire in c . With this representation, the function G becomes temperature dependent, distributed, heat source. For the sake of mathematical convenience and to provide a reference for the heat source function, the constant G0 is included to replace the constant part of (22). The term F (r, z) represents the initial function for transient heat conduction ⎛ α~d = ⎜ 1

⎞ ⎟ = αd / k

problem. The term, ⎝ ρ Cp ⎠ where is the diffusivity. h ....h Heat-transfer coefficients 1 4 , are different across all four surfaces, the values of which can be calculated by using heat-transfer empirical relations given in [2]. eq

eq

VII. RESULTS AND DISCUSSIONS Using FDM, DFT and related boundary equations and with coding in MATLAB and GEMINI softwares based on robust algorithm, was solved. In order to verifying and finding the hottest spot temperature, all of equations with using of DFT method solved again. All of computations were performed in the steady state mode. We give the second part of the equation (16) equal to zero and solve them. The simulation has been performed COMSOL software. COMSOL does the simulation on base of finite element method. Authors found the maximum internal temperature above the surrounding oil T (0, 0) - Toil=25°C. The surface temperature rise in the top of oil is

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

approximately T (top)-T (oil) =16.3 °C and bottom oil is T (bottom) –T (oil) =11.7 °C This modelling shows that the hot spot point is located in 70% of radius from the core surface to the last winding (Tap winding), see figure 8. According to the results of modelling with the MATLAB soft ware, it is found that for the OFAF condition heat in 86% height of core, in case of temperature increase due to over loading the transformer. Hottest spot temperature is 126.5 °C. Temperature differences in three kind calculation and simulation are less than 2 °C. Figure 9, shown temperature profile for varies kind of computations. In radial direction, maximum temperature is 128 °C and is located between low and high voltage windings. This is illustrated in figure 6. It shown this difference is about 1°C. We have extracted new temperature distributions formulae in height of core and winding due to DFT and from figure 8 are: T ( z ) = −22582 z 8 + 87587 z 7 − 1.38 × 10 5 z 6 + 1.12 × 10 5 z 5 − 750015 z 4 + 12029 z 3 − 1467 z 2 + 127 z + 101

(23)

Comparision of three kinds of temperature calculation 130

Temperature Distributin in Height of Tr.[oC]

Disceret Fourier Transform Finite Diffrential Method

125

Finite Element Method

120

115

110

105

100

0

0.1

0.2

0.3

0.4 0.5 0.6 Height in Per unit

0.7

0.8

0.9

1

Figure8: Temperature distribution in height of transformer for DFT, FDM and FEM methods

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

128 Discrete Fourier Transform Finite Diffrential Method

126

Finite elemnt method

Temperature [oC]

124

122

120

118

116

0

0.1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 Radius from core to tap winding surface in per unit

0.9

1

Figure9: Temperature distribution in radius and on the HST region of transformer for DFT, FDM and FEM methods

We have extracted new temperature distributions formulae in radius of core and winding due to DFT and from figure 9 are: T ( r ) = −18079 r 8 + 74330 r 7 − 1.24 × 10 5 r 6 + 1.08 × 10 5 r 5 − 52190 r 4 + 13632 r 3 − 1708 r 2 + 82.6r + 118

(24)

To overcome on these problems, authors have suggested oil-spraying devices [26, 27]. It can remove the HST. In other hand, transformer need to an apparatus for protecting over to thermal effects. In order to, authors designed a novel electronically relay and modules. It has many input and out put ports. Inputs are measurable temperatures, voltages; currents etc. outputs are alarm and trip that send to siren, indicators and circuit breakers. It is illustrated in figure 10. VIII. CONCLUSION In this paper shown that with the increasing of temperature due to over load or other same items, core power loss is remains constant, but copper loss and top of oil temperature will increase. These causes a temperature rise and create the hottest spot point. Hottest spot temperature and temperature distribution profile have obtained by three various methods, Finite difference, finite element and DFT

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

methods. Results have a reasonable fit with them. Two mathematical formulae in equations 23 and 24 were extracted and can used in design steps. These are used both horizontal and radial coordinates. Figure10: shematic diagram, for on line monitoring of power transformer

Top-oil temperature H winding current X winding current Y winding current

rules Winding hot-spot Temperature model

Sensors

Moisture sensor temperature

Moisture model

Moisture sensor

Cooling stage status

Fixed parameter Type of paper Reference water content for dry paper Oxygen content Top oil temperature set pint Hot spot temperature set point Load current set point

Insulation Aging Model Insulation aging is a function of temperature Aging is calculated automatically on the hottest winding Aging can be calculated either as per IEEE rules

output Insulation Aging Model Aging rate

Cumulative aging Display and trending

Cooling control The cooling system can be initiated from either: - Top-oil temperature - Load current -Winding hot-spot temperature Cooling control can detect discrepancies and raise alarm in case of cooling malfunction It is assumed that under significant load, the absolute water content in oil is uniform in the transformer Moisture and bubbling The relative water content in the winding can be derived from the moisture sensor When thermal equilibrium conditions are achieved, paper-oil partition curves can be applied

Cooling control Stage 2 ON/OFF control

Stage 3 ON/OFF control Order to nuzzle Control vs. status discrepancy alarm

Moisture and bubbling Water content in insulating paper Bubbling temperature Water condensation temp

Absolute water content in oil

As the solution of this problem and with considering of the magnetic field aspects, authors offered the using of fixed oil spraying devices, in other

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

publications. It sprays the oil on the hot spot point. The other way is installation of many spraying devices on the tank that can change the direction of nozzle proportional to location of the hot spot after its identifying. Its nozzles can rotate many direction and angles then it can spray the oil to the hottest spot point or area. Control system can be designed with genetic algorithm, neural network, fuzzy logic and other same algorithms that could be chosen for spraying. It noted that there’s no needed to use the piping instruments inside the oil tank. All the spraying system will be installed on the tank body. IX. APPENDIX 1 [3] Power transformer 250 MVA in IEEE loading guide 1995 Transformer Losses, W. No Load 78100 Pdc losses (I2 Rdc ) 411780 Eddy losses 41200 Stray losses 31660 Nominal voltage 118 KV 230KV Pdc at hot spot location 467 527 Eddy current losses at hot spot location 309 (0.65 pu) Per unit height to winding hot spot 1

157 (0.3 pu) 1

Temperature Rise °C . 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 duct oil 38.3 Initial average winding 33.2 Initial bottom oil 28 Initial hot spot 38.3 Transformer component weights, kg Mass of core and coil assembly 172200 Mass of tank 39700 Mass of oil 37887

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

X. APPENDIX 2 [3] Q GC+ Q LW+ Q GSL= Q AO+ Q LO Where, Q LW is the heat lost by the windings, W. Q GC is the heat generated by the core losses, W. Q GSL is the heat generated by stray losses, W. Q AO is the heat absorbed by the tank core oil, W. Q LO is the heat lost by the oil, W. Q GC=PCR are the rated core losses, W. XI. NOMENCLATURE Cp h K G t T Tb H B M x(t) Δt N xn r

Specific heat at constant pressure. Heat transfer coefficient. Thermal conductivity . Heat rate. Time. Temperature. Bottom temperature. Electric field Density of electric field Magnetic field Continuous-time signal Sampling period (interval) (samples) over T Periodic function Radius

Greek Symbols α diffiusivity parameter. Δt Time difference. ρ Density. μ Permeability. Subscripts i In the position i. cu Cupper kp Kraft paper pb press board

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

XII. REFERENCES [1] Robert M. Del vecchio, Bertrand poulin, Pierre T. Feghali, Dilipkumar M. shah, and Rajendra Ahuja, `` Transformer Design Principles with application to core – form transformers ``, CRC press, 2002. [2] 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 [3] IEEE Loading Guide for Mineral Oil Immersed Transformer, C57.91, pp. 18– 19, 46–53, 1995. [4] Jafar Mahmoudi, Mathematical modelling of fluid flow, heat transfer and solidification in a strip continuous casting process``, International Journal of Cast Metals Research IJC604.3d 20/1/06 13:22:12 ,The Charles worth Group, Wakefield +44(0)1924 369598- Rev 7.51n/W (Jan 20 2003). [5] 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 2007. [6] G.W. Swift, T.S. Molinski, W. Lehn , “A Fundamental Approach to Transformer Thermal Modelling–Part I: Theory and Equivalent Circuit,” IEEE Trans. on Power Delivery, vol.16, no.2 April 2001, pp.171-175.I [7] G.W. Swift, T.S. Molinski, R. Bray and R. Menzies, “A Fundamental Approach to Transformer Thermal Modelling–Part II: Field Verification,” IEEE Trans, on power delivery, vol.16, no.2 April 2001, pp.176-180. [8] D. Susa, M. Lehtonen, H. Nordman, “Dynamic Thermal Modelling of Power Transformers,” IEEE Trans. on Power Delivery, vol.20, Iss.1 Jan 2005, pp.197204. [9] D. Susa, M. Lehtonen, H. Nordman, “Dynamic Thermal Modelling of distribution Transformers,” The paper has been approved for publication in the IEEE Trans. on Power Delivery [10] P.T. Staats, W.M. Grady, A. Arapostathis, R. S. Thallam, “A Procedure for Derating a Substation Transformer in the Presence of Widespread Electric Vehicle battery Charging,” IEEE Trans. on Power Delivery, vol.12, No.4 Oct 1997, pp.1562-1568. [11] Working Group 12-09, “Experimental Determination of Power Transformer Hot-Spot Factor” Electra, no.161, Aug 1995, pp.35-39. [12] IEC Publication 76-2:1993, Power Transformers, Part 2. Temperature rises. [13] Working Group 12-09, “Analytical Determination of Transformer Windings Hot-Spot Factor” Electra, no.161, Aug 1995, pp.29-33. [14] Working Group 12-09, “A survey of facts and opinions on the maximum safe operating temperature of power transformers under emergency conditions” Electra, no.129, pp.53-63.

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Mousavi Takami and Mahmoudi: Numerical Modelling of Heat Generation and Distribution

[15] J. Saitz, T. Holopainen and A. Arkkio, Modelling and Simulation in Electromechanics Field Problems, HUT , Electromechanics Lab. 2002. [16] K. Haymer and R. Belmans, Numerical Modelling and Design of Electric Machines and Devices, WIT-Press, 1999. [17] M. David and Others, Finite Element Method Magnetic FEMM. [18] 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. [19] Kourosh Mousavi Takami, Evaluation of oil in over 20 year’s old oil immersed power transformer, Mazandaran University, May 2001. [20]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 [21] Kourosh Mousavi Takami, et al., April 2007, Numerical modelling on Thermal and hot spot evaluations of oil immersed power Transformers by FEMLAB and MATLAB software’s, eurosime conference, London, 1-42441106-8/07/2007 IEEE. [22] 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 [23] Kourosh Mousavi Takami, Hot Spot identification and find a best thermal model for large scale power transformers, April 2006, KTH University, Stockholm, Sweden. [24] Kourosh Mousavi Takami, et. al., Power Transformer Parameter Estimation with online data ACQUISITION and USING the Kalman Filter method, sssec conference, Stockholm, Sweden [25] Kourosh, Mousavi Takami, Jafar Mahmoudi, (2008) "Design of a New Oil Spraying Device for Hot Spot Cooling in Large Scale Electric Power Transformers," International Journal of Emerging Electric Power Systems: Vol. 9 : Iss. 2, Article 3. [26] Kourosh, Mousavi Takami, Jafar Mahmoudi, Identification of the best thermal formula and model for oil and winding of large sclae power transformers using prediction methods, SIMS 2007 , Sweden, ISSN (print): 1650-3686, ISSN (online): 1650-3740. [27] Kourosh, Mousavi Takami, Jafar Mahmoudi, Manufacturing and simulation of a novel copper heat Sink with copper pipe for heat removing in CPU, IEEE/ ICEPT2007 Conference, Shanghai- China, 1-4244-1392-3/07

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International Journal of Emerging Electric Power Systems, Vol. 9 [2008], Iss. 2, Art. 7

XIII. BIOGRAPHIES 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 at 2002. Currently, he is Ph.D. student at Mälardalen University in Sweden since 2005. He has over 11 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, Sweden and senior scientist in ISRI, Norway. 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.

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