Recent Developments of Electrical Drives - Part 3 ppt

The measured core loss of a turbine generator seems to include additional losses.. One of them is eddy current loss in the electrical steel sheets due to the axial magnetic flux.. Loss i

I-1 CORE LOSS IN TURBINE

GENERATORS: ANALYSIS OF NO-LOAD CORE LOSS BY 3D MAGNETIC FIELD

CALCULATION

A Nakahara1, K Takahashi1, K Ide1, J Kaneda1, K Hattori2,

T Watanabe2, H Mogi3, C Kaido3, E Minematsu4, and K Hanzawa5

1Hitachi Research Laboratory, Hitachi, Ltd., 7-1-1, Omikacho, Hitachi, Ibaraki 319-1292, Japan

2Hitachi Works, Power Systems, Hitachi Ltd., 3-1-1, Saiwaicho, Hitachi, Ibaraki 317-8511, Japan

kenichi hattori@pis.hitachi.co.jp, isao@keyaki.cc.u-tokai.ac.jp

3Steel Research Laboratories, Nippon Steel Corp., 20-1, Shintomi, Futtsu, Chiba 293-8511, Japan

mogi@re.nsc.co.jp

4Flat Products Division, Nippon Steel Corp., 6-3, Otemachi, 2-chome, Chiyoda-ku,

Tokyo 100-8071, Japan

5Yawata Works, Nippon Steel Corp., 1-1, Tobihatacho, Tobata-ku, Kitakyusyu,

Fukuoka 804-8501, Japan

Abstract Magnetic field analysis of no-load core loss in turbine generators is described The losses

in laminated steel sheets are calculated from the results of finite element magnetic field analysis The additional losses in metal portions other than the steel sheets are also calculated The sums of these losses were compared with the measured values for two generators and found to be 88% and 96% of the measured values The results revealed that the additional losses made up a considerable part of the core losses

Introduction

Turbine generators have been developed by using various design technologies to meet the needs of customers Reliable estimation of losses is essential in designing highly efficient turbine generators [1–3]

Among various losses, core loss is one of the most difficult to estimate for two reasons:

1 The cataloged data of electrical steel sheets are measured for a rectangular shape in

a uniform magnetic field Electrical steel sheets in an actual machine, however, are processed into complex shapes, and the induced field is not uniform

2 The measured core loss of a turbine generator seems to include additional losses One

of them is eddy current loss in the electrical steel sheets due to the axial magnetic flux Others include losses in metal parts other than the steel sheets

S Wiak, M Dems, K Kom˛eza (eds.), Recent Developments of Electrical Drives, 3–12.

2006 Springer.

This paper presents an analysis of the core losses under no-load conditions in turbine generators by utilizing a three-dimensional magnetic field calculation based on a finite element method The analysis consists of two steps First, we calculate the loss in laminated steel sheets from experimental data obtained with an Epstein frame In this calculation,

we take into account differences between the actual core loss and cataloged data Second,

we calculate the additional losses in metal parts other than the steel sheets Based on the analysis results, we also compare the total calculated core losses with measured values for two turbine generators

Calculation method

As noted above, the core losses are calculated in a two-step procedure First, we calculate the loss in the laminated steel sheets by using the experimental data obtained with an Epstein frame In this calculation, we take into account the rotational magnetic field and the harmonics

Second, we calculate the additional losses For metal parts other than the laminated steel sheets, we calculate the losses by three-dimensional finite element analysis We also use the finite element method to calculate the losses due to the axial flux in the laminated steel sheets, because the data obtained with the Epstein frame do not include these losses

Loss in laminated steel sheets The loss due to the alternating field in the laminated steel sheets can be calculated from the experimental data with the following equation:

Wi = Wh + We = Kh B α

maxf + Ke Bmax2 f2 (1)

where W i is the loss per weight of the sheets, W h and W eare the hysteresis and eddy current

losses per weight, respectively, K h and K eare coefficients obtained with the Epstein frame,

f is the frequency of the alternating magnetic field, and Bmaxis the maximum magnetic flux density occurring in one cycle

Although the magnetic field in an Epstein frame is a static alternating field, the magnetic field in an actual generator is a rotational field with harmonics Thus, the rotational and harmonic effects must be taken into account, and to calculate these effects, we apply two methods We utilize the method proposed by Yamazaki [4] to calculate the hysteresis loss, and the Fourier series expansion method to calculate the eddy current loss

In equation (1), it is assumed that Wh and We are proportional to f and f2respectively

for any level of the magnetic flux density, B The core loss, however, actually includes the excess loss due to the microstructure of a steel sheet [5–7] In addition, the B-dependency

of the hysteresis loss varies according to the level of B [8].

To consider the excess loss and the B-dependency of the hysteresis loss, various methods

have been proposed Though the eddy current loss is expressed by one term in equation (1), it is expressed by two terms in the methods proposed to consider the excess loss [4–6]

One term expresses the classical eddy current loss and is proportional to B2f2 The other

term expresses the excess loss and is assumed proportional to B1.5 f1.5 On the other hand,

a method proposed to express the B-dependency of the hysteresis loss changes the values

of the exponentα and of Kh for different levels of B in equation (1) [8] Different levels

defined in this method are from 0 to 1.4 T, from 1.4 to 1.6 T, and from 1.6 to 2.0 T

8 10 –5 0.0001 0.00012 0.00014 0.00016 0.00018

0.002 0.003 0.004 0.005 0.006 0.007

B [T]

Figure 1 B-dependency of K h and K e

These methods consider the B- or f -dependency of the core loss by changing the com-ponents of B or f Nevertheless, it is difficult to completely express these complex

depen-dencies Additionally, the dependencies differ according to the kind of steel sheet

Consequently, we propose a method to reflect the B- and f -dependencies of K h and Ke.

In equation (1), we assume thatα = 1.6, based on tests by Steinmetz [9] Fig 1 shows an example of the B-dependencies of K h (circles) and K e(triangles) obtained with an Epstein

frame In this case, the maximums of K h and K eare roughly twice and three times as large, respectively, as their minimums

In Fig 2, the dots represent the ratio, W i/f , at different frequencies, where Wiis the loss

in electrical steel sheets measured with an Epstein frame at 0.5 T for 50, 60, 100, 200, and

400 Hz Dividing equation (1) by f gives the following equation:

W i /f = Kh B1.6

Kh and Kecan thus be derived from the slope and intercept of a line connecting two points,

as shown in Fig 2 For example, Kh (50–60 Hz) indicates the value of Khderived from the

Frequency [Hz]

Ke(200–400Hz) Ke(100–200Hz)

Ke(60–100Hz)

Kh(50–60Hz) Ke(50–60Hz)

Figure 2 Derivation of K and K

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Measured Proposed Fixed at 1.0T

B [T]

Figure 3 Core loss reproduced by proposed method.

points corresponding to 50 and 60 Hz, and it is applied over the range from 50 to 60 Hz in

the calculation By repeating this operation for each level of B, tables showing the values

of Kh and Ke for various values of B and f can be constructed.

Fig 3 shows the core loss data, with the line representing measured results The circles represent values obtained by equation (1) in the proposed method, while the squares represent

values obtained by equation (1) with K h and K ederived at 1.0 T and 50–60 Hz As seen from the data, the approximation is not good enough On the other hand, the measured values are accurately reproduced by the proposed method Thus, the complex dependency

can be expressed by generating sufficient quantities of data for B and f

It is difficult to experimentally evaluate the genuine loss of the laminated steel sheets in

an actual generator because the measured loss inevitably includes the additional losses in metal parts other than the steel sheets For this reason, we compared the calculated values with the experimental results for a stator core model to verify the accuracy of the calculation The results are plotted in Fig 4 The difference between the calculated and measured values

is within 10%

0 0.5 1 1.5 2

Measured Calculated

B [T]

Figure 4 Core loss of the model core.

(6) Pole surface

Laminated steel sheet

Duct

Stator core segment

(2) Stator end structures

(3) Armature coil strand

(4) Core end

(5) Duct structures (1) Flux transition at the segment gap

Axial

Circumferential

Segment gap

Packet

(1) Flux transition at the segment gap

Figure 5 Causes of additional losses.

Additional losses

We can now calculate the additional losses, which are illustrated in Fig 5 They are calculated with a local model for each portion, because calculating the additional losses with a whole generator model would take too long during the design phase Fig 6 depicts an example

of a whole generator model for a two-pole machine, so the modeled region is half of the generator The magnetic flux levels in the local models are coordinated to match the levels in the whole generator model The local models separately account for the following portions

of the generator:

1 Flux transition at the segment gap There are gaps between two core segments in the

laminated steel sheets, so the magnetic flux transfers from one layer to another at these gaps As a result, eddy current losses due to the axial magnetic flux arise in the laminated steel sheets These losses are calculated with a local model for several layers of steel sheets

2 Stator end structures The eddy current losses in the clamping flanges and the shields

are calculated for each local model

3 Armature coil strand After calculating the magnetic flux density incoming to the

arma-ture end winding, the loss in the coil strand is calculated by a analytical formula

Clamping flange Stator core

(Laminated steel sheets)

Rotor

Shield Armature winding

Figure 6 Whole generator model.

Table 1 Specifications of turbine generators

Rating 220 MVA 170 MVA Voltage 18,000 13,200 Power factor 0.9 0.85

No of poles 2 2 Frequency 50 50 Coolant Air H 2

Core material NO GO

4 Core end The eddy current loss due to the axial magnetic flux is calculated for a local

model of this portion

5 Duct structures The eddy current loss in the duct pieces is calculated.

6 Pole surface The eddy current loss at the pole surface is calculated.

Results

Table 1 shows the specifications of the two turbine generators that we analyzed These two generators have a typical difference in their core materials: one is made of non-grain-oriented steel sheets (NO), while the other’s core is grain-oriented (GO)

Loss in laminated steel sheets The stator core of a turbine generator has cooling ducts, as shown in Fig 7 This causes the magnetic flux to concentrate at the corners of the steel sheets To consider this concentration,

we calculate the magnetic flux density of a one-packet model by using three-dimensional finite element analysis

Fig 8 shows the axial distributions of the radial magnetic flux The triangles represent the magnetic flux density in the stator teeth, while the squares represent that in the stator

Rotor

Radial

Axial

Magnetic flux

Modelled area

Packet Cooling duct

Stator Coil Teeth

Yoke

Stator core

Figure 7 Cooling ducts.

Axial

0.8 0.9 1 1.1

Axial Position

Teeth Yoke

Packet

Teeth Yoke

Center of packet Cooling duct

Radial

Figure 8 Concentration of magnetic flux at duct area.

yoke The magnetic flux density in the yoke is constant in the region from the duct side to the center of the packet On the other hand, the magnetic flux density in the teeth at the end

is about 5% larger than that at the center The eddy current loss due to the axial magnetic flux is calculated by using another model with finer elements

The magnetic flux vectors and the distributions of the core loss density in the laminated steel sheets for the 220 MVA and 170 MVA machines are depicted in Figs 9 and 10, res-pectively The magnetic flux vectors are shown by the blue arrows in Figs 9(a) and 10(a)

In Figs 9(b) and 10(b), the red and blue areas represent regions of higher and lower loss density, respectively The loss density is especially high at the tooth tips in both machines It

Radial

Axial

High Low Loss density

Figure 9 Loss density in laminated steel sheets (220MVA) (a) Magnetic flux vectors (b) Distribution

of loss density

Radial Axial

High Low

Loss density

Figure 10 Loss density in laminated steel sheets (170 MVA) (a) Magnetic flux vectors (b)

Distri-bution of loss density

is also high at the inner area of the stator yoke The differences in loss distribution between the two machines are due to the different stator core materials

The loss density in the stator yoke of the 170 MVA machine is lower than that of the

220 MVA machine because its stator core material is GO steel In contrast, the loss density

at the teeth of the 170 MVA machine is higher than that of the other machine due to the properties of the electrical steel sheets

Additional losses The eddy current loss densities in the clamping plate and shield are shown in Fig 11 The red and blue areas represent high and low density, respectively The loss is concentrated at the inner area in both parts because of the concentration of the magnetic flux there The additional losses as percentages of the total core losses are shown in Fig 12 Reflect-ing the different characteristics, the percentages differ between the two generators Several

Local model

Shield

Clamping flange

Clamping flange

Shield

Whole generator model

Figure 11 Eddy current loss of the shield.

0 5 10 15 20 25 30 35 40 45

(6)Pole Surface (5)Duct Structures (4)Core end (3)Coil End Strand (2)End Structures (1)Segment gap

Figure 12 Calculation results of additional losses.

factors influence the additional losses, including the electrical design, the structure, and the materials

Fig 13 shows the calculation results for the total core losses The calculated losses were 88% and 96% of the measured values for the 220 MVA and 170 MVA machines, respectively In both cases, the additional losses make up a considerable part of the core losses This confirms the necessity of calculating the additional losses when estimating the total core losses of turbine generators

Conclusions

We have shown that the so-called core loss of a turbine generator includes various losses besides those produced in the laminated steel sheets of the core We have also analyzed the causes of the losses in these sheets Part of these losses can be calculated by considering the rotational field and the harmonics Another part is due to the axial flux or field concentration Additional losses result from the metal parts other than the steel sheets By considering all

of these losses, the total core losses of two different types of generators were calculated

0 20 40 60 80 100

Additional losses Laminated Steel Sheets

Figure 13 Calculated total core losses.

The differences between the calculated and measured total core losses were within 12% This technique can thus contribute to the design of highly efficient turbine generators

References

[1] K Takahashi, K Ide, M Onoda, K Hattori, M Sato, M Takahashi, “Strand Current Dis-tributions of Turbine Generator Full-Scale Model Coil”, International Conference Electrical Machines 2002 (ICEM 2002), Brugge, Belgium, August 25–28, 2002

[2] K Ide, K Hattori, K Takahashi, K Kobashi, T Watanabe, “A Sophisticated Maximum Capacity Analysis for Large Turbine Generators Considering Limitation of Temperature”, International Electrical Machines and Drives Conference 2003 (IEMDC 2003), June 1–4, 2003, Madison, Wi

[3] K Hattori, K Ide, K Takahashi, K Kobashi, H Okabe, T Watanabe, “Performance Assessment Study of a 250MVA Air-Cooled Turbo Generator”, International Electrical Machines and Drives Conference 2003 (IEMDC 2003), June 1–4, 2003, Madison, Wi

[4] K Yamazaki, “Stray Load Loss Analysis of Induction Motors Due to Harmonic Electromagnetic Fields of Stator and Rotor”, International Conference Electrical Machines 2002 (ICEM 2002), Brugge, Belgium, August 25–28, 2002

[5] G Bertotti, General properties of power losses in soft ferromagnetic materials, IEEE Trans Magn., Vol 24, pp 621–630, 1988

[6] P Beckley, Modern steels for transformers and machines, Power Eng J., Vol 13, pp 190–200, 1999

[7] J Anuszczyk, Z Gmyrek, “The Calculation of Power Losses Under Rotational Magnetization Excess Losses Including”, International Conference Electrical Machines 2002 (ICEM 2002), Brugge, Belgium, August 25–28, 2002

[8] H Domeki, Y Ishihara, C Kaido, Y Kawase, S Kitamura, T Shimomura, N Takahashi, T Yamada, K Yamazaki, Investigation of benchmark model for estimating iron loss in rotating machine, IEEE Trans Magn., Vol 40, pp 794–797, 2004

[9] C.P Steinmetz, On the law of hysteresis, AIEE Trans., Vol 9, 1892, pp 3–64 Reprinted under

the title “A Steinmetz contribution to the AC power revolution” introduced by J.E Brittain, Proc IEEE, Vol 72, pp 196–221, 1984