I-1. CORE LOSS IN TURBINE GENERATORS: ANALYSIS OF NO-LOAD CORE LOSS BY 3D MAGNETIC FIELD CALCULATION A. Nakahara 1 , K. Takahashi 1 ,K.Ide 1 , J. Kaneda 1 , K. Hattori 2 , T. Watanabe 2 ,H.Mogi 3 , C. Kaido 3 , E. Minematsu 4 , and K. Hanzawa 5 1 Hitachi Research Laboratory, Hitachi, Ltd., 7-1-1, Omikacho, Hitachi, Ibaraki 319-1292, Japan anakaha@gm.hrl.hitachi.co.jp, takahiko@gm.hrl.hitachi.co.jp 2 Hitachi 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 3 Steel Research Laboratories, Nippon Steel Corp., 20-1, Shintomi, Futtsu, Chiba 293-8511, Japan mogi@re.nsc.co.jp 4 Flat Products Division, Nippon Steel Corp., 6-3, Otemachi, 2-chome, Chiyoda-ku, Tokyo 100-8071, Japan 5 Yawata 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. C 2006 Springer. 4 Nakahara et al. 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: W i = W h + W e = K h B α max f + K e B 2 max f 2 (1) where W i is the loss per weight of the sheets, W h and W e are the hysteresis and eddy current losses per weight, respectively, K h and K e are coefficients obtained with the Epstein frame, f is the frequency of the alternating magnetic field, and B max is 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 W h and W e are proportional to f and f 2 respectively 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 andthe B-dependency of thehysteresis 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 B 2 f 2 . The other term expresses the excess loss and is assumed proportional to B 1.5 f 1.5 . On the other hand, a method proposed to express the B-dependency of the hysteresis loss changes the values of the exponent α and of K h 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. I-1. Core Loss in Turbine Generators 5 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 0 0.5 1 1.5 2 Ke Kh 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 K e . In equation (1), we assume that α = 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 e are 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 W i is 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 = K h B 1.6 max + K e B 2 max f (2) K h and K e can thus be derived from the slope and intercept of a line connecting two points, as shown in Fig. 2. For example, K h (50–60 Hz) indicates the value of K h derived from the 0 100 200 300 400 500 Frequency [Hz] Ke(200–400Hz) Ke(100–200Hz) Ke(60–100Hz) Kh(50–60Hz) Ke(50–60Hz) Wi/f Figure 2. Derivation of K h and K e . 6 Nakahara et al. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.5 1 1.5 2 Measured Proposed Fixed at 1.0T Core Loss [W/kg] 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 K h and K e 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 representvaluesobtainedbyequation(1)intheproposedmethod,whilethesquaresrepresent values obtained by equation (1) with K h and K e derived 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 theexperimental resultsfor astatorcore modelto verify theaccuracyof thecalculation. 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 0 0.3 0.6 0.9 1.2 1.5 Measured Calculated Core Loss [W] B [T] Figure 4. Core loss of the model core. I-1. Core Loss in Turbine Generators 7 Rotor (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 Wecannowcalculatetheadditionallosses,whichareillustratedinFig.5.Theyare 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 inthe local models are coordinatedto 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. 8 Nakahara et al. 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 generatorshaveatypicaldifferenceintheircorematerials:oneis 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 toconcentrate atthe corners ofthe steelsheets. To consider thisconcentration, 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. I-1. Core Loss in Turbine Generators 9 Packet Axial 0.8 0.9 1 1.1 Axial Position Magnetic flux density [p.u.] Teeth Yoke Packet Teeth Yoke Center of packetCooling 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 (a) (b) Axial High Low Loss density Figure 9. Lossdensityin laminated steel sheets (220MVA).(a) Magneticflux vectors. (b) Distribution of loss density. 10 Nakahara et al. Radial Axial High Low Loss density (a) (b) 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 shownin 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. I-1. Core Loss in Turbine Generators 11 0 5 10 15 20 25 30 35 40 45 220MVA 170MVA Additional losses [% in total core loss] (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 andthe harmonics. Anotherpart isdue tothe axialflux orfield 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 220MVA 170MVA Core Losses [% in measured core loss] Additional losses Laminated Steel Sheets Figure 13. Calculated total core losses. 12 Nakahara et al. 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. 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Hitachi Ltd., 3- 1 -1 , Saiwaicho, Hitachi, Ibaraki 31 7-8 511, Japan kenichi hattori@pis.hitachi.co.jp, isao@keyaki.cc.u-tokai.ac.jp 3 Steel Research Laboratories, Nippon Steel Corp., 2 0-1 , Shintomi,. Futtsu, Chiba 29 3- 8 511, Japan mogi@re.nsc.co.jp 4 Flat Products Division, Nippon Steel Corp., 6 -3 , Otemachi, 2-chome, Chiyoda-ku, Tokyo 10 0-8 071, Japan 5 Yawata Works, Nippon Steel Corp., 1-1 , Tobihatacho,. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 3 12. C 2006 Springer. 4 Nakahara et al. This paper presents an analysis of the core losses under no-load conditions in turbine generators