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EMTS10_1_34

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  1. Changiz Rashidzadeh and Dr. Robert W. Cox An Effective Method for Improving Efficiency in Two-Pole AC Induction Machines two-pole machines, such distributions are not used because it is difficult to implement windings with coil spans larger than 2/3 of a pole pitch (Alger 1970). This paper proposes a new and technically feasible approach for reducing the belt harmonics in two-pole machines. ABSTRACT It is difficult to significantly reduce the space harmonics of order 5 and 7 in two-pole AC windings. This paper demonstrates a new method for solving this problem using broader phase groups with multiple winding layers. The approach is demonstrated in both a low-power induction machine with concentric windings and in a high-power machine with double-layer lap windings. In both cases, the space harmonics of order 5 and 7 are reduced by approximately a factor of four. The paper begins by considering the nature of the magneto-motive force (MMF) wave produced by a three-phase armature winding. It discusses typical coil spans for double-layer windings, and shows why these spans are difficult to use in two- pole machines. Subsequently, the paper considers how to improve the MMF waveform in low- power machines with concentric windings. It then shows an approach that improves the MMF waveform in a machine with double-layer lap windings. The paper concludes with a discussion of the proposed technique. INTRODUCTION The Secretary of the Navy has clearly stated his desire to reduce the dependence on fossil fuels. To achieve this goal, he has noted that the Navy must use energy in a more efficient manner (Cavas 2010). Given this mandate, the Navy will need to carefully consider the efficiency of new and existing electrical loads. Since motor-driven devices represent a significant portion of the overall electrical power demand on a warship, motor efficiency is of paramount importance. This paper describes a method for improving the efficiency of two-pole induction machines. THREE-PHASE ARMATURE WINDINGS Ideally, the air-gap MMF wave produced by a three-phase armature sinusoidally distributed in space (Veinott 1959 and Fitzgerald et al. 2003). In practice, the actual MMF wave can be resolved into a fundamental sine wave plus a number of harmonics. A primary goal for the design engineer is to create a distributed three-phase armature winding that minimizes the higher-order harmonics of the fundamental so that the actual MMF approximates a sinusoid (Veinott 1959 and Fitzgerald et al. 2003). These so-called space harmonics produced by the stator create rotating fields that induce secondary currents and hence produce unwanted torques. These harmonic fields can be considered as separate low-power motors that are direct- coupled to the same shaft as the fundamental and electrically connected in series with it. The torques produced by these fields create stray load losses and increase motor heating (Alger 1970 and Agarwal 1960). winding would be Two-pole induction motors are used in many shipboard applications. One factor that reduces the efficiency of these devices is the existence of higher order space harmonics resulting from non- ideal winding patterns. Of particular interest are the so-called belt harmonics of order 5, 7, 11, 13, etc. Their presence increases temperature, reduces efficiency, increases reactance, and increases the number of unwanted harmonic currents present in the power system (Alger 1970 and Veinott 1959). Typically, these space harmonics are reduced by controlling the pitch of the machine’s armature windings. In machines with four or more poles, for instance, it is common to reduce these harmonics using windings that span 5/6 of a single pole pitch. In

  2. The most significant harmonics produced by balanced three-phase machines are the so-called belt harmonics. With a single concentrated full- pitched coil, these harmonics are the higher-order terms in the series ∑ = 1 n where p is the number of pole pairs and the upper sign holds for n = 1, 7, 13, etc., the lower sign holds for n = 5, 11, etc., and all other terms are zero (Kirtley 2003 and Alger 1970). Several methods are used to reduce the amplitudes Fnof these harmonic waveforms, and the exact approach employed depends on the type of winding. In motors with concentric windings, belt harmonics are typically mitigated by placing a different number of turns in each slot in a phase group, thus attempting to approximate a sinusoidal winding distribution (Veinott 1959). This technique is most commonly used in small, low-power machines. In medium to large machines, it is much more practical to use double- layer lap or wave windings in which two form- wound coils are placed in the same slot. With these double-layer windings, one can reduce belt harmonics by using coil spans that are less than a single pole pitch (Alger 1970). When windings are distributed in several slots, the rotating MMF is of the form ∑ = 1 n where the coefficients kbn and kpn are known respectively as the breadth and pitch factors at the n-th harmonic. These quantities describe the attenuations provided by windings that are short- pitched and distributed in several locations along the periphery of the stator. Often these two values are reported as a single winding factor of the form wn k k = By definition, the winding factor is the ratio of the MMF produced by the actual winding to the MMF that would have been produced by a single full- pitched, concentrated winding with the same number of turns (Kirtley 2003). The pitch factor accounts for the effect of short-pitched coils, and the breadth factor accounts for the distribution of phase windings over several slots. For a winding with a pitch angle α, π n α n (4) ⎛ ⎞ ⎛ ⎞ = ⎜⎝ ⎟⎠ ⎜⎝ ⎟⎠ sin sin kpn . 2 2 Similarly, for a winding consisting of m coils in slots separated by an angle γ, (1) ∞ (5) γ ( ), ⎛ ⎞ nm = θ m ω MMF F sin np t ⎜⎝ ⎟⎠ sin . n 2 n = kbn γ ⎛ ⎞ ⎜⎝ ⎟⎠ sin m 2 In double layer windings, it is possible to use short-pitching to completely cancel certain harmonics. For instance, if one uses a coil pitch ⎛ − = α (6) ⎞ n 1⎟⎠ o ⎜⎝ 180 , n the pitch factor becomes ( ) π − 2 π n (7) ⎛ ⎞ ⎛ ⎞ 1 n = ⎜⎝ ⎟⎠ ⎜⎝ ⎟⎠ sin sin kpn . 2 Since we are considering only odd harmonics, the rightmost sine term in Eq. 7 will always be zero. Thus, if we want to cancel the 5th harmonic, we should use a coil span equal to 4/5ths of a pole pitch, and if we want to cancel the seventh harmonic, we should use a span that is 6/7ths of a pole pitch. The common compromise is to use a 5/6ths pitch. This choice equally reduces the amount of 5th and 7th harmonics, and is commonly used in most machines with four or more poles (Alger 1970). In two-pole machines, it is difficult to achieve a 5/6 winding pitch. Such a coil would have to physically span 150 degrees. Not only is such a machine difficult to manufacture, but a winding with such long end turns would have large leakage reactance and considerable resistance. In practice, two-pole machines are thus made with shorter pitches. Even still, about 55 to 75% of the stator resistance in a typical two-pole machine is the result of the end turns (Melfi 1995). With the sub-optimal coil spans used in most two-pole machines, the winding factors at the various belt harmonics tend to be higher and the losses caused by these waveforms tend to increase. Remedies for these effects are examined in the following two sections. (2) ∞ ( ) = θ m ω MMF k k F sin np t , bn pn n (3) k . bn pn

  3. IMPROVING MMF WAVEFORMS IN TWO-POLE MACHINES WITH CONCENTRIC WINDINGS In small three-phase machines with low power ratings, it is common to use what are known as concentric windings. In this design, coil groups of different spans are wrapped concentrically around a single pole. These are single-layer windings with only one coil in any individual slot. In machines with these windings, each coil in a given phase group has a different span than the others. The coils do, however, have a common center axis (Veinott 1959). The MMF produced by concentric windings can be improved by placing a different number of turns in each slot. This section considers a typical winding pattern for a two-pole machine with concentric windings. It also demonstrates an improved arrangement. Figure 1: Developed diagram for the two-pole, 24-slot machine with concentric windings. Only connections for phase A are shown. Current directions are noted. Figure 2: MMF produced by placing a DC current into phase A of the machine described in Fig. 1. To quantify the effectiveness of this winding pattern, it is best to determine its winding factors. As noted previously, each coil in a concentric winding has a different pitch but all of them have a common center axis. A close look at the meaning of breadth factor shows that it really accounts for the fact that each coil in a phase winding with multiple coils may link a flux that is slightly out-of-phase with that linked by the others (Kirtley 2003). Since each coil in a concentric winding is wound around a common center, each links an in-phase flux and there is no breadth factor to consider. Each individual coil, however, has a different pitch, and thus has its own individual pitch factor. For two of the four windings, the coil pitch is 135 degrees, and for the other two it is 165 degrees. The overall pitch factor at harmonic number n is thus the average of the pitch factors for the four coils, i.e. ⎡ ⎟⎠ 2 4 Traditional Concentric Two-Pole Winding Consider a two-pole, three-phase machine with 24 stator slots. In this machine, each phase group consists of four coils, two of which span 9 slots and two of which span 11 slots. Figure 1 is a developed diagram of this machine showing only the phase A connections. This arrangement is very typical in machines with concentric windings. Figure 2 shows the MMF produced by placing a DC current into this winding. Note that there are discrete steps at the locations where there is current. The production of this staircase- like waveform is the primary benefit of the concentric winding. With only one full-pitched coil, the waveform would have been square and the harmonics would have been considerably more significant. The use of appropriately placed multiple coils reduces harmonic content. (8) ⎛ ⎞ π o ⎛ ⎞ 1 135 n ⎜⎜ ⎝ ⎟⎟ ⎠ = ⎜⎝ 2 sin sin k n ⎢ ⎣ wn 2 . ⎤ ⎛ ⎞ π o ⎛ ⎞ 165 n ⎜⎜ ⎝ ⎟⎟ ⎠ + ⎜⎝ ⎟⎠ 2 sin sin n ⎥ ⎦ 2 2 Table 1 shows the magnitude of this winding

  4. The MMF produced by a DC current in this new winding is shown in Fig. 4. Note that the steps in the waveform are twice as large at the locations where there are two times as many turns of wire. It is clear from a visual inspection that this waveform is closer to sinusoidal than the MMF shown in Fig. 2. factor at the fundamental and several of its relevant harmonics. Although these winding factors provide attenuation, they can be reduced even further if one considers a different winding approach. Table 1: Magnitudes of the winding factors obtained from Eq. 8 for several low-order harmonics. kw1 0.957662 kw5 0.205335 kw7 0.157559 kw11 0.126079 kw13 0.126079 Modified Concentric Two-Pole Winding One way to improve the winding pattern shown above is to increase the number of coils in each phase group and to modify the number of turns in each coil. Figure 3 shows a developed diagram for one possible modified winding. In this case, each phase group consists of 6 coils, each having a different pitch. The two innermost coils have two times as many turns as the four outermost coils. To implement this, the two innermost coils would likely fill an entire slot, whereas the outermost coils would fill only half a slot and share the remainder with a coil from another phase. This is now effectively a double-layer coil. Later, we will show how this same effect could be implemented using a two-layer lap winding with 5/6 pitch. Figure 4: MMF produced by placing a DC current into phase A of the machine described in Fig. 3. The winding factors for this modified arrangement are once again computed by averaging the pitch factor for each of the individual coils. In this case, we must compute a weighted average, however, as two of the coils have twice the number of turns. The winding factor at the n-th harmonic is thus ⎡ ⎟⎠ 2 4 (9) ⎛ ⎞ π o ⎛ ⎞ 1 165 n ⎜⎜ ⎝ ⎟⎟ ⎠ = ⎜⎝ 2 sin sin k n ⎢ ⎣ . wn 2 ⎛ ⎞ π o ⎛ ⎞ 135 n ⎜⎜ ⎝ ⎟⎟ ⎠ + ⎜⎝ ⎟⎠ sin sin n 2 2 ⎤ ⎛ ⎞ π o ⎛ ⎞ 105 n ⎜⎜ ⎝ ⎟⎟ ⎠ + ⎜⎝ ⎟⎠ sin sin n ⎥ ⎦ 2 2 Table 2 shows the magnitude of this winding factor at the fundamental and several of its relevant harmonics. Note the significant change at the two dominant harmonics, namely the 5th and the 7th. With the new winding pattern, these harmonics are approximately a factor of four smaller than they were when using the original approach. Such a drastic change would significantly reduce losses and other deleterious effects introduced by the MMF waveforms at these frequencies. Figure 3: Developed diagram for the two-pole, 24-slot machine with modified concentric windings. Only connections for phase A are shown. Two lines are drawn for two of the coils to denote the fact that they carry twice as many turns as the others. Current directions are noted.

  5. Traditional Double-Layer Two-Pole Lap Winding Consider a two-pole, three-phase machine with 36 stator slots. This is a relatively common device. In such a machine, a single pole pitch is 18 slots, or one half of the total number. As described above, the favorable coil span would be 5/6 of a pole pitch. To achieve this, each coil would need to span 15 slots. Since such a large span is difficult to manufacture and produces undesirable effects, a shorter span is usually selected. In this case, the span is 2/3 of a pole pitch, which corresponds to 12 slots. A developed diagram showing only the connections of the windings in phase A is presented in Fig. 5. Note that we have used phase groups consisting of coils placed in 6 consecutive slots. The angle between individual slots is 10 degrees, so that each coil spans an angle α = 120 degrees. The corresponding MMF produced by a DC current in this winding is shown in Fig. 6. Table 2: Magnitudes of the winding factors obtained from Eq. 9 for several low-order harmonics. kw1 0.925031 kw5 0.053145 kw7 0.040779 kw11 0.121783 kw13 0.121783 Discussion Harmonics are reduced when using the modified winding pattern proposed here because of the shift from a single layer to two layers. Multi-layer concentric arrangements, however, are not normally used in practice. Double-layer concentric designs can be implemented, and there are examples in the patent literature (Mochizuki et al. 1999). In large machines with high power ratings, this approach would not be very practical, as the end-turns of each coil are longer than those required by a comparable lap winding (Alger 1970). The fundamental concept demonstrated in this example, however, can be extended to larger machines. The next section discusses this issue in more detail. Figure 5: Developed diagram for the two-pole, 36-slot machine with double-layer windings. Only connections for phase A are shown. Current directions are noted. Because the coils in each phase of this machine are not wound on a common center, the flux linking each is out-of-phase with the flux linking the others. Thus, this winding has both a pitch factor and a breadth factor. Equation 4 shows that the pitch factor at the n-th harmonic is IMPROVED TWO-POLE WINDING PATTERNS WITH DOUBLE-LAYER WINDINGS In large machines with considerable output power, double-layer lap windings are extremely common. When using these, the lengths of the end-turns tend to be smaller and the exposed surface area tends to be greater. As a result, there is lower loss and improved heat rejection (Alger 1970). The benefits of such windings tend to be reduced in two-pole machines where the required length of the end turns is still considerable. Here, we examine how the approach from the previous section can be extended to include double-layer lap windings. Once again, the analysis is performed using a specific example. (10) ⎛ ⎞ π o ⎛ ⎞ 120 n n ⎜⎜ ⎝ ⎟⎟ ⎠ = ⎜⎝ ⎟⎠ sin sin k , pn 2 2 and Eq. 5 shows that the breadth factor is ( ) (11) . × o sin 3 10 n = k bn ⎛ ⎞ o 10 n ⎜⎜ ⎝ ⎟⎟ ⎠ 6 sin 2 The overall winding factor at each harmonic

  6. frequency is thus the product of Eqs. 10 and 11. Table 3 shows the magnitude of this quantity at the fundamental and at the first several belt harmonics. Note that kw5 and kw7 are relatively large in comparison to kw1. As a result, the effects of the 5th and 7th space harmonics in this machine will be relatively significant. number of turns as before and another six coils with half the number of turns as before. Figure 8 shows the current distribution when a DC current is passed through phase A. The larger circles in that figure denote locations where there are more turns, and the open circles denote slots that do not have any phase A windings. The resulting MMF is shown in Fig. 9. Clearly, this waveform is much closer to sinusoidal than it was in the previous case. Figure 7: Developed diagram showing how the modified phase A winding should be inserted into the two-pole, 36-slot machine. Note that the two sets of lap windings are offset by 3 slots, and that each coil has half the number of turns as in Fig. 5. Figure 6: MMF produced by placing a DC current into phase A of the machine described in Fig. 5. Table 3: Magnitudes of the winding factors obtained from Eqs. 10 and 11 for several low-order harmonics. kw1 0.828044 kw5 0.170766 kw7 0.125822 Figure 8: Developed diagram showing the current distribution with the windings presented in Fig. 7. Enclosed dots denote current flowing out of the page, enclosed crosses denote current flowing into the page, and open circles denote slots with no current. Larger circles are used to indicate slots in which there are two times as many turns. kw11 0.088102 kw13 0.079629 Modified Double-Layer Two-Pole Lap Winding As was done in the case of the concentric winding, we can also reduce the harmonic content produced by the lap winding by adding layers and further spreading each phase group. To do so, we construct each phase using two different sets of lap windings, each spanning 120 degrees as before. The two sets of windings are offset from each other by 3 slots. Figure 7 shows how these windings are inserted into the machine. Note that each individual coil is comprised of half the number of turns used previously. The end result is that each pole face has nine coils with the same Figure 9: MMF produced by the current distribution shown in Fig. 8. The use of this new winding pattern significantly

  7. reduces the winding factors. To determine these quantities, it is best to separately consider each set of lap windings shown in Fig. 7. The overall winding factor can then be determined from the vector sum of the factors for each of the individual lap windings. The lowermost lap winding shown in Fig. 7 is positioned the same as the one in the original machine. Each coil in this new winding, however, has half the number of turns as the original. Thus, the factor for the lowermost winding is wn wn k = Comparing these results with those shown in Table 3, it is clear that there has been a significant reduction in the amplitudes of the 5th and 7th harmonic terms. This reduction would alleviate the deleterious effects caused by these higher order waveforms. Table 4: Magnitudes of the winding factors obtained from Eq. 16 for several low-order harmonics. kw1 0.799829 kw5 0.044197 kw7 0.032565 (12) k , old kw11 0.0851 , 1 , 2 kw13 0.076916 where kwn,old is the value determined for the original machine at the n-th harmonic. Since the uppermost lap winding in Fig. 7 is identical, its winding factor, kwn,2, is also kwn,old/2. To determine the overall winding factor, we note that the two individual windings produce MMFs with the same amplitude but a 30 degree spatial phase shift. At any given harmonic, the winding factor is thus the amplitude of the following sum Discussion One issue that arises in this case is that the modified machine has four-layer windings. Although this arrangement is atypical, it is not infeasible. Several implementation strategies could be considered. A careful observation of Fig. 7 shows that no one individual slot contains coils from more than two phases. Similarly, no individual slot has more than two coils from any one phase. Thus, slots containing four coils could be arranged as shown in Fig. 10. It is possible that the slot size would need to be modified, but not drastically. This issue is currently under investigation by the authors. ( θ )) (13) θ + + o k sin( n ) k sin( n 30 . wn 1 , wn 2 , Since kwn,1 =kwn,2, the amplitude of this waveform is 30 cos( 1 ( 1 , wn wn n k k + = (14) + o 2 2 o . )) sin ( n 30 ) Substituting Eq. 12 into Eq. 14, we find that (15) k . wn , orig = + + o 2 2 o k 1 ( cos( 30 n )) sin ( 30 n ) wn 2 After a series of trigonometric manipulations, this can be simplified to (16) o 30 n Figure 10: A slot containing four coils sides. This approach maintains the fundamental double-layer winding pattern. Other approaches could be considered. CONCLUSION . = k k cos( ) wn wn , orig 2 The final result in Eq. 16 shows that the magnitude of each harmonic produced by this new winding is reduced by a factor related to the cosine of half of the offset between the two lap windings. This fact is discussed in more detail below. Table 4 shows the magnitude of kwn at the fundamental and several It is interesting to note that there is a general form for the winding-factor reductions presented in both the concentric winding case and in the lap belt harmonics.

  8. prototype machine. With this technique, belt harmonics could be reduced to near negligible values, thus leading to machines with higher efficiencies, higher power factors, and lower temperature rises. winding case. For instance, the MMF produced by the modified concentric winding presented in Fig. 3 could have been produced using two lap windings, each having a 5/6 pitch. The required arrangement is shown in Fig. 11. Note the 30 degree phase offset between the two sets of windings. A careful analysis such as the one in the previous section shows that the combination of these two lap windings again leads to a reduction factor of the form REFERENCES Agarwal, P. 1960. Equivalent circuits and performance calculations of canned motors. AIEE Transactions. 79(3): 635-42. Alger, P. 1970. Induction Machines: Their Behavior and Uses, New York: Gordon and Breach. Cavas, C. 2010. Ray Mabus: US Navy Secretary. Article in DefenseNews, 11 January. Fitzgerald, A. C. Kingsley, S. Umans. 2003. Electric Machinery. New York: McGraw-Hill. Kirtley, J. 2003. Winding inductances. Note from MIT Course 6.685. MIT. Cambridge, MA. Melfi, M. 1995. Optimum pole configuration of AC induction motors used on adjustable frequency power supplies. In Record of Conf. Papers for Petroleum and Chemical Industry Conference. IEEE. September, Denver, CO. Mochizuki, M. and T. Kawamura. 1999. Method of making armature winding of double-layer concentric-wound or lap-winding type for dynamoelectric machine. U.S. Patent No. 5,898, 251. Veinott, C. 1959. Theory and Design of Small Induction Machines. New York: McGraw-Hill. cos(δ (17) n , ) 2 where δ is the offset between the two lap windings. If one multiplies the values in Table 1 by this factor, then one obtains the values in Table 2. Note that this is the same reduction factor that occurred in the case of the 36-slot machine. This result applies more generally to other similar machines, and it is a product of the proposed winding arrangement. Figure 11: Developed diagram showing how the modified concentric winding in Fig. 3 could be created using two lap windings offset by 30 degrees. The winding approach discussed in this paper could be used to reduce space harmonics in any machine, regardless of the number of poles. Furthermore, it could be extended to more layers if needed. The primary limitations are imposed by insulation requirements and the design of the stator core. Changiz Rashidzadeh was born in Iran on Jan. 11, 1965. He graduated from the University of Tabriz, Iran, in 1988. His employment experience includes Moto-Gen Co. Industries in Tabriz, Iran. Currently, he is an Electric Motor Design Engineer at Baldor Electric in King’s Mountain, NC. and Navid-Motor The authors continue to investigate the method described here, and they soon plan to construct a

  9. Charlotte. His research is focused on the design, analysis, and maintenance of electrical actuators, power-electronic drives, analog instruments, and sensors. Dr. Robert Cox received the S.B., M.Eng., and Ph.D. degrees from the Massachusetts Institute of Technology (MIT) in 2001, 2002, and 2006, respectively. He is currently Assistant Professor of Electrical and Computer Engineering at UNC

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