On the Application of Combined Windings for Synchronous Machines
Abstract Generated abstract
This paper examines the use of combined windings in synchronous machines, especially for brushless excitation systems where the main machine and exciter can differ substantially in power. It develops relations for current density, magnetomotive force, thermal loading, copper losses, and conductor weight, noting that rectifier operation in these closed winding circuits requires a power-based relation between rms and rectified current rather than usual transfer coefficients. The analysis indicates that combined windings can save conductor material when the combined machines are of comparable power, while in generator exciter or motor exciter combinations conductor use may be higher than with separate windings. Even in such cases, the authors argue that combined windings remain useful because they improve manufacturability and reliability, reduce slot insulation, and can provide additional machine functions when designed with a high second-cascade winding factor and suitable pitch.
Full Text
On the Application of Combined Windings for Synchronous Machines
A. I. Felzing, M. L. Kostyrev, A. I. Skorospeshkin
(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)
In recent years, ever-increasing interest has been shown in so-called combined windings of electrical machines [1, 2]. A combined winding replaces several, more often two, independent windings with different numbers of pole pairs by a single winding performing the same functions as two separate windings. The machine becomes more manufacturable, the consumption of insulating material is reduced, and in a number of cases it is possible to achieve savings in conductor material as well [3, 4]. In addition, a machine with combined windings acquires a number of new properties. For example, in brushless synchronous generators the combined winding on the rotor, in addition to the basic functions of the output winding of the first cascade and the excitation winding of the second cascade, can perform the role of a damper winding, and in a single-phase generator, that of a current-feedback winding [3, 5].
An assessment of the effectiveness of combined windings used in single-machine converters when combining machines of approximately equal power is given in [3, 4]. However, the results obtained cannot be fully extended to windings for brushless excitation of synchronous machines, since in this case machines (generator and exciter, motor and exciter) that differ substantially in power are combined. Moreover, this type of combined winding differs in its mode of operation. Windings for brushless excitation of synchronous machines are closed on themselves through a rectifier, being simultaneously both a source and a consumer of electrical energy (Fig. 1).
In connection with this, it is necessary to determine the advisability of replacing two separate windings on the rotor by one combined winding for brushless excitation of a synchronous machine with both a symmetrical and an asymmetrical (single-phase) output winding.
To assess the effectiveness of replacing two separate windings by a combined one, we shall assume that the current densities in the separate windings are identical, and that the magnetomotive forces for the second cascade and the specific thermal loads of the separate and combined windings are also equal.
From the condition of equality of the specific thermal loads, the effective current density of the combined winding is determined by the expression
\[ \Delta_C=\frac{A_1\cdot \Delta_1 + A_2\cdot \Delta_2}{\sqrt{A_{1C}^{2}+A_{2C}^{2}}}, \tag{1} \]
where $A_1$, $A_2$ and $\Delta_1$, $\Delta_2$ are the linear loadings and current densities of the separate windings of the first and second stages of the machine;
$A_{1c}$, $A_{2c}$ are the linear loadings of the combined winding for the first and second stages, produced respectively by the alternating and direct components of the phase current.
Fig. 1. Combined windings for brushless excitation of synchronous machines
In conventional rectifier circuits and rectifier operation, transfer coefficients for voltage and current are used to relate rms and rectified values. In doing so, the commutation angle of the valves is often practically not taken into account. In combined windings (Fig. 1), the rectifier operates in short-circuit mode. The valves conduct current practically throughout the entire period, and therefore the usual transfer coefficients for current and voltage cannot be used in this case. The relation between the rms and rectified current in such circuits can be determined from the condition of equality of powers on the ac and dc sides. For the circuits shown in Fig. 1, if losses in the valves are neglected, we have
\[ I_{\sim}=I_{-}, \tag{2} \]
i.e., the average value of the rectified current is equal to the rms value of the steady-state three-phase short-circuit current of the first stage.
From the condition of equality of m.m.f. for the second stage, taking expression (2) into account, the effective current density of the combined winding is
\[ \Delta_c=\frac{\Delta}{\sqrt{2}\cdot K_2 \cdot C_A}, \tag{3} \]
where
\[ C_A=\frac{A_2}{A_1+A_2} \]
is a coefficient characterizing the distribution of the linear loading over the stages of a machine with separate windings combined in one magnetic core,
\[ K_2=\frac{K_{02}}{K_{0c2}}, \]
where $K_{02}$ and $K_{0c2}$ are the winding factors of the separate and combined windings with respect to the field of the second stage. In the general case, the coefficient $K_2$ may differ from unity. However, designing combined windings with $K_2>1$ is inexpedient because it worsens their utilization in the second stage. The reduction of $K_2<1$ is limited by the fact that the winding factor $K_{02}$ for synchronous machines is usually sufficiently high. Therefore, in what follows, without significant error one may take $K_2=1$.
Figure 2 gives the dependence of the relative current density of the combined winding as a function of the coefficient $C_A$, calculated from expression (3) under the condition $K_2=1$. As can be seen, when combining windings of machines comparable in power ($C_A=0.4 \div 0.7$), for example, mo-
motor—generator, \(\dfrac{\Delta_c}{\Delta} > 1\), and a saving of conductor material can be obtained, which agrees with the conclusions drawn for single-machine converters. When combining machines that differ substantially in power, \(C_A = (0.7 \div 0.95)\), for example, motor—exciter or generator—exciter, \(\dfrac{\Delta_c}{\Delta} < 1\), and the expenditure of conductor material in the combined winding is somewhat higher than in the case of separate windings.
Fig. 2. Relative current density of the combined winding
It should be noted that the effective current density determined by expression (3) corresponds to the condition of maintaining the specific thermal load. At the same time, equality of copper losses is not maintained, since the end portion of the combined winding, in comparison with one of the separate windings, is either lengthened or shortened. The effective current density of the combined winding, from the condition of equality of copper losses in a machine with separate and combined windings, is
\[ \Delta_c = \frac{ \left( l_1 \frac{1 - C_A}{C_A} + l_2 \right)\Delta }{ \sqrt{2}\,K_2 }, \tag{4} \]
where \(l_1\) and \(l_2\) are the ratios of the mean turn lengths of the sections of, respectively, the first and second separate winding to the mean turn length of a section of the combined winding.
Let us estimate the expenditure of conductor material in a machine with separate and combined windings under the condition of maintaining equality of copper losses, expressing the latter through current density and weight:
\[ \Delta_1^2 G_1 + \Delta_2^2 G_2 = \Delta_c^2 G_c. \tag{5} \]
Taking into account the equality of the current densities in the separate windings, as well as expressions (5) and (4), the ratio of the total weight of copper of the separate windings to the weight of copper of the combined winding is
\[ \frac{G}{G_c} = \left[ \frac{ l_1 - (l_1 - l_2)C_A }{ \sqrt{2}K_2 C_A } \right]^2. \tag{6} \]
In Fig. 3 the plots of \(\dfrac{G}{G_C}=f(C_A)\), calculated from expression (6) under the condition \(K_2=l_2=1\) and for various \(l_1\), are constructed.
Fig. 3. Relative weight of the combined winding
It is evident from the figure that, with the proper selection and design of a combined winding, a considerable saving of conductor material can be obtained, especially when combining the windings of machines that are approximately equal in power.
In order for the copper consumption in the combined winding for brushless excitation of synchronous machines to remain approximately at the level of the copper consumption in separate windings, combined windings should be designed with the maximum possible winding factor with respect to the field of the second cascade and with a pitch approximately equal to the pole pitch of the cascade with the larger number of poles.
On the basis of the investigations carried out, the following conclusions may be drawn:
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The combining of windings is effective from the point of view of saving conductor material when combining machines of approximately equal power, which agrees with the conclusions drawn for single-machine converters.
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When combining machines that differ substantially in power (generator—exciter, motor—exciter), the costs of conductor material in the combined winding may turn out to be higher than with separate windings; nevertheless, even in this case the use of combined windings is expedient. The design of the machine becomes more technological and reliable, the consumption of slot insulation is reduced. The machine acquires a number of new useful properties.
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Combined windings for brushless excitation of synchronous machines should be designed with the maximum possible winding factor with respect to the field of the second cascade and with a pitch approximately equal to the pole pitch of the cascade with the larger number of poles.
LITERATURE
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H. Harz. Synchronmaschine ohne Schleifringe. Patent of the FRG, cl. 21 d²1, No. 953636, 6.12.1956.
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V. N. Breev, Yu. V. Baryshnikov, A. G. Plastun. Application of combined windings in the EPS, collection “Frequency of Industrial Alternating Current and Problems of Its Optimization,” Kishinev, 1969.
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V. I. Zagryadskii. Combined electrical machines and prospects for their development. “Electric Power Engineering and Automation,” issue 5, 1969.
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A. P. Fel’zing, M. L. Kostyrev, A. I. Skorospeshkin. Calculation of the characteristics of a contactless single-phase synchronous generator of increased frequency. “Proceedings of the TPI,” vol. 212.