A New Design Variant of a Transformer Controlled by Shunt Biasing
Abstract Generated abstract
This paper proposes a five-limb design for a transformer regulated by magnetic biasing of the shunt, addressing the problem of odd-harmonic electromotive forces induced in control windings and the resulting overvoltages. The design relocates the control windings to a separate central shunt limb and arranges the magnetic core and working windings so that alternating flux in the control limb cancels or contains only even-order induction changes in all operating modes. The author describes the flux distribution, regulation principle, operating ranges, feedback use for current or voltage regulation, and recommended geometric ratios for compactness or minimum weight. A prototype was manufactured and tested, and the design is presented as practical without increasing dimensions or weight relative to existing variants.
Full Text
A New Design Variant of a Transformer Regulated by Magnetic Biasing of the Shunt
V. P. OBRUSNIK
(Recommended by the scientific seminar of the Electromechanical Faculty)
At present, a large number of different designs of transformers regulated by magnetic biasing of shunts (TRMBS) are known [1, 2, etc.]. They are of definite practical interest as regulators of alternating current and voltage, and one could list a wide range of electrical regulation systems in which the TRMBS is successfully used. However, these devices are not without shortcomings, among which may be included the induction of alternating emf of odd harmonics in the control windings. This is a very serious drawback, since with a large number of turns in the control winding large overvoltages may arise in it, reaching several kilovolts or more, which is dangerous for the insulation and impermissible from the standpoint of safety engineering.
In existing TRMBS designs, in order to reduce overvoltages in the control circuits, sectioning of the biasing windings is used, with subsequent cross-connection of sections located on different legs of the shunt. Sectioning gives a certain effect, but it does not eliminate the induction of odd emf and adds considerable technologi-
Fig. 1.
...technical difficulties in manufacturing the apparatus, since each section must have two terminals and must be carefully insulated.
Fig. 2.
Figure 1 presents the new design, proposed by the author, of a five-limb transformer regulated by magnetic biasing of the shunt (TRMS), which makes it possible to eliminate completely the drawback mentioned above without resorting to sectioning of the control windings. It differs from the known designs in the shape of the magnetic core and in the arrangement of the windings. The functional circuit for connecting the windings is shown in Fig. 2.
The following designations are adopted here:
\(W_{\text{н}}, W_{\text{в}}\) — the outer and inner AC windings.
\(W_d\) — the control windings.
\(h_0\) — window height.
\(a_0, b_0\) — width and thickness of limbs 1, 2, belonging to the main magnetic core.
\(a_{\text{ш}}, b_{\text{ш}}\) — width and thickness of limbs 3, 4, 5, belonging to the magnetic core of the shunt.
\(c_0\) — window width of the main magnetic core.
\(c_{\text{ш}}\) — window width of the magnetic core of the shunt.
\(\Phi_1, \Phi_2, \Phi_3, \Phi_4\) — alternating fluxes flowing, respectively, through limbs 1, 2, 3, 4.
\(\Phi_d\) — constant biasing flux produced by the control windings.
The magnetic system of the apparatus may be imagined as consisting of two magnetic cores fused into one: the outer, main magnetic core (limbs 1, 2 and portions of the yokes) and the inner, magnetic core of the shunt (limbs 3, 4, 5 and portions of the yokes). In Fig. 1 they are conventionally separated by a dotted line.
On limbs 1, 2 of the main magnetic core there are placed coils of the AC winding \(W_{\text{в}}\), which we shall call the inner working winding. Limbs 1, 3 and 2, 4, belonging to the main magnetic core and to the magnetic shunt, together with the coils of the inner working winding located between them, are encompassed by the coils of the outer AC winding \(W_{\text{н}}\). The connection diagram for these coils is shown in Fig. 2. Both AC windings, the inner and the outer, may be assigned the name “primary” or “secondary,” depending on whether they are connected to the network or to the load.
On the middle limb of the magnetic core of the shunt, designated in Fig. 1 by the numeral 5, there is placed a coil with control windings (in the general case there may be several control windings). The width of limb 5 is twice the width of limbs 3, 4. The entire magnetic core is symmetrical with respect to the axial lines.
A distinctive feature of the proposed design is that the control windings \(W_d\) are not located on the limbs encompassed by the working windings, as is customary, but are placed separately on limb 5 specially provided for them.
The distribution of fluxes in the magnetic system of the apparatus during its operation can be represented as in Fig. 2.
If the load is disconnected, the alternating flux closes only through rods 1, 2, 3, 4, since in rod 5 it will cancel itself mutually. With the load connected and with a control signal present, in rod 5 only an even-order change in induction is possible. Thus, in all operating modes of the TRPSh, the possibility of inducing emf’s of odd harmonics in its control windings is excluded.
The flux $\Phi_d$, produced by the magnetomotive force of the control windings, closes mainly through the magnetic core of the shunt, i.e., through rods 5, 3, 4 and the yoke sections. By changing the magnitude of $\Phi_d$, it is possible to vary the constant component of the induction of this magnetic core.
Part of the total alternating magnetizing flux—$\Phi_3$ and $\Phi_4$—branching into rods 3 and 4 of the magnetic shunt, does not link with the turns of the secondary winding and does not induce an emf in it. As a result, the coupling coefficient between the working windings is less than unity. By varying, through biasing, the constant component of induction in cores 3 and 4, one can control the amount of alternating flux branching into them and, consequently, the magnitude of the secondary emf: under load from $0$ to $U_1 \dfrac{W_2}{W_1}$, and at no load from
$$ U_1 \frac{W_2}{W_1}\cdot \frac{S_0}{S_0+S_{\mathrm{sh}}} \quad \text{to} \quad U_1 \frac{W_2}{W_1}, $$
where $S_0=a_0 b_0$, $S_{\mathrm{sh}}=a_{\mathrm{sh}} b_{\mathrm{sh}}$.
The TRPSh designs proposed here and those known earlier have practically identical physics of the processes occurring in them and the same character of static and dynamic characteristics. The parameters of the proposed TRPSh can be calculated using the literature [1, 2, 3]. The optimal ratios of geometrical dimensions are given in Table 1.
The proposed design variant of the TRPSh was manufactured and tested by the author at the Department of Electrification of Industrial Enterprises of the Tomsk Polytechnic Institute.
In the absence of feedbacks, the apparatus can be used as a current regulator. With deep positive current feedback with coefficients $K_{\mathrm{os}}=W_{\mathrm{os}}/W_{\mathrm{n}}=1 \div 1.03$, when the feedback winding is connected in series with the outer working winding, and $K_{\mathrm{os}}=W_{\mathrm{os}}/W_{\mathrm{v}}=1 \div 1.03$, when it is connected in series with the inner working winding, the TRPSh has rigid external characteristics and possesses high sensitivity to the control signal. In this case it can be used as a voltage regulator.
The dimensions and weight of the proposed TRPSh are no greater, and in some cases smaller, than those of known designs. The most compact and convenient-to-manufacture design is obtained when the shunt cross sections are close in magnitude to the cross section of the main magnetic core, namely, when $S_{\mathrm{sh}}/S_0=1 \div 0.7$. Mathematical analysis of the optimal dimensions of the magnetic core makes it possible, for the indicated ratios $S_{\mathrm{sh}}/S_0$, to recommend the following data (see Table 1).
Table 1
| $\dfrac{h_0}{a_k}$ | $h_{\mathrm{ya}}$ | $\dfrac{c_0}{a_0}$ | $\dfrac{b_0}{a_0}$ | $b_{\mathrm{sh}}$ | $\dfrac{c_{\mathrm{sh}}}{a_0}$ | $a_{\mathrm{sh}}$ | |
|---|---|---|---|---|---|---|---|
| For minimum dimensions | 5 | $a_0+a_{\mathrm{sh}}$ | $0.45 \div 0.5$ | 2.5 | $b_0+c_0$ | $1 \div 1.2$ | $\dfrac{S_{\mathrm{sh}}}{b_{\mathrm{sh}}}$ |
| For minimum weight | 5 | $a_0+a_{\mathrm{sh}}$ | $0.8 \div 1$ | 3.0 | $b_0+c_0$ | $1.9 \div 2$ | $\dfrac{S_{\mathrm{sh}}}{b_{\mathrm{sh}}}$ |
When using the table, the cross section of the main magnetic circuit should be calculated from the expressions:
for minimum overall dimensions,
\[ S_0=\frac{10^4}{5.8a_0}\cdot \sqrt{\frac{P_1}{B_{\mathrm{to}}\cdot j\cdot k_{\mathrm{m}}\cdot k_{\mathrm{c}}}}, \]
for minimum weight,
\[ S_0=\frac{10^4}{8.4a_0}\cdot \sqrt{\frac{P_1}{B_{\mathrm{to}}\cdot j\cdot k_{\mathrm{m}}\cdot k_{\mathrm{c}}}}, \]
where: \(P_1=U_1\cdot I_{1\,\mathrm{nom}}\) [VA] is the rated power of the TRPSh;
\(B_{\mathrm{to}}\) [Gs] is the amplitude value of the induction in the main magnetic circuit when the shunts are fully saturated (chosen slightly below the knee of the main magnetization curve of cores 1, 2);
\(j\), \(k_{\mathrm{m}}\) are the averaged current density and copper fill factor for the working windings,
\[ k_{\mathrm{m}}\simeq 0.3\div 0.4,\qquad j\simeq (200\div 300); \]
\(k_{\mathrm{c}}\) is the steel fill factor.
The stacking of the magnetic circuit is the usual one for five-limb cores.
The proposed new design variant of the TRPSh may be recommended for practical application along with other TRPSh designs.
REFERENCES
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A. M. Bamdas, V. A. Somov, A. S. Shmidt. Transformers and Stabilizers Regulated by Magnetization of Shunts. Gosenergoizdat, 1959.
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A. M. Bamdas, S. V. Shapiro, O. D. Gatmaneiko. Determination of optimal designs of transformers and autotransformers regulated by magnetization, and their calculation. Transactions of the GPI named after A. A. Zhdanov, vol. XVIII, issue 1, 1962.
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V. P. Obrusnik. Determination of the parameters of TRPSh shunts optimal for a specified operating mode. Proceedings of the TPI named after S. M. Kirov, vol. 117, 1963.