CN210429528U - Coreless transformer based on secondary side series fractional order circuit - Google Patents
Coreless transformer based on secondary side series fractional order circuit Download PDFInfo
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- CN210429528U CN210429528U CN201921157978.3U CN201921157978U CN210429528U CN 210429528 U CN210429528 U CN 210429528U CN 201921157978 U CN201921157978 U CN 201921157978U CN 210429528 U CN210429528 U CN 210429528U
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Abstract
The utility model discloses a coreless transformer based on a secondary side series fractional order circuit, which comprises a primary side loop and a secondary side loop; the primary side loop comprises a primary side fractional order capacitor with the order larger than 1 and a primary side coil with internal resistance, and the primary side fractional order capacitor and the primary side coil are connected in series; the secondary side loop comprises a secondary side coil with internal resistance, a secondary side fractional order capacitor and a load, and the secondary side coil, the secondary side fractional order capacitor and the load are connected in series; and a transformer core is not arranged between the primary side coil and the secondary side coil. The utility model discloses utilize the order to be greater than 1 once side fractional order electric capacity and provide the energy for transformer load, simultaneously when the order is fixed the operating frequency and the appearance value of once side fractional order electric capacity can follow no iron core transformer parameter variation automatically to realize no iron core transformer and can both keep high efficiency high power work under the load of different power factors, solved traditional transformer heavy, problem with high costs.
Description
Technical Field
The utility model belongs to the technical field of the technique of transformer and specifically relates to indicate a no iron core transformer based on secondary side tandem type fractional order circuit.
Background
In 1831, faraday utility model, called "faraday induction coil", was the first elementary transformer in the world, in 1885, the west house company engineers william stanza made the first practical transformer, after which the transformer began to be an extremely versatile power device, mainly used for power transmission, voltage conversion and insulation. The conventional transformer is a device for changing an ac voltage based on the principle of electromagnetic induction, and mainly includes a primary coil, a secondary coil, and an iron core (magnetic core), where the primary coil and the secondary coil are coupled via the iron core. The iron core has the function of strengthening the magnetic coupling between the two coils, so that the transformer realizes efficient power transmission. However, the conventional transformer has high cost and heavy weight due to the existence of the iron core. In order to remove the iron core of the transformer, numerous scholars at home and abroad begin to research the construction technology of the iron-core-free transformer, however, most of the existing iron-core-free transformers only realize high-efficiency electric energy transmission by simply increasing the frequency or can only work at high efficiency and high power under resistive load.
SUMMERY OF THE UTILITY MODEL
An object of the utility model is to overcome prior art's shortcoming and not enough, provide a no iron core transformer based on secondary side series connection type fractional order circuit, utilize fractional order circuit to realize a transformer that need not the iron core, can replace the transformer that the tradition has the iron core, make transformer reduce cost and weight become for probably. The primary side fractional order capacitor with the order greater than 1 is used for providing energy for a transformer load, and meanwhile, when the order is fixed, the working frequency and the capacitance value of the primary side fractional order capacitor can automatically follow the parameter change of the coreless transformer, so that the coreless transformer can keep high-efficiency and high-power work under loads with different power factors, and the problems of large weight and high cost of the traditional transformer are solved.
In order to achieve the above object, the present invention provides a technical solution: a coreless transformer based on a secondary side series fractional order circuit comprises a primary side loop and a secondary side loop; the primary side loop comprises a primary side fractional order capacitor with the order greater than 1 and a primary side coil with internal resistance, and the primary side fractional order capacitor and the primary side coil are connected in series; the secondary side loop comprises a secondary side coil with internal resistance, a secondary side fractional order capacitor and a load, and the secondary side coil, the secondary side fractional order capacitor and the load are connected in series; a transformer core is not arranged between the primary side coil and the secondary side coil;
the primary side fractional order capacitor with the order greater than 1 has the property of negative resistance, can provide energy for the transformer, and has two working modes: firstly, the order of the capacitor is constant, and the working frequency and the capacitance value automatically change along with the parameters of the coreless transformer so as to keep the capacitor to work stably; secondly, the working frequency is fixed, and the order and the capacitance value automatically follow the parameter change of the coreless transformer so as to keep the capacitor to work stably.
Further, the differential relation between the voltage and the current of the primary-side fractional order capacitor and the secondary-side fractional order capacitor satisfies:
the phase relation satisfies
Wherein iCIs a fractional order of the capacitor current, vCIs the fractional order of the capacitor voltage, α is the fractional order of the capacitor, CαIs the fractional order capacitance value, and the order of the first-side fractional order capacitance is 1 < α1< 2, the order of the secondary side fractional order capacitor is 0 < α2≤2。
Further, the capacitance value and the order of the secondary side fractional order capacitor are fixed.
Compared with the prior art, the utility model, have following advantage and beneficial effect:
1. the utility model discloses a transformer need not the iron core, simple structure.
2. Compared with the traditional transformer, the weight is greatly reduced.
3. Under different power factor loads, the transformer can still keep high-efficiency and high-power operation.
Drawings
Fig. 1 is a model diagram of the coreless transformer of the present invention in an embodiment.
Fig. 2 is a graph of efficiency versus load for a coreless transformer in an embodiment.
Fig. 3 is a graph of output power versus load for a coreless transformer in an embodiment.
Detailed Description
To further illustrate the aspects and features of the present invention, the following detailed description of the embodiments of the present invention is provided in conjunction with the accompanying drawings, but the invention is not limited thereto.
As shown in fig. 1, the coreless transformer based on the secondary side series fractional order circuit provided in the present embodiment includes a primary side loop and a secondary side loop; the primary side loop comprises a primary side fractional order capacitor C with the order greater than 1α1And with an internal resistance R1Primary side coil L of1The primary side fractional order capacitance Cα1And a primary side coil L1Are connected in series; the secondary side loop comprises a secondary side loop with an internal resistance R2Secondary side coil L of2Secondary side fractional order capacitor Cα2And a load RLThe secondary side coil L2Secondary side fractional order capacitor Cα2And a load RLAre connected in series; the primary side coil L1And a secondary side coil L2The transformer iron core is not arranged between the two parts; wherein, the order is greater than the first side fractional order capacitance C of 1α1Having the property of negative resistance, being the load R of the transformerLProviding energy.
The primary side fractional order capacitor with the order greater than 1 in the embodiment has the characteristic of constant apparent power, and has two working modes: firstly, the order of a capacitor is constant, and the working frequency and the capacitance value automatically change along with the parameters of the coreless transformer; secondly, the working frequency is fixed, and the order and the capacitance value automatically follow the parameter change of the coreless transformer.
According to the coupled mode theory, the coupled mode equation of the coreless transformer shown in fig. 1 is:
in the formula, g1、τ2The gain of the primary side loop and the loss of the secondary side circuit, and g1＝-(τCa1+τL1)，τ2＝τCa2+τL2+τRLIn which τ isCa1、τL1、τCa2、τL2、τRLThe loss rates of the elements of the coreless transformer are respectively,
where k is the mutual inductance coupling coefficient, ω, of the primary and secondary side coils1,ω2The resonant angular frequencies of the primary side loop and the secondary side loop respectively are expressed as follows:
the specific expression of the loss rate of each element is as follows:
the condition that the iron core-free transformer has the steady state solution can be obtained by the formula (1) as follows:
further, the compounds represented by the formulae (1) and (8)
The efficiency of the available coreless transformer is generally expressed as:
the output power of the coreless transformer is generally expressed as follows:
wherein:
in the formula, VCa1Is the effective value of the fractional order capacitor voltage.
From equation (1), the operating frequency of the coreless transformer is solved as follows:
when the primary-side fractional order capacitor works in the fixed order mode, let α1＝α0Is constant, therefore, the load resistance loss coefficient of the coreless transformer obtained by the above formula when the order of the primary side fractional order capacitor is fixed needs to satisfy:
τRL_Cis the critical operating point of a coreless transformer. When tau isRL＞＝τRL_CTime, primary sideThe fractional order capacitor can not work in the order fixed mode, otherwise, the primary side fractional order capacitor can not work stably without working frequency solution, so the primary side fractional order capacitor is automatically switched to the working frequency fixed mode, namely, omega is omega2。
When the primary-side fractional order capacitor operates in a fixed order mode, it can be obtained from equations (10) - (14)
The transmission efficiency is:
the output power is approximately:
wherein S isCa1Is the apparent power, Q, of the primary-side fractional order capacitorLTIs the quality factor of the primary side loop. Therefore, according to the formula, the transmission efficiency and the output power of the coreless transformer are independent of the mutual inductance and the secondary side resonance frequency, namely, the transmission efficiency and the output power of the coreless transformer are not influenced by the power factor of the load.
When the primary-side fractional order capacitor works in the fixed working frequency mode, the transmission efficiency and the output power of the coreless transformer obtained by the equations (9) - (14) are respectively:
the parameters of the transformer without the iron core are set as follows: l is1＝L250 muH, secondary side fractional order capacitance order α21, coupling coefficient k 0.25, secondary side rated resonance frequencyRate of omega 202 pi x 80kHz, internal resistance R1＝R20.06, the order of the first order fractional order capacitor is chosen to be α0＝1.07，SCα15000 a; the critical load can be obtained as RL14.3 Ω. Therefore, the relationship curves of the transmission efficiency, the output power and the load of the coreless transformer can be obtained as shown in fig. 2 and fig. 3, respectively. As can be seen from fig. 2 and 3, the coreless transformer has a constant transmission efficiency and output power in the operating range.
According to the above analysis, the utility model discloses a no iron core transformer based on secondary side series connection fractional order circuit, in the load scope of design, no matter be the change of load or secondary side resonant frequency's skew, no iron core transformer can all realize the invariable efficient transmission of efficiency and output, and this and traditional no iron core transformer exist than difference, the utility model discloses no iron core transformer's advantage is obvious, is worth promoting.
The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be equivalent replacement modes, and all are included in the scope of the present invention.
Claims (3)
1. A no iron core transformer based on secondary side series connection type fractional order circuit which characterized in that: comprises a primary side loop and a secondary side loop; the primary side loop comprises a primary side fractional order capacitor (C) with order greater than 1α1) And with internal resistance (R)1) Primary side coil (L)1) The primary side fractional order capacitance (C)α1) And a primary side coil (L)1) Are connected in series; the secondary side loop comprises a secondary side loop with an internal resistance (R)2) Secondary side coil (L)2) Secondary side fractional order capacitor (C)α2) And a load (R)L) The secondary side coil (L)2) Secondary side fractional order capacitor (C)α2) And a load (R)L) Are connected in series; the primary side coil (L)1) And a secondary side coil (L)2) The transformer iron core is not arranged between the two parts;
wherein the order is greater than 1, and the primary side fractional order capacitor (C)α1) Has the property of negative resistance, can provide energy for the transformer, and has two working modes: firstly, the order of the capacitor is constant, and the working frequency and the capacitance value automatically change along with the parameters of the coreless transformer so as to keep the capacitor to work stably; secondly, the working frequency is fixed, and the order and the capacitance value automatically follow the parameter change of the coreless transformer so as to keep the capacitor to work stably.
2. The coreless transformer of claim 1, wherein the secondary side series fractional order circuit based on the coreless transformer comprises: the primary side fractional order capacitance (C)α1) And a secondary side fractional order capacitor (C)α2) The voltage and current differential relation satisfies:
the phase relation satisfies
Wherein iCIs a fractional order of the capacitor current, vCIs the fractional order of the capacitor voltage, α is the fractional order of the capacitor, CαIs a fractional order capacitance value, and a primary side fractional order capacitance (C)α1) Order 1 < α1< 2, secondary side fractional order capacitance (C)α2) Order 0 < α2≤2。
3. The coreless transformer of claim 1, wherein the secondary side series fractional order circuit based on the coreless transformer comprises: the secondary side fractional order capacitance (C)α2) Is fixed.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110444379A (en) * | 2019-07-23 | 2019-11-12 | 华南理工大学 | A kind of iron-free core transformer based on secondary side tandem type fractional order circuit |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110444379A (en) * | 2019-07-23 | 2019-11-12 | 华南理工大学 | A kind of iron-free core transformer based on secondary side tandem type fractional order circuit |
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