WO2017011932A1

WO2017011932A1 - Novel transformer

Info

Publication number: WO2017011932A1
Application number: PCT/CN2015/000746
Authority: WO
Inventors: 方志
Original assignee: 方志
Priority date: 2015-07-19
Filing date: 2015-11-02
Publication date: 2017-01-26
Also published as: CN105261460A

Abstract

A novel transformer. On the basis of a conventional transformer, an auxiliary secondary winding is added. The winding and a capacitor form a loop. In the loop, the impedance of the capacitor is greater than the inductive reactance of the winding, such that the circuit is capacitive. That is, the phase of a current is ahead of the phase of a total voltage. When a current i₀(t) passes through a primary winding, induced electromotive forces on a secondary winding and the auxiliary secondary winding are e₂(t) and e₃(t), which have the same phase. When the secondary winding and a load form a loop, a current i₂(t) and a generated magnetic induction intensity B_n2(t) lag behind the phase of e₂(t) by π/2. When the auxiliary secondary winding forms a loop, a current i₃(t) and a generated magnetic induction intensity B_n3(t) are ahead of the phase of e₃(t) by π/2, a phase difference between B_n2(t) and B_n3(t) is π, and B_n2(t) and B_n3(t) are in opposite directions. When B_n2(t) and B_n3(t) are equal in size, the sum of B_n2(t) and B_n3(t) is zero, and the two currents do not induce any windings.

Description

A new type of transformer

[Technical Field]

A new type of transformer is an improvement of existing power transformers, and the technical field belongs to electrical engineering.

【Background technique】

Usually, the AC is passed through the transformer. Although there are many kinds of waveforms of the AC, this article uses the simple harmonic AC as an example. Unlike direct current, the electromotive force, voltage, and current of an alternating current are a function of time. Like the mechanical harmonic vibration, the alternating electromotive force e(t), the alternating current voltage u(t) and the alternating current i(t) of the alternating current can be expressed by the sine function or the cosine function of the time t, taking the cosine function as an example, the alternating current The electromotive force e(t), voltage u(t) and current i(t) can be expressed as:

among them:

e ₀ is the peak value of the alternating electromotive force in volts.

u ₀ is the peak value of the AC voltage in volts.

i ₀ is the peak value of the alternating current in amps.

ω is the angular frequency of the alternating current, ω=2πf, and the unit is radians/second.

f is the frequency of the alternating current in Hertz.

t is the time in seconds.

The phase of the alternating electromotive force, in radians.

The initial phase of the alternating electromotive force, in radians.

The phase of the alternating current voltage, in radians.

The initial phase of the alternating current voltage, in radians.

The phase of the alternating current, in radians.

The initial phase of the alternating current, in radians.

In direct current, there is generally only one component of ohmic resistance, and its resistance value is the ratio of voltage to current across the resistor.

But in alternating current, in addition to ohmic resistors, there are capacitors and inductors.

Capacitor and inductive components have different properties than ohmic resistors under alternating current conditions. Their impedance is a function of ω, and the phase of the current through the component does not coincide with the phase of the voltage across the component. The ratio of the peak value of the AC voltage of the component to the peak value of the AC current passing through; the impedance of the defined circuit is the ratio of the peak value of the AC voltage of the circuit to the peak value of the AC current passing through.

In an AC circuit, the terminal voltages of different components in a series circuit have different phases, and the currents in different components of the parallel circuit have different phases, in calculating the total voltage of the combination of different components in the series circuit, or different components in the parallel circuit When the total current of the combination is used, a vector solution or a complex solution can be used. In this paper, a vector solution is used.

The following describes the characteristics of the ohmic resistor, the capacitor component, the inductor component, and some combinations in the AC circuit.

Figure 1 is a schematic diagram of a circuit consisting of an electromotive force of an alternating current and an ohmic resistor. Since the ohmic resistance is similar in the nature of the AC circuit to its DC circuit, the AC voltage u(t) at both ends and the AC current i(t) flowing through it have a simple proportional relationship, the AC voltage u(t) and the AC current i The phase of (t) remains unchanged. The alternating current i(t) flowing through the ohmic resistor and the alternating current voltage u(t) and phase relationship at both ends can be expressed by the following mathematical relationships:

among them:

u ₀ is the peak value of the AC voltage across the resistor in volts.

i ₀ is the peak value of the alternating current through the resistor in amps.

Z _R is the resistance value of the resistor in ohms.

R is the resistance value of the resistor in ohms.

The phase of the alternating current voltage, in radians.

The initial phase of the alternating current voltage, in radians.

The phase of the alternating current, in radians.

The initial phase of the alternating current, in radians.

f is the frequency of the alternating current in Hertz.

t is the time in seconds.

The ohmic resistance in the alternating current circuit maintains the phase of the alternating current voltage across the alternating current and the alternating current flowing through it. 2 is a schematic diagram showing the phase relationship between the alternating current passing through the ohmic resistor and the phase of the alternating current voltage across it.

Figure 3 is a schematic diagram of a circuit composed of an electromotive force of an alternating current and a capacitor. Both the terminal voltage u(t) of the capacitor and the charge q(t) across the capacitor and the current i(t) flowing through the capacitor are harmonically changed over time.

Assume: q(t) = Q ₀ cos(ωt);

Where Q ₀ is the peak value of the electricity, and the unit is Coulomb.

Since the terminal voltage of the capacitor is the charge value divided by the capacitance value of the capacitor,

Therefore:

Since the current is defined as the derivative of charge versus time, it is:

Therefore: i ₀ = ωQ ₀ ;

Therefore:

Therefore, the terminal voltage u(t) of the capacitor, the current i(t) flowing, the impedance, and the phase relationship between the voltage and the current can be expressed by the following formula:

among them:

u ₀ is the peak value of the AC voltage across the capacitor in volts.

i ₀ is the peak value of the AC current through the capacitor in amps.

C is the capacitance value of the capacitor in Farads.

Z _C is the impedance value of the capacitor in ohms.

The phase of the alternating current, in radians.

The initial phase of the alternating current, in radians.

The phase of the alternating current voltage, in radians.

The initial phase of the alternating current voltage, in radians.

f is the frequency of the alternating current in Hertz.

t is the time in seconds.

From the above equation, we can see the nature of the capacitor in the AC circuit, and its impedance is

The phase difference between the voltage and current of the terminal is

That is, the voltage is behind the current

Phase.

When it is connected in series with other components, since the components have the same current phase, the phase of the terminal voltage is behind the phase of the current.

When it is combined with other components to form a parallel circuit, since each component has the same voltage phase, the phase of its current exceeds the phase of the front-end voltage.

FIG. 4 is a schematic diagram showing the phase relationship between the alternating current passing through the capacitor and the phase of the alternating current voltage at both ends thereof.

Figure 5 is a schematic diagram of a circuit composed of an electromotive force of an alternating current and an inductor. For the sake of discussion, it is assumed that the inductance is pure inductance, and the ohmic resistance of the inductor and the connecting wire is negligible. The current i(t) in the circuit and the terminal voltage u(t) of the inductor are harmonically changed.

Assume that the current is i(t)=i ₀ cos(ωt);

Since the inductance is pure inductance, its ohmic resistance is negligible, so the self-induced electromotive force of the inductor is equal to the terminal voltage and the direction is opposite.

Therefore:

Therefore: u ₀ = ωLi ₀ ;

Therefore, the terminal voltage u(t) of the inductor, the current i(t) flowing through the inductor, the impedance and the phase relationship can be expressed by the following formula:

Z _L =ωL;

among them:

u ₀ is the peak value of the AC voltage across the inductor in volts.

i ₀ is the peak value of the alternating current through the inductor in amps.

L is the inductance value of the inductor in Henry.

Z _L is the impedance value of the inductor in ohms.

The phase of the alternating current, in radians.

The initial phase of the alternating current, in radians.

The phase of the alternating current voltage, in radians.

The initial phase of the alternating current voltage, in radians.

f is the frequency of the alternating current in Hertz.

t is the time in seconds.

From the above equation, we can see the nature of the inductor in the AC circuit. The impedance is Z _L = ωL, and the phase difference between the terminal voltage and the current is

The phase of the terminal voltage leading current

When it is connected in series with other components, since the components have the same current phase, the phase of the terminal voltage leads the phase of the current.

When it is combined with other components to form a parallel circuit, since each component has the same voltage phase, the phase of its current is behind the phase of the terminal voltage.

Fig. 6 is a schematic diagram showing the phase relationship between the alternating current passing through the inductor and the phase of the alternating current voltage at both ends thereof.

Figure 7 is a schematic diagram of a circuit in which an electromotive force of an alternating current is connected in series with an inductor and an ohmic resistor. For ease of discussion, the inductor is assumed to be a pure inductor and its ohmic resistance is negligible. The current i(t) in the circuit, the total voltage u(t) including the ohmic resistance and the inductance, is harmonically changed.

Since the inductor and the ohmic resistor are connected in series, the current flowing through them is the same, that is, the same phase and the same peak value i ₀ in the inductor and the ohmic resistor. From the previous instructions:

The peak value of the terminal voltage of the ohmic resistance u _R0 = i ₀ Z _R = i ₀ R;

The peak value of the terminal voltage of the inductor u _L0 = i ₀ Z _L = ωLi ₀ ;

Voltage lead current across the inductor

Phase, the voltage across the ohmic resistor is in phase with the current; therefore, calculating the peak value of the total voltage containing these two voltages requires a vector solution.

Figure 8 is a schematic diagram showing the relative relationship between the current and the voltage passing through the circuit. In the figure, based on the phase of the current, the phase of the voltage across the ohmic resistor is in phase with the phase of the current, and the peak value of the voltage across the two ends, R _R0 , the phase of the voltage across the inductor leads the current.

Draw the peak value of the voltage at both ends, u _L0 .

Let the peak value of the total voltage including the inductor and the resistor be u ₀ , then:

u ₀ ² =(u _R0 ) ² +(u _L0 ) ² =(i ₀ R) ² +(ωLi ₀ ) ² =i ₀ ² (R ² +(ωL) ² );

Then the impedance Z of the circuit is:

then:

Set the phase of the total voltage lead current including the inductor and the resistor to

The unit is radians.

then:

Therefore, in the AC circuit, the total voltage u(t), current i(t), impedance, and phase relationship including the inductor and the resistor can be expressed by the following formula:

among them:

u ₀ is the peak value of the total voltage including the inductor and the resistor in volts.

i ₀ is the peak value of the current through the inductor and resistor in amps.

L is the inductance value of the inductor in Henry.

R is the resistance value of the resistor in ohms.

Z is the impedance value of the series circuit including the inductor and the resistor, in ohms.

The phase of the alternating current, in radians.

The initial phase of the alternating current, in radians.

The phase of the alternating current voltage, in radians.

The initial phase of the alternating current voltage, in radians.

f is the frequency of the alternating current in Hertz.

t is the time in seconds.

From the above equation, we can see the nature of the inductor and the ohmic resistor connected in series in the AC circuit. The impedance is

The phase difference between the total voltage and current including the resistor and the inductor is

That is, the phase of the total voltage lead current is

Figure 9 is a schematic diagram of a circuit in which an electromotive force of an alternating current is connected in series with an inductor, an ohmic resistor, and a capacitor. For ease of discussion, the inductor is assumed to be a pure inductor and its ohmic resistance is negligible. The current i(t) in the circuit, the total voltage u(t) including the inductance, the resistance, and the capacitance is simply harmonically changed.

In fact, this is a resonant circuit, because the voltage across the capacitor is behind the phase of the current.

The phase of the voltage leading the current across the inductor is

When the impedance of the capacitor

When the impedance ωL of the inductor is equal, that is,

Frequency of alternating current

When their impedances cancel each other out, the impedance in the circuit is the smallest, only the ohmic resistance, the circuit is in resonance, and the current passing through is at its maximum.

when

Time, ie

The circuit is inductive. The AC circuit includes the total voltage phase of the inductor, the resistor, and the capacitor. The phase of the current is ahead of the total voltage.

when

Time, ie

The circuit is capacitive, and the total voltage phase of the AC circuit including the inductor, the resistor, and the capacitor lags behind the phase of the current, and the phase of the current leads the total voltage.

When the frequency f of the current is constant, the capacitance value of the capacitor C can be selected to satisfy

Make the circuit capacitive.

The following assumes that the capacitance value of the capacitor C is satisfied.

That is, the circuit is capacitive, and this case will be described.

Since the inductance, the ohmic resistance, and the capacitance are in series, the current flowing through them is the same, that is, having the same phase and the same peak value i ₀ in each element. From the previous instructions:

The peak value of the voltage across the ohmic resistor u _R0 = i ₀ Z _R = i ₀ R;

The peak value of the voltage across the inductor u _L0 = i ₀ Z _L = ωLi ₀ ;

Peak voltage across the capacitor

Since the voltage across the inductor leads the phase of the current

The voltage across the capacitor is behind the phase of the current.

The voltage across the ohmic resistor is in phase with the current; therefore, calculating the peak value of the total voltage containing these three voltages requires a vector solution.

Fig. 10 is a view showing the relationship between the current passing through the circuit and the phase of the voltage across the respective elements. In the figure, based on the phase of the current, the phase of the voltage across the ohmic resistor is in phase with the phase of the current, and the peak value of the voltage across the two ends, R _R0 , the phase of the voltage across the inductor leads the current.

Draw the peak value u _L0 of the voltage across the inductor. The phase of the voltage across the capacitor lags behind the current.

Draw the peak value u _C0 of the voltage across the capacitor.

When vector graphics are performed on three vectors, any two vectors can be calculated according to the vector solution, and the calculation result and the third vector are calculated by the vector solution.

First, u _C0 and u _L0 are calculated. Since the phase difference between u _C0 and u _L0 is π, u _C0 plus u _L0 is equal to u _C0 minus u _L0 , ie

See Figure 10.

Let the peak value of the total voltage including the inductor, resistor and capacitor be u ₀ , then:

Then the impedance Z of the circuit is:

Let the current lead the phase of the total voltage including the inductor, resistor and capacitor as

The unit is radians.

then

Therefore, in the AC circuit, the total voltage u(t), current i(t), impedance, and phase relationship including inductance, resistance, and capacitance can be expressed by the following formula:

among them:

u ₀ is the peak value of the total voltage including the inductor, resistor, and capacitor in volts.

i ₀ is the peak value of the current through the inductor, resistor, and capacitor in amps.

L is the inductance value of the inductor in Henry.

C is the capacitance value of the capacitor in Farads.

R is the resistance value of the resistor in ohms.

Z is the impedance value of the series circuit including inductor, resistor and capacitor in ohms.

The phase of the alternating current, in radians.

The initial phase of the alternating current, in radians.

The phase of the alternating current voltage, in radians.

The initial phase of the alternating current voltage, in radians.

f is the frequency of the alternating current in Hertz.

t is the time in seconds.

From the above equations, we can see the nature of the series connection of inductance, ohmic resistance and capacitance in the AC circuit.

Time, ie

The circuit is capacitive, the phase of the total voltage lags behind the phase of the current, that is, the phase of the current leads the phase of the total voltage, and its impedance is

The phase difference between the total voltage and current is:

That is, the total voltage lags behind the phase of the current.

Figure 11 is a schematic structural view of a conventional transformer. A conventional transformer generally consists of an iron core and two windings wound on top of it, which are connected to a power supply for inputting the primary winding and a load for outputting the secondary winding.

For ease of explanation, it is assumed that the transformer is an ideal transformer, ie;

(1) There is no magnetic flux leakage, that is, the magnetic flux passing through any one of the windings in the iron core is the same.

(2) The ohmic resistance of both windings is very small, and the voltage loss of the ohmic resistor and the Joule heating loss are negligible.

(3) There is no iron loss in the iron core, that is, the hysteresis loss and eddy current loss in the iron core are ignored.

(4) The inductive reactance of the primary winding and the secondary winding is very large.

assumed:

The length of the magnetic circuit in the iron core is l, and the unit is meter;

The core has a cross-sectional area of S in square meters;

The number of turns of the primary winding is N ₁ ;

The number of turns of the secondary winding is N ₂ ;

Then: the self-inductance coefficient of the primary winding

The unit is Henry;

Then: the self-inductance coefficient of the secondary winding

The unit is Henry;

Where μ ₀ is the magnetic permeability in vacuum, μ ₀ = 4π × 10 ^-7 units is Newton / (amperes) ² .

μ is the relative magnetic permeability of the iron core, defined as the ratio of the self-inductance coefficient of the coil in the iron core and the self-inductance coefficient of the coil in the vacuum, ie

Dimensionless.

For ease of explanation, it is assumed that the secondary winding is in an open state, that is, no current flows through the secondary winding.

According to the principle of electromagnetic induction, the alternating current passing through the primary winding, irrespective of the winding of the primary winding and the direction of the current passing through, the magnetic induction generated by the current in the core always induces resistance to the winding against the supply voltage of the winding. . There is no relationship between the winding method of the primary winding and the current direction through the winding, so the direction of the winding of the primary winding and the direction of the current passing through are not specifically indicated in the following description.

For the same reason, when the secondary winding is induced by the magnetic induction generated in the primary winding by the current generated in the primary winding, there is an induced electromotive force at both ends thereof, and when it forms a loop with the load, the current passing through it is iron. The direction in which the magnetic induction is generated in the core is always opposite to the direction of the magnetic induction generated in the core by the current passing through the primary winding. There is no relationship with the winding method of the secondary winding and the direction of the terminal voltage of the induced electromotive force, so the direction of the terminal winding of the secondary winding and the induced electromotive force is not specifically indicated in the following description.

The relationship between the winding method of the winding and the direction of the magnetic induction generated by the winding current direction in the core can be found in the electromagnetics tutorial.

Assuming that the power supply e(t)=e ₀ cos(ωt) to the primary winding forms a loop with the primary winding, assuming that the resistance of the connecting conductor between the power supply and the winding is negligible, the terminal voltage of the primary winding is:

u ₁ (t)=u ₁₀ cos(ωt);

Where: e ₀ = u ₁₀ ; u ₁₀ is the peak value of the voltage in volts;

Assuming that the primary winding is purely inductive and its ohmic resistance is negligible, the circuit is similar to the circuit diagram of Figure 5. The primary winding is self-inductive L in Figure 5, because the primary winding is an inductive component, so the phase of the current passing is behind the voltage. The phase is

Since the secondary winding is in an open state, that is, only current flows in the primary winding, and the current in the primary winding is said to be the exciting current i ₀ (t);

then:

among them

The current peak in the primary winding, in amps.

ΩL ₁ is the impedance of the primary winding in ohms;

Where: ω is the angular frequency of the alternating current, ω = 2πf, and the unit is radians/second.

f is the frequency of the alternating current in Hertz.

According to the ampere loop theorem of the magnetic circuit, when the current passes through the primary winding, a magnetic induction is generated in the iron core.

The amperage loop theorem of the magnetic circuit in vacuum is:

The amperage loop theorem of the magnetic circuit in the core can be:

When the exciting current i ₀ (t) passes through the primary winding, the magnetic induction is generated in the iron core as B ₀ (t).

then:

Where B ₀ (t) is the magnetic induction intensity in Tesla.

B ₀ (t) has the same angular frequency and initial phase as current i ₀ (t).

According to Faraday's law of electromagnetic induction, when the magnetic induction B ₀ (t) passes through the core, an alternating electric field is induced around the core, so that there is an induced electromotive force at both ends of the winding; the magnetic induction B ₀ (t) is The induced electromotive force generated in the primary winding is a self-induced electromotive force, and the induced electromotive force generated in the secondary winding is a mutual electromotive force; and the electromotive force induced by the magnetic induction intensity B ₀ (t) on any winding has the same angular frequency and initial phase .

The mathematical representation of Faraday's law of electromagnetic induction is:

Where Φ is the magnetic flux in the iron core, Φ=B×S, and the unit is Weber.

Magnetic induction B ₀ (t) is provided exciting current i ₀ (t) induced electromotive force generated in the primary winding is e ₀ (t);

then:

because

Therefore:

So there is u ₁ (t)=u ₁₀ cos(ωt)=-e ₀ (t); the phase of e ₀ (t) is behind the phase π of u ₁ (t); the phase of e ₀ (t) is behind i ₀ ( Phase of t)

The phase of u ₁ (t) leads the phase of i ₀ (t)

With the excitation current i ₀ (t) the magnetic flux density B ₀ (t) induced electromotive force generated in the secondary winding of e ₂ (t); then:

because

Have

Let u ₂ (t) be the terminal voltage of the secondary winding, since the secondary winding is in the off state;

then:

Therefore:

Explain that in the ideal state, the ratio of the peak value of the terminal voltage of the primary winding to the peak value of the terminal voltage of the secondary winding is equal to the ratio of the number of turns of the primary winding to the number of turns of the secondary winding, the phase difference is π, and the secondary winding The terminal voltage is behind the terminal voltage of the primary winding.

Based on the phase of the exciting current i ₀ (t) in the primary winding, Figure 12 shows the phase of u ₁ (t) leading current i ₀ (t)

And u ₂ (t) phase backward current i ₀ (t) phase

Schematic diagram of the relative relationship.

When the secondary winding forms a loop, it is similar to the circuit loop of FIG. The induced electromotive force e ₂ (t) at both ends of the secondary winding is equivalent to the power supply in FIG. 7 , that is, the total voltage of the circuit loop; the secondary winding is equivalent to the self-inductance L in FIG. 7 , and the load is equivalent to the resistance in FIG. 7 . R; the difference is that in Figure 7, the power supply and the self-inductive winding are two different entities, which are connected by wires, but when the secondary winding forms a loop, the excitation current i ₀ (t) of the primary winding induces the secondary winding. The electromotive force e ₂ (t) is at both ends of the secondary winding. When there is current passing, the self-induced electromotive force of the secondary winding is also at the two ends of the secondary winding, which is the same entity, but is essentially the same as the circuit of FIG. of.

Using the vector solution, the total voltage e ₂ (t) of the circuit loop is subtracted from the self-induced electromotive force of the self-inductance L, and the terminal voltage of the secondary winding, that is, the terminal voltage across the resistor R is obtained.

In the secondary winding, a current flows through, and the phase of the current lags behind the phase of the total voltage.

Where ωL ₂ is the inductive reactance of the secondary winding, R is the resistance of the load, and the unit is ohm; for convenience of explanation, it is assumed that the inductive reactance of the secondary winding is very large, and the phase of the current is behind the total voltage phase.

Because the terminal voltage of the secondary winding is behind the terminal voltage in the primary winding, the phase difference is π, and the excitation current i ₀ (t) in the primary winding is behind the terminal voltage of the primary winding, and the phase difference is

Therefore, the current in the secondary winding is behind the excitation current i ₀ (t) in the primary winding, and the phase difference is π.

Due to the magnetic induction generated in the secondary winding by the current in the secondary winding, the secondary winding has a self-induced electromotive force, which causes the terminal voltage of the secondary winding to drop; at the same time, a mutual inductance electromotive force is applied to the primary winding to increase the current in the primary winding. At the beginning When the current in the winding is increased, the magnetic induction intensity in the iron core is increased, causing the self-inductance electromotive force of the primary winding to rise, the mutual inductance electromotive force of the secondary winding to rise, the terminal voltage to rise, and the above process is completed in an instant, and then in a stable state.

In the steady state, the terminal voltage of the primary winding and the terminal voltage of the secondary winding remain unchanged.

The relationship between the current in the primary winding and the current in the secondary winding in the steady state is explained below.

Because of the terminal voltage of the secondary winding

Therefore, the current in the secondary winding can be set to

Where i ₂₀ is the peak current in the secondary winding in amps.

Let the current i ₂ (t) produce a magnetic induction in the core of B ₂ (t);

then:

According to Faraday's law, when the magnetic induction B ₂ (t) passes through the core, an alternating electric field is induced around the core, so that there is an induced electromotive force at both ends of the winding. The induced electromotive force generated in the secondary winding by the magnetic induction intensity B ₂ (t) is a self-induced electromotive force, and the induced electromotive force generated in the primary winding is a mutual electromotive force. And the magnetic induction B ₂ (t) has the same angular frequency and initial phase induced on any winding.

This current is provided i ₂ (t) generated by the magnetic induction B ₂ (t) induced electromotive force across the primary winding of e ₂₁ (t); then:

That is, the current i ₂ (t) in the secondary winding to the mutual inductance of the primary winding e ₂₁ (t), after a period of (2π) lag, has the same phase as the terminal voltage of the primary winding, superimposed on the primary winding The terminal voltage increases the terminal voltage in the primary winding. Since the increased voltage is in phase with the terminal voltage of the primary winding, the current i ₁ (t) added in the primary winding has the same phase as the excitation i ₀ (t) in the primary winding because of the increase in voltage. (See Figure 11).

The current in the primary winding is increased due to the mutual electromotive force e ₂₁ (t).

Since the terminal voltage increase value of the primary winding is:

Since the self-inductance coefficient of the primary winding is:

Let the current added in the primary winding be:

Where i ₁₀ is the peak value of the increased current in the primary winding in amps.

Then there are:

Then there;

It is stated that the ratio of the peak value i ₁₀ of the increased current in the primary winding to the peak value i ₂₀ of the current in the secondary winding is inversely proportional to the number of turns of the two windings.

due to

So have

which is:

Describe the conventional transformer, the phase difference between the increased current i ₁ (t) in the primary winding and the current i ₂ (t) in the secondary winding is π, the peak value of the increased current in the primary winding and the peak value of the current in the secondary winding The ratio is inversely proportional to the number of turns of the two windings.

Therefore, the increase in current passing through the primary winding is;

Or simply, since the terminal voltages of the primary winding and the secondary winding remain unchanged after the current in the secondary winding passes, the current i ₂ (t) in the secondary winding and the increased current i ₁ in the primary winding ( t) The magnetic induction in the core is equal in magnitude and opposite in direction, ie:

Set the current added in the primary winding to

The increased current in the primary winding is i ₁ (t) the magnetic induction B ₁ (t) generated in the core;

then

Because: B ₂ (t) + B ₁ (t) = 0; B ₂ (t) = -B ₁ (t);

The same is true:

due to

So have:

which is:

Based on the phase of the induced electromotive force e ₂ (t) on the secondary winding, Figure 13 shows the phase lead induced electromotive force e ₂ (t) phase of i ₁ (t)

And the phase of i ₂ (t) is behind the induced electromotive force e ₂ (t) phase

Schematic diagram of the relative relationship. Where B ₁ (t) is in phase with i ₁ (t) and B ₂ (t) is in phase with i ₂ (t).

Current in the secondary winding is provided i ₂ (t) generated by the magnetic induction B ₂ (t) of the self-induced emf on the secondary winding of e ₂₂ (t); then:

Since the increased current i ₁ (t) in the primary winding produces a magnetic induction B ₁ (t) in the core:

A primary winding disposed increasing current i ₁ (t) generated by the magnetic induction B ₁ (t), the mutual inductance of the electromotive force on the secondary winding of e ₁₂ (t); then:

Therefore, there are: e ₂₂ (t) + e ₁₂ (t) = 0:

It shows that in the ideal state of the traditional transformer, the current i ₂ (t) in the secondary winding senses the secondary winding equal to the increased current i ₁ (t) in the primary winding senses the secondary winding, maintaining the end of the secondary winding The voltage does not change.

Since the terminal voltage of the secondary winding is the same when it is in the off state and the current flowing through the loop, the current in the secondary winding and the increased current in the primary winding, the magnetic induction generated in the ideal transformer core is Equal in magnitude and opposite in direction, the induction of the windings in the core cancels each other, so that the terminal voltage of the winding does not change. Assuming that there is a detection winding in the core (not shown in Figure 11), when the secondary winding is open, only when the excitation current passes through the primary winding, the detected state of the winding is detected, and the secondary winding is formed. In the loop, and as the load changes, the state detected by the sense winding is the same.

When a current flows through the secondary winding, the current generates a magnetic induction intensity in the iron core, and the magnetic induction intensity changes the magnetic induction intensity B ₀ (t) established by the original excitation current i ₀ (t) in the iron core, and then in the primary winding the current changes, the result is to maintain the original exciting current i ₀ (t) the magnetic induction B ₀ created in the iron core (t) remains unchanged state.

According to the condition that the terminal voltage of the primary winding remains unchanged, the relationship between the peak value of the current in the secondary winding and the peak value of the current in the primary winding is obtained:

According to this relationship, it is proved that the sum of the induced current in the primary winding to the secondary winding and the induction of the current in the secondary winding to the secondary winding is zero, and the terminal voltage of the secondary winding remains unchanged.

The current in the primary winding is i ₀ (t) + i ₁ (t), since the inductive reactance of the primary winding is very large, indicating that the exciting current i ₀ (t) of the ideal transformer is very small. Therefore, i ₁ (t) is much larger than i ₀ (t) in the primary winding, so i ₁ (t) ≈ i ₀ (t) + i ₁ (t) can be considered. Because of:

u ₁ (t)=u ₁₀ ×cos(ωt);

and so

Let the input power of the primary winding be Pin:

(in watts);

Let the output power of the secondary winding be Pout:

(in watts);

So: Pin=Pout;

due to

Therefore:

due to

In a complete time period, the integral to time t is zero, while

Therefore: Pin and Pout are reactive power.

Because the traditional transformer is ideal, the input power and output power are reactive power.

According to the principle of electromagnetic induction, under the ideal state, the traditional transformer has an induced electromotive force on the secondary winding under the action of the excitation current of the primary winding. When the secondary winding and the load form a loop, current flows through the secondary winding. The current induces the primary winding to increase the current in the primary winding such that the input power of the primary winding is equal to the output power of the secondary winding. The process of transferring power from the primary winding to the secondary winding is completed.

For the above background, please refer to Zhao Kaihua, Chen Ximou, Electromagnetism (third edition) Higher Education Press.

[Summary of the Invention]

The invention is based on a conventional transformer, in which an auxiliary secondary winding is added to the iron core, and the auxiliary secondary winding forms a loop with a capacitor. In this loop, the impedance of the capacitor is greater than the inductive reactance of the auxiliary secondary winding, making the loop capacitive, ie the phase of the current leads the phase of the total voltage.

Figure 14 is a schematic structural view of a novel transformer. In addition to adding an auxiliary secondary winding to the core, the auxiliary secondary winding and a capacitor form a loop. The other parts are the same as traditional transformers. A conventional transformer generally consists of an iron core and two windings wound on top of it, which are connected to a power supply for inputting the primary winding and a load for outputting the secondary winding.

For ease of explanation, it is assumed that a new type of transformer is an ideal transformer, ie;

(1) There is no magnetic flux leakage, that is, the magnetic flux passing through any one of the windings in any one of the cores is the same.

(2) The resistance of the three windings is very small, and the voltage loss of the ohmic resistor and the Joule heating loss are negligible.

(4) The inductive reactance of the primary winding, the secondary winding, and the auxiliary secondary winding is very large.

assumed:

The magnetic path length in the iron core is ln, and the unit is meter;

The core has a cross-sectional area of Sn in square meters;

The number of turns of the primary winding is Nn ₁ ;

The number of turns of the secondary winding is Nn ₂ ;

The number of turns of the auxiliary secondary winding is Nn ₃ ;

Then: the self-inductance coefficient of the primary winding

The unit is Henry;

Then: the self-inductance coefficient of the secondary winding

The unit is Henry;

Then: the self-inductance coefficient of the auxiliary secondary winding

The unit is Henry;

Dimensionless.

A new type of transformer is no different from a conventional transformer, assuming that the auxiliary secondary winding is in an open state.

Assuming that the power supply e(t)=e ₀ cos(ωt) to the primary winding, the terminal voltage of the primary winding is;

u ₁ (t)=u ₁₀ cos(ωt); where e ₀ = u ₁₀ ; u ₁₀ is the peak value of the voltage in volts.

Since the primary winding is an inductive component, its ohmic resistance is negligible. Therefore, when the primary winding forms a loop, the phase of the current passing through is opposite to the phase of the terminal voltage of the primary winding.

Assuming that the secondary winding and the auxiliary secondary winding are in an open state, the current in the primary winding is said to be the exciting current i ₀ (t);

then:

among them

The current peak in the primary winding, in amps.

When the current i ₀ (t) is passed through the primary winding, a magnetic induction intensity Bn ₀ (t) is generated in the iron core;

then:

Bn ₀ (t) has the same angular frequency and initial phase as current i ₀ (t).

The magnetic induction intensity Bn ₀ (t) generates an induced electric field around the core, causing an alternating electromotive force at both ends of each winding, and the alternating electromotive forces in all the windings have the same angular frequency and initial phase.

Magnetic induction Bn ₀ (t) is provided to the current i ₀ (t) induced electromotive force generated in the primary winding is e ₀ (t);

then:

Then: u ₁ (t)=u ₁₀ cos(ωt)=-e ₀ (t); the phase of e ₀ (t) is behind the phase π of u ₁ (t); the phase of e ₀ (t) is behind i ₀ ( Phase of t)

Magnetic induction Bn ₀ (t) is provided to the current i ₀ (t) induced electromotive force generated in the secondary winding of e ₂ (t);

then:

The terminal voltage of the secondary winding is lower than the terminal voltage of the primary winding, and the phase difference is π. The ratio of the peak value of the terminal voltage of the primary winding to the peak value of the terminal voltage of the secondary winding is equal to the ratio of the number of turns of the primary winding to the number of turns of the secondary winding.

Magnetic induction Bn ₀ (t) is provided to the current i ₀ (t) is generated on the auxiliary secondary winding of the induced electromotive force e ₃ (t);

then:

Let u ₃ (t) be the terminal voltage of the auxiliary secondary winding, since the auxiliary secondary winding is in the off state;

then:

The terminal voltage of the auxiliary secondary winding is lower than the terminal voltage of the primary winding, and the phase difference is π. The ratio of the peak value of the terminal voltage of the auxiliary primary winding to the peak value of the terminal voltage of the primary winding is equal to the ratio of the number of turns of the auxiliary secondary winding to the number of turns of the primary winding.

At the same time, e ₀ (t), e ₂ (t) and e ₃ (t) have the same angular frequency and initial phase.

The secondary winding is then looped with the general load to assist the secondary winding in an open state, and a current flows through the secondary winding. The phase of the current lags behind the total voltage (ie, the induced electromotive force e ₂ (t)).

Where ωLn ₂ is the inductive reactance of the secondary winding, R is the resistance of the load, and the unit of ωLn ₂ and R is ohms; for convenience of explanation, it is assumed that the inductive reactance of the secondary winding is very large, and the internal resistance of the secondary winding is negligible. The phase of the current lags behind the total voltage (ie, the induced electromotive force e ₂ (t))

Therefore, it can be set:

The current in the secondary winding is

Where i ₂₀ is the peak current in the secondary winding in amps.

Setting a current i ₂ (t) to generate a magnetic induction Bn ₂ (t) in the core;

then:

The magnetic induction intensity Bn ₂ (t) generates an induced electromotive force on the primary winding to increase the current in the primary winding, and the current increase value in the primary winding is i ₁ (t);

then:

And have:

with

Therefore, there are:

When the current increase value i ₁ (t) passes through the primary winding, a magnetic induction intensity Bn ₁ (t) is generated in the iron core;

then:

Therefore: Bn ₂ (t) and Bn ₁ (t) are equal in magnitude, and the phase difference is π, that is, the direction is opposite.

The current increase value i ₁ (t) and the excitation current i ₀ (t) have the same angular frequency and initial phase. The magnetic inductions Bn ₀ (t) and Bn ₁ (t) have the same angular frequency and initial phase.

This is because, in addition to the excitation current i ₀ (t), the two currents i ₁ (t) and i ₂ (t) pass through the primary winding and the secondary winding, respectively, but they are generated in the iron core. The magnetic induction intensities Bn ₁ (t) and Bn ₂ (t) are equal in magnitude and opposite in direction, so that the induction of the auxiliary magnetic windings cancels each other without changing the terminal voltage of the auxiliary secondary winding.

If the auxiliary secondary winding forms a loop with another general load, the same secondary winding is similar to the load forming loop, and the phase of the current in the auxiliary secondary winding lags behind the phase of the induced electromotive force e ₃ (t)

So far, its performance is consistent with conventional transformers, similar to a conventional transformer consisting of one primary winding and two secondary windings.

The general load on the auxiliary secondary winding is then disconnected, which forms a loop with the auxiliary secondary winding, which is similar to the circuit of FIG. Since the auxiliary secondary winding has an induced electromotive force e ₃ (t), similar to the electromotive force in Figure 9, the total voltage of the circuit loop; the auxiliary secondary winding itself is an inductive component, similar to the inductor in Figure 9, the capacitance is similar The capacitance in Figure 9, the internal resistance of the auxiliary secondary winding is similar to the resistance in Figure 9.

The loop is a resonant circuit, such as the impedance of a capacitor

Greater than the impedance ωLn _{3 of the} inductor (where C ₃ is the capacitance of the capacitor in Farads), the circuit is capacitive, that is, the phase of the current leads the phase of the total voltage (ie, the induced electromotive force e ₃ (t)).

The impedance Z of this circuit is:

(where r ₃ is the internal resistance of the auxiliary secondary winding in ohms);

Let the current lead the total voltage phase

The unit is radians.

then:

For the sake of explanation, it is assumed that r _{3 is} small,

Very large, the current leads the phase of the induced electromotive force e ₃ (t) to

The current set in the auxiliary secondary winding is i ₃ (t);

then:

among them:

i ₃₀ is the current peak in the secondary winding in amps.

Note that when the main parameters of a new type of transformer, such as u ₁₀ , Nn ₁ , Nn ₂ , Nn ₃ and the capacitance C ₃ value in the loop of the auxiliary secondary winding, the current i ₃ (t) in the auxiliary secondary winding is determined. Basically determined, and the phase relationship between the current and the total voltage is also determined and remains unchanged. This current i ₃ (t) does not change as the current i ₂ (t) in the secondary winding changes with the load, nor does it increase the current i ₁ (t) in the primary winding with the current in the secondary winding The change in i ₂ (t) changes.

It is assumed that the current i ₃ (t) in the auxiliary secondary winding generates a magnetic induction Bn ₃ (t) in the core.

then:

Currents i ₀ (t), i ₁ (t), and i ₃ (t) have the same angular frequency and initial phase. The magnetic induction intensities Bn ₀ (t), Bn ₁ (t), and Bn ₃ (t) have the same angular frequency and initial phase.

When the auxiliary secondary winding forms a loop with the general load, the phase of the current i ₃ (t) in the auxiliary secondary winding lags behind the phase of the induced electromotive force e ₃ (t)

When the auxiliary secondary winding and a capacitor form a loop, and satisfy the impedance of the capacitor

When the impedance is larger than the inductance ωLn ₃ , the phase of the current leads the phase of the induced electromotive force e ₃ (t)

A phase change of π has occurred.

Figure 15 shows a new type of transformer. Under ideal conditions, since the induced electromotive forces e ₂ (t) and e ₃ (t) have the same angular frequency and initial phase, they can be considered as the same reference, and the induced electromotive force of the secondary winding. e ₂ (t) is a reference diagram showing the relative relationship between the current i ₂ (t) and the current i ₃ (t) and the corresponding magnetic inductions Bn ₂ (t) and Bn ₃ (t).

Figure 16 shows a novel transformer in the ideal state, based on the terminal voltage u ₁ (t) of the primary winding, the current i ₀ (t) and the current i ₃ (t) and the corresponding magnetic induction Bn ₀ (t) and Schematic diagram of the phase relative relationship of Bn ₃ (t).

When the phase of the current in the auxiliary secondary winding changes by a π, a lot of things must happen.

The excitation current in the primary winding is

The current in the auxiliary secondary winding is

Therefore, the phases of the two currents are the same, indicating the current i ₃ (t) passing through the auxiliary secondary winding and the exciting current i ₀ (t) in the primary winding, and the magnetic inductions Bn ₃ (t) and Bn generated in the core. ₀ (t) has the same phase and has the same effect on the secondary winding, ie the induced electromotive force is generated in the same phase to the secondary winding. From this perspective, the auxiliary secondary winding can also be called the auxiliary primary winding, or it is considered to be another primary winding. Since the secondary winding acts as the input power in the conventional transformer, the auxiliary secondary winding is in this new type. There is also input power in the transformer system.

The difference is that the current in the primary winding is provided by the power supply and the current in the secondary winding is provided by the induced electromotive force e ₃ (t) generated by the excitation current i ₀ (t).

To assist current i in the secondary winding ₂ in terms of the relationship between i (t) a (t) ₃ and a secondary winding current. Current in the secondary winding when current is passed through the secondary winding

Magnetic induction Bn ₂ (t) generated in the core; when there is current in the auxiliary secondary winding

When passed, the current induces a magnetic induction Bn ₃ (t) in the core. Since the auxiliary secondary winding current i ₃ (t) and the current i ₂ (t) in the secondary winding have a phase difference of π, the phase difference between Bn ₂ (t) and Bn ₃ (t) is π, and the direction is opposite; The magnetic induction in opposite directions is opposite in direction to the induced electromotive force of any winding (primary winding, secondary winding and auxiliary secondary winding) on the core.

When the two magnetic inductions Bn ₂ (t) and Bn ₃ (t) are numerically equal, the induced electromotive forces of the primary winding, the secondary winding and the auxiliary secondary winding are completely canceled, that is, the secondary winding and the auxiliary secondary winding The self-inductance is zero, the terminal voltages do not change due to their current passing through; the current passing through the secondary winding and the auxiliary secondary winding has zero mutual inductance to the primary winding, and the primary winding has its terminal voltage unchanged, correspondingly The current passed does not change.

Since Bn ₂ (t) and Bn ₃ (t) are equal in magnitude, the directions are opposite.

Therefore: Bn ₂ (t) + Bn ₃ (t) = 0; that is: Bn ₂ (t) = -Bn ₃ (t);

due to

Have:

due to:

Have:

Have:

Due to the terminal voltage of the secondary winding:

Let Bn ₂ (t) and Bn ₃ (t) be equal in magnitude. When the directions are opposite, the output power of the secondary winding is P:

then:

(in watts);

In the formula,

To assist in the peak of the induced electromotive force of the secondary winding;

To assist the impedance of the secondary winding loop;

Although the output occurs on the secondary winding, the above equation mainly reflects the parameters of the auxiliary secondary winding, such as the peak value of the induced electromotive force of the auxiliary secondary winding and the impedance of the loop. Since the current in the auxiliary secondary winding acts as a power input in the system, it is indicated that when the secondary winding has a power P output, correspondingly there is a power P input in the auxiliary secondary winding, so that the output power of the secondary winding P The input power P of the auxiliary secondary winding is equal, eliminating the need for a power input in the primary winding.

From the electromagnetic point of view, since the magnetic induction intensity Bn ₂ (t) and the magnetic induction intensity Bn ₃ (t) are equal in value, since their phase difference is π, the direction is opposite; the induced electromotive force to the secondary winding is zero, A state in which the exciting current i ₀ (t) in the primary winding is maintained.

At this time, the output power P of the secondary winding is mainly related to the parameters of the auxiliary secondary winding, which reflects the input power of the auxiliary secondary winding under ideal conditions, so P can be called the input power of the auxiliary secondary winding under ideal conditions. P _fz .

Therefore:

due to:

Therefore:

In the formula,

To assist the impedance of the secondary winding loop, the impedance of the loop and the phase of the current lead voltage

It is related to the input power P _{fz of the} auxiliary secondary winding under ideal conditions and the phase of the current lead voltage

There are relationships.

When the auxiliary secondary winding is in the open state, it is actually a conventional transformer, and when there is a power P output in the secondary winding, and P is greater than _Pfz , there is accordingly a power P input in the primary winding. The auxiliary secondary winding is then in a closed state, the magnetic induction due to the current in the auxiliary secondary winding partially canceling the magnetic induction generated by the current in the secondary winding, or having an input of power _Pfz in the auxiliary secondary winding, At this time, the magnetic induction in the core is the same as the output power of the secondary winding (PP _fz ), and the corresponding input power in the primary winding is (PP _fz ).

Note that when the auxiliary secondary winding is in the closed state, when the output power of the secondary winding is P, the input power of the primary winding is (PP _fz ), the output power of a new type of transformer is greater than the input power, and the difference is P-( PP _fz )=P _fz .

The special case is: when the output power of the secondary winding is P=P _fz , the input power of the primary winding is PP _fz =0, and the current in the primary winding is only the excitation current i ₀ (t).

To realize a new transformer output power is greater than the input power, the difference is P _fz, is essentially an auxiliary secondary winding current phase i i ₂ (t) a ₃ (t) and the phase of the current in the secondary winding There is a difference of π. Since the current i ₂ (t) in the secondary winding is behind the phase of the induced electromotive force e ₂ (t) in the secondary winding

The induced electromotive force e ₂ (t) in the secondary winding is the same as the phase of the induced electromotive force e ₃ (t) in the auxiliary secondary winding, so that the current i ₃ (t) in the auxiliary secondary winding needs to lead the induced electromotive force e ₃ Phase of (t)

Therefore, the auxiliary secondary winding needs to form a loop with the capacitor, and the impedance of the capacitor is greater than the inductive reactance of the auxiliary secondary winding, so that the loop is capacitive, ie:

which is:

Where C ₃ is the capacitance value of the capacitor, and the unit is Farah.

due to

Therefore:

due to

In a complete time period, the integral to time t is zero, while

Therefore, P and P _fz are reactive power.

Since a new type of transformer is ideal, the output power of the primary winding and the input power of the auxiliary secondary are reactive power.

Usually, the output power P of the secondary winding will change greatly with the change of the load. The corresponding current i ₂ (t) will change with the load. When P>P _fz , there is a primary winding. PP _fz power input, similar to traditional transformers. A new type of transformer is in normal operation.

Since the size of P _fz is constant, when P < P _fz , the corresponding

Bn ₂ (t) < Bn ₃ (t). Similar to the secondary winding being in the open state, there is current in the secondary winding, since the phase of the current i ₃ (t) in the secondary winding is the same as the phase of the excitation current i ₀ (t) in the primary winding , the magnetic induction intensity of the generated Bn ₃ (t) the magnetic flux density Bn ₀ (t) generated by the primary winding magnetizing current i ₀ (t) is in phase, the Bn ₃ (t) of the primary winding from The electromotive force is increased and the field current i ₀ (t) in the primary winding is reduced or even zero. Although in the ideal state the phase of the current i ₃ (t) in the auxiliary secondary winding is the same as the excitation current i ₀ (t) in the primary winding, it produces a magnetic induction Bn ₃ (t) and the primary winding magnetic induction Bn ₀ (t) excitation current i ₀ (t) produced is the same, but in practice there is a difference, the magnetic flux density Bn ₀ (t) excitation current i ₀ (t) generated by induction electromotive force e _{The basis of 2} (t) and e ₃ (t), if the excitation current i ₀ (t) is zero, an unpredictable condition may occur.

It is therefore necessary technical measures needed for P _FZ be adjusted to ensure that the process for the entire run dry and so big P P _fz. The main measures for adjusting P _fz are: changing the capacitance value C ₃ of the capacitor, changing the impedance of the auxiliary secondary winding loop to change the current of the auxiliary secondary winding loop; splitting the auxiliary secondary winding, and then selecting The partially split winding is disconnected, and the above measures will be described in the section of the specific embodiment.

The above is an explanation of the working principle of a new type of transformer under ideal conditions.

[Description of the Drawings]

Figure 1 is a schematic diagram of a circuit consisting of an electromotive force of an alternating current and an ohmic resistor.

FIG. 2 is a schematic diagram showing the relative relationship between the AC current passing through the ohmic resistor of FIG. 1 and the phase of the terminal voltage thereof.

Figure 3 is a schematic diagram of a circuit composed of an electromotive force of an alternating current and a capacitor.

FIG. 4 is a schematic diagram showing the phase relationship between the alternating current passing through the capacitor in FIG. 3 and the alternating current voltage at both ends thereof.

Figure 5 is a schematic diagram of a circuit composed of an electromotive force of an alternating current and an inductor.

FIG. 6 is a schematic diagram showing the phase relationship between the alternating current passing through the inductor of FIG. 5 and the alternating current voltage at both ends thereof.

Figure 7 is a schematic diagram of a circuit in which an electromotive force of an alternating current is connected in series with an inductor and an ohmic resistor.

Fig. 8 is a view showing the relationship between the current passing through the circuit of Fig. 7 and the phase of the voltage across the respective elements.

Figure 9 is a schematic diagram of a circuit in which an electromotive force of an alternating current is connected in series with an inductor, a resistor and a capacitor.

Fig. 10 is a view showing the relative relationship between the current passing through the circuit of Fig. 9 and the voltage across the respective elements.

Figure 11 is a schematic structural view of a conventional transformer.

Figure 12 shows the traditional transformer in the ideal state, based on the excitation current i ₀ (t) in the primary winding, u ₁ (t) lead current i ₀ (t) phase

And u ₂ (t) phase backward current i ₀ (t) phase

Schematic diagram of the relative relationship.

Figure 13 shows the traditional transformer in the ideal state, based on the phase of the induced electromotive force e ₂ (t) of the secondary winding, i ₁ (t) leads the e ₂ (t) phase

And the phase of i ₂ (t) is behind the phase of e ₂ (t)

And the corresponding phase relationship of the magnetic induction intensities B ₁ (t) and B ₂ (t).

Figure 14 is a schematic structural view of a novel transformer.

Figure 15 shows a new type of transformer. Under ideal conditions, since the induced electromotive forces e ₂ (t) and e ₃ (t) have the same frequency and initial phase, they can be considered as the same reference, and the induced electromotive force of the secondary winding is e. ₂ (t) is a reference diagram showing the relative relationship between the current i ₂ (t) and the current i ₃ (t) and the corresponding magnetic inductions Bn ₂ (t) and Bn ₃ (t).

Figure 17 shows a new type of transformer. In the actual state, since the induced electromotive forces e ₂ (t) and e ₃ (t) have the same frequency and initial phase, they can be considered as the same reference, and the secondary winding is induced. The electromotive force e ₂ (t) is a reference, and the relative relationship between the current i ₂ (t) and the current i ₃ (t) and the phases of the corresponding magnetic inductions Bn ₂ (t) and Bn ₃ (t).

【Detailed ways】

The main difference between a new type of transformer and a conventional transformer is the addition of an auxiliary secondary winding that forms a loop with the capacitor. Because the primary and secondary windings are present in conventional transformers, and their role in a new type of transformer is similar to that of a conventional transformer.

In a ideal state, a new type of transformer has many differences from the actual state. Most of the differences exist in the ideal state and actual state of the traditional transformer, such as: magnetic flux leakage, winding voltage loss and Joule heating loss, hysteresis loss and eddy current loss in the core, etc. Description.

In the ideal state of a new type of transformer, it is assumed that the phase of the exciting current i ₀ (t) in the primary winding is behind the phase of the terminal voltage u ₁ (t)

But in fact its phase difference is:

Therefore: the excitation current in the primary winding is:

Correspondingly, the induced electromotive force e ₂ (t) on the secondary winding is;

The induced electromotive force on the auxiliary secondary winding is e ₃ (t);

among them:

The phase of the end voltage behind the excitation current i ₀ (t) in the primary winding, in units of radians;

r ₁ is the internal resistance of the primary winding, and the unit is ohm;

Ln ₁ is the self-inductance coefficient of the primary winding, and the unit is Henry;

Since ωLn _{1 is} large, r _{1 is} small, and the actual state differs from the ideal state very little, this assumption is reasonable, and the conventional transformer is also operating under such assumptions.

In the ideal state of a new type of transformer, it is assumed that the phase of the current i ₂ (t) in the secondary winding is behind the phase of the induced electromotive force e ₂ (t)

But in fact, although the type of load will be different, it will eventually appear in some form of ohmic resistance. If the load is ohmic resistance R, the phase difference is actually

Therefore: the current in the secondary winding

among them:

The phase of the induced electromotive force e ₂ (t) behind the current i ₂ (t) in the secondary winding, in units of radians;

R is the resistance value of the load, and the unit is ohm;

Ln ₂ is the self-inductance coefficient of the secondary winding, and the unit is Henry;

Since ωLn _{2 is} large, R is small, and the actual state differs from the ideal state very little, this assumption is reasonable, and the conventional transformer is also operating under such assumptions.

It is also assumed that the induced electromotive force e ₂ (t) is the terminal voltage u ₂ (t) of the secondary winding. In fact, this assumption is reasonable when the secondary winding is in the off state.

However, if the secondary winding forms a loop with the load, the terminal voltage u ₂ (t) of the secondary winding changes and is no longer the same as the induced electromotive force e ₂ (t). When the secondary winding and the load form a loop, the circuit is as shown in Fig. 7. The voltage across the resistor R is the terminal voltage of the secondary winding, but the phase is no longer the phase of the induced electromotive force e ₂ (t), but passes through The phase of the current i ₂ (t). According to the actual operation of the transformer, the terminal voltage remains constant, so the peak value of the terminal voltage has the peak value of the induced electromotive force e ₂ (t), and the peak value of the induced electromotive force e ₂ (t) is

Therefore, the terminal voltage u ₂ (t) of the secondary winding is:

In the ideal state of a new type of transformer, it is assumed that the phase of the current i ₃ (t) in the auxiliary secondary winding leads the phase of the induced electromotive force e ₃ (t)

But in fact, the phase difference is

Therefore: the current in the auxiliary secondary winding

among them:

To assist the current i ₃ (t) in the secondary winding to lead the phase of the induced electromotive force e ₃ (t) in units of radians;

r ₃ is the internal resistance value of the auxiliary secondary winding, and the unit is ohm;

Ln ₃ is the self-inductance coefficient of the auxiliary secondary winding, and the unit is Henry;

C ₃ is the capacitance value of the capacitor in the loop, and the unit is Farah;

Assumption

Time

Very large, corresponding impedance

To be very large, the current passing through the winding will be small, and the utilization efficiency of the winding will be very low, so it is actually necessary to choose a reasonable one.

Value, adjust appropriately

The magnitude of the value is used to increase the current through and increase the efficiency of the winding.

But no matter how it is adjusted, the impedance of the capacitor

Still far greater than the impedance ωLn _{3 of the} auxiliary secondary winding to avoid

When the loop is in resonance.

Figure 17 shows a new type of transformer. In the actual state, since the induced electromotive forces e ₂ (t) and e ₃ (t) have the same angular frequency and initial phase, they can be considered as the same reference, and the induced electromotive force of the secondary winding. e ₂ (t) is a reference diagram showing the relative relationship between the current i ₂ (t) and the current i ₃ (t) and the phases of the respective magnetic inductions Bn ₂ (t) and Bn ₃ (t).

In Fig. 17, the current i ₂ (t) and the corresponding magnetic induction Bn ₂ (t) are generated so that the phase of the induced electromotive force is e ₂ (t)

The magnetic induction intensity Bn ₂ (t) is in a direction perpendicular to e ₂ (t), that is, a component in the X direction

The magnetic induction intensity Bn ₂ (t) is in a direction parallel to e ₂ (t), that is, a component in the Y direction

The current i ₃ (t) and the corresponding magnetic induction intensity Bn ₃ (t) lead the phase of the induced electromotive force e ₃ (t) to

The induced electromotive force e ₃ (t) and the induced electromotive force e ₂ (t) are in phase. Therefore, the current i ₃ (t) and the corresponding magnetic induction intensity Bn ₃ (t) lead the phase of the induced electromotive force e ₂ (t)

The magnetic induction intensity Bn ₃ (t) is in a direction perpendicular to e ₂ (t), that is, a component in the X direction

The magnetic induction intensity Bn ₃ (t) is in a direction parallel to e ₂ (t), that is, a component in the Y direction

As seen from Fig. 17, Bn _2x (t) and Bn _3x (t) are opposite in direction and cancel each other out; Bn _2y (t) and Bn _3y (t) are in the same direction and cannot cancel each other.

due to

among them:

due to

Therefore:

due to

Obviously, when

Equal to 1,

equal

When Bn _3x (t) has a mathematical maximum. But physically

equal

Time,

Very large, since Bn _3y (t) is a vertical component, it cannot be cancelled, resulting in a large self-inductance of the auxiliary secondary winding and a large mutual inductance to other windings. When the self-inductance of the auxiliary secondary winding is large, if the current passes, the terminal voltage will drop rapidly, and the increased current in the primary winding is required to keep the terminal voltage constant, similar to a conventional transformer. Therefore, the maximum value of Bn _3x (t) in mathematics is physically meaningless, and it is physically determined based on other conditions.

Value.

select

Value of the loop

Not too large, so that there is enough current in the winding, and it is not too

Very large, the auxiliary secondary winding has a large self-inductance.

During the actual operation of a conventional transformer, the current i ₂ (t) in the secondary winding lags behind the phase of the induced electromotive force e ₂ (t)

The value is determined by the actual load situation and will vary slightly depending on the load, but no matter how it changes, the actual runtime

The value is close to the ideal state

That is, the component Bn _2y (t) in the Y direction of the magnetic induction intensity Bn ₂ (t) is small, the induction to the primary winding is small, and the secondary winding loop has sufficient output power;

or

Value and

The difference in value is not big, the so-called difference is not much: when

When

Not large, the auxiliary secondary winding has little self-inductance and can operate normally;

When the auxiliary secondary winding loop has an appropriate impedance, a normal current is passed.

The value can be taken within the above range.

when

After the value is determined, due to:

When Bn _2x (t) and Bn _3x (t) are equal in magnitude and opposite directions; then: Bn _2x (t) + Bn _3x (t) = 0;

That is: Bn _3x (t) = -Bn _2x (t); then:

then:

due to:

then:

Therefore:

due to

Assuming that Bn _2y (t) and Bn _3y (t) are both small and their sum is small, their inductance on the primary winding is negligible, and their induction of the secondary and auxiliary secondary windings is negligible. Then, when Bn _3x (t)=-Bn _2x (t); the magnetic induction Bn ₂ (t) generated by the current i ₂ (t) in the secondary winding, and the magnetic induction generated by the auxiliary secondary winding current i ₃ (t) When the intensity Bn ₃ (t) is equal in magnitude, the direction is opposite; the induced electromotive force to the secondary winding and the auxiliary secondary winding is zero, the induced electromotive force to the primary winding is zero, and the current passing through the primary winding is maintained as the exciting current The state of i ₀ (t) is unchanged.

Let the output power of the secondary winding be P:

then:

In the formula,

To assist the impedance of the secondary winding loop;

The reason is that the magnetic induction intensity Bn _2x (t) and the magnetic induction intensity Bn _3x (t) are equal in value, since their phase difference is π, the direction is opposite; the induced electromotive force to the secondary winding is zero, and the primary winding is maintained. The state in which the exciting current i ₀ (t) is constant.

At this time, the output power P of the secondary winding is mainly related to the parameters of the auxiliary secondary winding, which reflects the input power of the auxiliary secondary winding in the actual state, so P can be called the input power of the auxiliary secondary winding in the actual state. P _sj . Therefore:

due to

Therefore:

As in a full time period,

The integral to time t is zero, so:

In the formula:

In a complete time period, the integral to time t is zero and is reactive power.

In the formula:

For active power.

due to

with

Close to

and so

Close to π, so

Close to -1, the above formula is greater than zero.

When the auxiliary secondary winding is in the open state, it is actually a conventional transformer, and when there is a power P output in the secondary winding, and P is greater than P _sj , there is accordingly a power P input in the primary winding.

The auxiliary secondary winding is then in a closed state, the magnetic induction due to the current in the auxiliary secondary winding partially canceling the magnetic induction generated by the current in the secondary winding, or the input of the power _Psj in the auxiliary secondary winding, At this time, the magnetic induction in the core is the same as the output power of the secondary winding (PP _sj ), and the corresponding input power in the primary winding is (PP _sj ).

The output power of a new type of transformer is greater than the input power, and the difference is P-(PP _sj )=P _sj .

The special case is: when the output power of the secondary winding is P=P _sj , the input power of the primary winding is PP _sj =0, and the current in the primary winding is only the excitation current i ₀ (t).

The output power of a new type of transformer is greater than the input power, and the difference is P _sj . The output power of the secondary winding is greater than the input power of the primary winding is W;

then:

Where W is electrical energy, the unit is joule; t is time, the unit is second.

Therefore, a new type of transformer can provide power for devices that require electrical energy, as well as for places that require electrical energy.

Capacitor plays a key role in the auxiliary secondary winding of a new type of transformer and the circuit formed by the capacitor. The capacitance of the capacitor must meet

In order to make the loop capacitive, that is, the current leads the phase of the induced electromotive force.

However, the situation will be complicated in actual use, except that the capacitance value must be satisfied.

In addition, it is also required that the withstand voltage performance of the capacitor is greater than the actual withstand voltage requirement of the circuit, and the maximum current allowed by the capacitor is greater than the maximum current value at the circuit. When the output power of the secondary winding changes, a variable capacitor is needed to adjust the impedance of the auxiliary secondary winding loop.

When a single capacitor cannot meet the above requirements at the same time, it can be connected in series by a plurality of capacitors, then parallel to form a capacitor display, and a capacitor display to replace that capacitor in the circuit. This capacitor display can meet the above requirements at the same time.

For the maximum withstand voltage value of the capacitor in the loop and the maximum current passed, the specific variation can be found in the tutorial on AC circuits.

Let the capacitance value of a single capacitor be Ci, the withstand voltage value of a single capacitor be Vi, and the maximum current allowed to pass by a single capacitor is Ai. If the single capacitor cannot meet the capacitance value, the maximum withstand voltage in the circuit, and the maximum current allowable, the N capacitors can be connected in series, and then the M circuits connected in series are connected in parallel. a new circuit, the capacitance value of the circuit

The withstand voltage of the capacitor in this circuit is N × Vi, and the value of the maximum current allowed by the capacitance in the circuit is M × Ai. The single capacitor capacitance value Ci, and the magnitude relation of C _3, by selecting the values of M and N, so that the capacitance of the display can be met

The maximum withstand voltage in the circuit and the maximum current allowed to pass.

At the same time, the capacitor display is also a variable capacitor, in which the K (K takes 0 to M-1) column is in the off state, and the MK column is in the closed state, the capacitance value is

The change in capacitance value can be achieved by changing the magnitude of the K value to achieve the change of impedance, and finally the current and input power of the auxiliary secondary winding loop are changed.

In addition to using variable capacitors to vary the impedance and input power of the auxiliary secondary winding loop, the secondary secondary winding can be split to selectively regulate the split secondary secondary winding to adjust Auxiliary secondary winding current and input power.

Suppose that for a secondary winding with a number of turns Nn3, divided into N auxiliary secondary windings according to the number of turns of the winding, the number of turns of each auxiliary secondary winding after splitting is

The internal resistance of each auxiliary secondary winding after splitting is

After the split, the peak value of the induced electromotive force of each auxiliary secondary winding is

The self-inductance coefficient of each auxiliary secondary winding after splitting is

Let the current in the primary auxiliary secondary winding lead the phase of the induced electromotive force

then:

Let all the auxiliary secondary windings and the capacitor C _3i form a loop after all the splits, and the current leads the phase of the induced electromotive force.

then:

Assumption:

then:

To illustrate the problem, a new type of transformer is assumed to be ideal before the split secondary winding is split and split.

Set the current i _3i (t) through which each auxiliary secondary winding passes after splitting;

then:

It is shown that under the condition that the phase of the induced electromotive force is the same, the current passing through each auxiliary secondary winding after splitting is the same as the current passing through the auxiliary secondary before splitting. When let K (K take 1 to N) split auxiliary secondary windings in the closed state, let the NK split auxiliary secondary windings be in the off state, and the magnetic induction generated by the current in this state is Bn _3k (t):

then:

The magnetic induction in the core can be adjusted by changing the size of K to adjust the input power of the auxiliary secondary winding. When K=N, it means that the N split auxiliary secondary windings are the same as the auxiliary secondary windings before the splitting, and they can also be combined into one auxiliary secondary winding; when K is not equal to N, it can also Combine, and then let the other NK split auxiliary secondary windings be fully or partially closed. In this case, the split is not actually averaged, indicating that the split can be split without averaging.

Let the input power of each auxiliary secondary winding after splitting be P _sji : then:

The input power P _sjN through which the N auxiliary secondary windings can pass after _splitting is:

It is shown that under the condition that the phase of the induced electromotive force is the same, the input secondary power can be equally divided into N, and the total input power can be the same as the input power before the split.

When the K (K takes 1 to N) split auxiliary secondary windings are in the closed state, the NK split auxiliary secondary windings are in the off state, and the input power of the auxiliary secondary windings is set in this state. For P _sjk :

then:

The input power of the auxiliary secondary winding can be adjusted accordingly by changing the size of K. When K=N, it means that the N split auxiliary secondary windings can be combined into one original auxiliary secondary winding; when K is not equal to N, they can also be combined; then let the other NK split secondary times All or part of the windings are in a closed state, in which case the splitting is not actually performed on average, indicating that the splitting may not be split on average.

The splitting can make the induced electromotive force of each split auxiliary secondary winding smaller, which is beneficial to the insulation of the winding; after splitting, the capacitor C _3i in each auxiliary secondary winding can easily satisfy the capacitance value in the circuit. The requirements of the withstand voltage; at the same time, it is possible to selectively have several circuits in the off state for adjusting the magnitude of the auxiliary secondary winding current i ₃ (t) and the input power of the auxiliary secondary winding.

By adjusting the input power of the auxiliary secondary winding, it is possible to make the input power of the auxiliary secondary winding not greater than the output power in the secondary winding when the output power in the secondary winding changes greatly.

Under the condition that the current lead-in induced electromotive force has the same phase, a large auxiliary secondary winding can be split, or multiple auxiliary secondary windings can be combined, that is, an auxiliary secondary winding can be disposed in any core free space. Let it form a loop with the capacitor, which can be considered as the result of a large auxiliary secondary winding split, which achieves the purpose of increasing the input power of the auxiliary secondary winding.

[Industrial Applicability]

The novel transformer of the invention can make the output power greater than the input power, and the corresponding output electric energy is greater than the input electric energy, can replace the fossil fuel power generation; and can also provide electric energy for the device or place that needs electric energy.

Claims

A conventional transformer generally consists of a core and two windings wound on top of it, which are connected to a power supply, the primary winding for input and the secondary winding connected to the load for output;

In the ideal state, under the action of the power supply, the excitation current flows through the primary winding, and the phase of the current lags behind the phase of the power supply.
The current generates a magnetic induction intensity in the iron core, and the magnetic induction intensity induces an electromotive force on the secondary winding, the phase of the electromotive force is π behind the power supply source; the secondary winding and the general load form a loop, and the secondary winding is in the secondary winding There is current passing, because there is current in the secondary winding, so the secondary winding has a power output, the phase of the current is behind the phase of the excitation current is π; the magnetic induction generated by the current generates an induced electromotive force in the primary winding, and the electromotive force passes through a After the complete period (2π) is behind, it has the same phase as the power supply, increasing the current of the primary winding, increasing the input of the primary winding, making the input power on the primary winding equal to the output power on the secondary winding, completing the power. The process of transferring from the primary winding to the secondary winding;

A new type of transformer is based on a conventional transformer, and an auxiliary secondary winding is added to the iron core, which is characterized by: an iron core and three windings wound on the upper side thereof, wherein the power supply is connected to the power supply. The input is the primary winding, the load is connected to the load for the secondary winding; there is also an auxiliary secondary winding, which forms a loop with a capacitor; in this loop, the impedance of the capacitor is greater than the auxiliary secondary The inductive reactance of the winding makes the loop capacitive, that is, the phase of the current leads the phase of the total voltage;

When there is current in the primary winding, there is an induced electromotive force e 2 (t) on the secondary winding and an induced electromotive force e 3 (t), e 2 (t) and e 3 (t) on the auxiliary secondary winding. ) have the same initial phase and angular frequency;

When the secondary winding forms a loop with the general load, a current i 2 (t) passes through the loop, wherein the phase of the current i 2 (t) lags behind the phase of the induced electromotive force e 2 (t)

Current i 2 (t) produces in-phase magnetic induction Bn 2 (t) in the core;

When the auxiliary secondary winding and the capacitor form a loop, a current i 3 (t) passes through the loop, and the phase of the current i 3 (t) leads the phase of the induced electromotive force e 3 (t) to

Current i 3 (t) produces in-phase magnetic induction Bn 3 (t) in the core;

Since e 2 (t) and e 3 (t) have the same initial phase and angular frequency, they can be considered as the same reference;

The magnetic induction intensity Bn 2 (t) is in the direction perpendicular to e 2 (t), that is, the component in the X direction
The magnetic induction intensity Bn 2 (t) is in a direction parallel to e 2 (t), that is, a component in the Y direction

The magnetic induction intensity Bn 3 (t) is in the direction perpendicular to e2(t), that is, the component in the X direction.
The magnetic induction intensity Bn 3 (t) is in a direction parallel to e 2 (t), that is, a component in the Y direction

Since Bn 2x (t) and Bn 3x (t) are opposite to each other, they cancel each other out, which cancels out the magnetic induction generated by the current in the secondary winding. As a result, the magnetic induction Bn 2 (t) reduces the inductance of the primary winding, and accordingly the primary The input to the winding is reduced such that the output power of the secondary winding is greater than the input power of the primary winding, and accordingly the output power of the secondary winding is greater than the input power of the primary winding.
A novel transformer according to claim 1 wherein the electrical energy is provided to the device requiring electrical energy or to the location where electrical energy is required.
A novel transformer according to claim 1 wherein the auxiliary secondary winding can be split into a plurality of auxiliary secondary windings.