Chinny opir. Active Opir
Let's look at the attacking lanceug.
Vaughn is formed from the dzherel variable voltage, successful wires and such a deacogo adventure. Moreover, the inductance of the vanishing is too small, and the opir R is too great. Previously, the cost of the venture was called a support. Now it is called її active support.
Active Opir
Opir R called active, to the fact that in the lance it will be driven by such a support, the lance will use energy, which needs to be in the form of a generator. It is important to note that the voltage on the clamps of the lancet follows the order of the harmonic law:
U = Um * cos (ω * t).
The mittve value of the struma force can be calculated according to Ohm's law, it will be proportional to the mittyev value of the voltage.
I = u / R = Um * cos (ω * t) / R = Im * cos (ω * t).
Zrobimo vysnovok: the conductor with an active support has a phase difference between the coliving tanks and the strength of the struma is daily.
Chinne meaning sili strumu
The amplitude of the force of the struma is determined by the following formula:
The average value of the square of the struma strength for the period is calculated using the following formula:
Here Im is the amplitude of the coercion of the force of the strum. Yakshcho mi now virahuёmo square root from the average value of the square of the force of the struma, then we subtract the value, as it is called the average value of the force snake struma.
The letter I is used to denote the dignified meaning of the power of the strum.
I = √(i^2) = Im/√2.
The chinne value of the strength of the changing strum will be more powerful than the strength of such a steady strum, at any time during the same time in the conductor, when you look at it, you can see styles and warmth, and when you change the strum. In order to determine the dignified value of the voltage, there is an offensive formula.
U = √(u^2) = Um/√2.
Now conceivable fiery meaning strum and tensile strength, for viras Im = Um/R. We take:
Denmark viraz є Ohm's law for the lancer's cutter with a resistor, like a current of a change strum. Like in times of mechanical coliving, in a changing streak, we have little evidence of the strength of the streak, tensile at any moment of the hour. More important than nobility hot characteristics kolivan - so, like amplitude, frequency, period, value of the force of the struma and the voltage, which is to be blown.
Before speech, varto indicates that voltmeters and ammeters, recognized for a changeable struma, register the very value of the voltage and force of the struma.
There is one more important value in front of the mittevim, those who can once win for the calculation of the average value of the tension P of the strum.
but) Active Opir R, r - the purpose of the idealization of the lanceg element, in which the irreversible transformation of electrical energy into thermal energy is taken into account:
BUT.
b) Inductance L is an idealization element of the lancer, which is characterized by the ability to accumulate the energy of the magnetic field. The inductance is numerically more advanced in relation to the flow circuit to the struma, which is how the flow circuit is marked:
,
(3.6)
de 
- Potіk zcheplennya coils of inductance,
N-number of turns of the coil,
F- Magnetic flux.
.
c) Amnesty C - idealized element electric lansyug which is characterized by the building to accumulate the energy of the electric field.
,
(3.7)
de 
- charge on the plates and plates of the capacitor,
- Potential difference between capacitor plates.
Ємніст С - do not lie in 
and it is determined by the dimensions, the shape of the capacitor, and also by the electrical power of the medium, which is between the plates of the capacitor.
.
Chinne meaning of the snake strum
The ringing, which is blamed for the influx of the sound EPC, which periodically changes, is called the powerful electromagnetic ringing. The impressions of the electromagnetic colivannya, which have been installed, can be seen as passing a changeable stream into the lances, to avenge a resistor, an inductance coil and a capacitor.
On fig. 3.5 representations of the graph of a variable sinusoidal struma.
Rice. 3.5. Schedule of the snake strumu
The chinne value of the snake struma is more important than such a value of the fast strum, like in an hour, which is older than the period of the snake strum, we see in the same support such an amount of warmth that the given strum. Vychayatsya for such a formula 3.8.
. (3.8)
Active, reactive and similar opir in lancers of the snake strum
Strum in active support
,
(3.9)
de I r , U r- dynamic value of the struma and the voltage on the active support R.
Zsuv phases between the strum and the voltage on the resistor is equal to zero (div. Fig. 3.6).
Rice. 3.6. vector diagram stream and voltage on resistors
Strum in inductance
,
(3.10)
de I L , U L- fluctuating value of struma and voltage on the inductive support X L .
,
(3.11)
de ω – cyclic frequency, which is equal to zero, then when fast stream the inductance coil has no support.
lecture number 3
4. Electric lance with active and inductive elements.
Lanciug is made up of elements, the power of which we already know. Let's analyze the work of this lancer.
Let the strum at the lances change according to the law:
i = im sint.
Then the voltage on the active support is determined by the formula:
uR = uRm sint,
so, as on tsіy dіlyantsі strum that voltage zbіgayutsya in phase. Coil voltage:
uL = uLm sin (t + /2),
oskіlki on the coil inductance, the voltage viperedzhaє strum phase per cut equal /2. Let's have a vector diagram for the analyzed lancer. We add the struma vector to the back, then the voltage vector on the active support, which changes in phase with the struma vector. The vector of the voltage on the inductive element, which extends the vector of the struma on the cut/2, is applicable to the end of the voltage vector on the active support.
The vectors U R ,U L ,U make up a right-angle tricot. Let's see Ohm's law for the first Lanzug. On the
substantiating the Pythagorean theorem, for a rectangular tricutnik, the voltage can be:
U = (UR 2 + UL 2) 1/2.
Ale U R \u003d IR, and U L \u003d IX L, also
U \u003d (I2 R2 + I2 XL 2) 1/2 \u003d I (R2 + XL 2) 1/2,
Stars follow Ohm's law for this lancer
I = U / (R2 + XL 2) 1/2.
Let us introduce the value (R 2 + X L 2 ) 1/2 = Z de Z - the last opir of the lance. Todi Ohm's law in the future I will see:
Shards of the new opir of the lancer Z are assigned to the Pythagorean theorem, to which it is confirmed the tricutnik of supports:
The oskіlki at the last load of the voltage on the plots are directly proportional to the supports, then the tricot support is similar to the voltage of the trikutnik.
Zsuv phases between the strum and the tension vyznachaetsya from the tricot of the supports:
tg = XL/R, cos = R/Z.
For successive lancer Let's wash up kut vіd strumu vector. Oskіlki vector povnogo podіnnya vrugi razrusheniya in phase є shdo vector strum on the end of the anti-godinnikov's arrow, tsey kut may be positive.
Sumarna mitteva the voltage in lance is determined by the formula:
u = um sin(t+),
The average or active tension for the same lancet characterizes the amount of energy spent on the active support i, also
P = UR I.
UR = Ucos.
Reactive potency characterizes the intensity of energy exchange between the coil of inductance and the electrical energy:
Q=UL I
From the vector diagrams it can be seen that
UL = U sin.
The concept of total tightness is assessed for the assessment of borderline tightness electrical machines. The new tightness of the snake struma is the tightness, like going to the dzherel to the rescue and signing for the following formula:
Part of the feeling of tension in the spontaneity transforms into a core - active tension, after which there may be a mechanical movement, warmth, light and more.
Another part of the total tightness, as if it were not possible for me to calm down, I was less likely to wake up in some magnetic fields.
Spivvіdnoshennia between the values of the new, active and reactive tension well, as i mizh povnym, active and reactive stress. If all sides of the tricot are multiplied by the force of the struma I, then we take a new tricot - the tricot of tightness, the hypotenuse of some kind of more recent tightness, the horizontal leg - active tension, And the vertical leg - reactive tightness:
S = (P2 + Q2) 1/2.
The intensity is reduced in volt-amperes (VA). Mitteva tension is expressed by spivvіdnoshennia:
p = ui = um im sin (t +) sin t = um im (sin t cos + sin cos t) = um im (sin 2 cos + sin sin t cos t) = um im [cos (1 - cos 2 t )/2+
sin (sin 2 t) / 2] = (um im / 2) = UI cos - UI cos (2 t +).
in such a manner, mitteva tightness folds in the same way with UI cos - constant storage, that sinusoidal storage frequency. The energy process in Lancuse vanishes L and R is composed of two different energy processes: in the first place, energy is irrevocably transferred from the dzherel to the active opir, deva is transformed into other forms of energy; in a different way, the energy is circulating between the dzherel and the magnetic field of the primach. The smaller the cos, the bigger role is played by the central energy.
5. Electric lance with active and mnіsnym elements.
Vivchenya technique R-C lanceug similar Vivchennu R-L lanceugs.
We set the strum i = i m sin t. Then the voltage on the active support:
uR = uRm sint.
The voltage on the capacitor varies in phase in the stream per coil.
uC = uCm sin(t - /2).
Let's have a vector diagram for this lancer:
From the vector diagrams you can see that
U \u003d (UR 2 + UC 2) 1/2.
Ale U R \u003d IR, and U C \u003d IX C, also
U \u003d (I2 R2 + I2 XC 2) 1/2 \u003d I (R2 + XC 2) 1/2,
I \u003d U / (R2 + XC 2) 1/2.
Let us introduce the value (R 2 + X Z 2) 1/2 = Z , where Z is the last opir of the lance. Ohm's law for this Lanzug:
Rotation of the yogo side shows the rotation of the sides of the voltage tricot on the vector diagram. The zvv of the phases in this direction is negative, so that the voltage is in the phase in the stream:
tg \u003d - XС / R, cos \u003d R / Z.
In the energetic mode, the lancet does not interfere with the lancet with resistive and inductive elements
The average tension is marked by a constant warehouse fatigue:
Reactive pressure characterizes the intensity of the exchange of energy between the capacitor and the electrical energy:
Q = UC I sin.
so yak< 0 , то реактивная мощностьQ < 0 . Физически это означает, что когда емкость отдает энергию, индуктивность ее потребляет, если они находятся в одной цепи.
Trikutnik of tightness for a glanced Lansyug may look:
Spivvіdnoshennia between these strains can be removed from trikutnik:
S = (P2 + Q2) 1/2.
6.Electric lance with active, inductive and mnist elements.
Electric lance with the last connection of active, inductive and єmnіshnіh elementіv called the last kolyalnym contour.
Strum at the Lanciug:
Voltage on the active support:
Voltage on the inductance coil:
i = im sint.
uR = uRm sint.
uL = uLm sin(t+/2).
Capacitor voltage:
uC = uCm sin(t - /2).
Let's use the vector diagram to figure out what X L< X C , то есть U L =IX L < U C =IX C .
The vector of the resulting stress U locks the vector loop U R , U L , U C . The vector (U L + U C ) determines the voltage on the inductance and capacitance. As can be seen from the diagrams, the voltage may be less than the voltage on the inductance and capacitance. By the process of exchange of energy between inductance and capacity.
Ohm's law is taken away for the looked Lancug. The module of the vector (U L +U C ) is shown as the difference between the values (U L - U C ) , which is shown by the vector diagrams
U = (UR 2 + (UL - UC) 2) 1/2.
Ale UR \u003d IR, and UC \u003d IXC and UL \u003d IXL, also
U \u003d I (R2 + (XL - XC) 2) 1/2,
I \u003d U / (R2 + XC 2) 1/2.
Let us introduce the value (R 2 + (X L - X С ) 2 ) 1/2 = Z de Z - the last opir of the lancer. Ohm's law for this Lanzug:
The difference between the inductive and єmnіsnym support (X L - X C) is called the reactive support of the Lanziug.
Trikutnik supports for this lansyug may look:
When X L > X Z, the reactive opir is positive and the opir is active-inductive. Prix L< X С реактивное сопротивление отрицательно и сопротивление цепи носит активноемкостной характер. Знак сдвига фаз между током и напряжением получим автоматически, так как реактивное сопротивление - величина алгебраическая:
In this way, when X L X H overrides either the inductive or the imaginary opir, then from the energy point of the gap R, L і C is reduced to the Lancer R, L or R, C.
Mitteva tightness:
p = ui = UI cos – UI cos (2t+).
The sign is determined by tg = X/R. Active, reactive, and the tension of such a lancet is characterized by equalities:
P = UI cos, Q = U I sin, S = UI = (P2 + Q2) 1/2.
Tricot of tightness for this lancet may look like:
Coefficient of tension.
On the current industrial undertakings greater savings in the electric energy of the coiled stream and active-inductive induction in the sight asynchronous electric motors, power transformers, power transformers, reworking machines. In such an ambition, as a result of the overrun of the strum, the e.r.s. self-induction, which is connected to the zsuv phase between the strum and the tension. Tsej zsuv on a phase sound zbіlshuєtsya, and zmenshuєtsya at a small navantazhennі. For example, if the cos of the engine of a serpentine strum with a full thrust becomes 0.75 - 0.8, then with a small thrust of the wind it changes to
As the tightness was relieved by all the primacies in their lancets, and it was completely appointed, then with a constant pressure on the grips, the primachas of their strums:
I = P/(Ucos)
With changes in cos, the pressure of power plants and substations will increase with the same tightness that is seen.
Vodnocha electric generators, transformers and power transmission lines
pevna voltage and strum. It is not guilty to overestimate the strum at a reduced cos, so how to live their generators and to increase the nominal tension Snom = Unom Inom, after which the stench is not guilty to appear overwhelmed. In order to keep the generator strum without exceeding the nominal value with a decrease in cos, it is necessary to reduce the active pressure. In this rank, the reduction of the slowness of the increase in the constant reduction of the intensity of the synchronous generators, transformers and transmission lines. The stinks are for nothing zavantazhuyutsya for the account of the inductive jet strum
cos, which characterizes the degree of established tension, is often called the tension coefficient.
The coefficient of tension is the term for active tension to the full: cos = P/S
The tension coefficient shows that part of the electrical energy is irrevocably converted to another type of energy and, zocrema, vikoristovuetsya on vikonannya cordless roboti. Cos 0.85 - 0.9 is considered normal. With a low coefficient of exhaustion at the enterprise, which saves electricity, a fine is imposed, for a high one - the enterprise is awarded.
To improve the coefficient of tension, low visits are carried out:
1. the engines of the strumum are replaced, there is little pressure, with engines of less tightness; 2. Capacitors are switched on in parallel.
PARALLELLY Z'EDNANNYA RECEPTION IN ZMINNY STROUM.
Let's look at the electric lance, which is made up of two priymachiv, connected in parallel to the sine wave voltage.
u = um sint.
The first adopter has the following elements R1 і L, the other one has R2 і С.
Electric lances of this kind are called parallel kolyalnymi circuits.
Virazi for mittevs the meaning of strums in the first and other ridges of the looked-out lancet may have a clearly inductive and illusory character:
i1 = i1m sin(t-1); i2 = i2m sin(t+2);
Chinne significance of the struma is such a zsuvu of phases between the struma and elastically depends on the advancing viraziv:
for the first neck
I1 = U / (R1 2 + XL 2) 1/2; cos1 = R1 / (R1 2 + XL 2) 1/2;
for another nick
I2 = U / (R2 2 + XC 2) 1/2; cos2 = R2 / (R2 2 + XC 2) 1/2;
Knowing the struma in the throats, it is not possible to determine the significance of the struma in the unbroken part of the lancet, let's just add the struma i1 and i2, since in case of this it is necessary to correct the phases of the cuti1 and 2. Therefore, the strum at the unbroken part of the lancet is assigned as the geometric sum of the strum at the tails. Let's look at the vector diagram. When prompted by vector diagrams, the strums are taken as the cob vector and the stress vector is taken. Vectors of strums at the sleeves are straightened with the improvement of the current zsuv in phase according to the relation to the stress vector. The vector diagram can be seen:
Z tsієї vector diagrams indicate the magnitude of the struma in the non-decomposed part of the lancet and the zvu phases between the strum and the tension in the non-decomposed part of the lance.
The method of vector diagrams, like a graphical method, does not allow high accuracy. The quantities themselves can be determined analytically. To introduce the concept of active and reactive storage struma for the neck with the subsequent addition of active and reactive elements. The active warehouse stream runs in phase with the applied voltage. The reactive storage jet is put in when the applied voltage is applied to the coil /2:
Active folded struma in the unbroken part of the lancet is more active than the amount of active strums that are folded near the skin nail:
I a \u003d I 1a + I 2a.
De I1a = I1 cos1, I2a = I2 cos2.
The reactive storage jet in the first tube is in phase with the voltage on /2, and the reactive storage jet of the other tube
viperezhaє napruzhu /2. In this way, the reactive warehouse struma in the unbroken part of the lancelet is more diverse than the reactive struma in the first and the other tails, tobto
Ir \u003d I1r - I2r.
De I1p = I1 sin1, I2a = I2 sin2.
Viraz povnogo strumu in the unbroken part of the lancet may look
I \u003d (Ia 2 + Ir 2) 1/2.
Kut zsuvu phases, as vyplyaє z vector diagrams, signify spіvvіdnennia:
tg = Ir / Ia
At the top, if n electric receivers are connected in parallel:
I aI Rn, I pI LnI Cn.
RESONANCE REVEATING AT ZMINNY'S STROUM'S lancers.
In electrical engineering, under the resonant mode of the robotic lanceuge, the changeable struma has a mode, in which the lancer operable is purely active. According to the age of life, the elements of the lancet are driven in the resonant mode as an active support, so the strum and the voltage in the part of the ungalvanized lancet move in phase.
The reactive pressure of the lansyug is near zero.
There are two main vibrations to resonance: with the last connection of reactive elements in the circuit with a coil, there can be resonance of the voltage, and with parallel connection - resonance of the streams.
Voltage resonance. Resonance of the voltage is called the phenomenon of the lancer with the last combination of elements, if the strum of the lancer fluctuates in phase with the tension of the dzherel.
We know the resonance of the voltage. In order for the strum at the lancer to move in phase with the voltage, the reactive opir is guilty of reaching zero, since
tg = X / R = (XL - XC) / R.
In this rank, the mental resonance of the tension is equal jet prop lanceug to zero, but
XL=XC.
Ale X L \u003d L, and X C \u003d 1 / C, de - the frequency of the living room. As a result, you can write:
Virishyuchi tse urvnennya schodo know:
1/(LC)1/2 =0.
At the resonance of the voltage, the frequency of the dzherel is equal to its own frequency of the knocking circuit. Resonance of the voltage is shown by the vector diagram:
On the basis of diagrams and Ohm's law, for the first lance, we formulate signs of the resonance of the voltage.
1. The latest opir of the lansyug is minimal and purely active.
2. The strum at the lancet fluctuates in phase with the tension of the dzherel and reaches the maximum value. 3. The voltage on the coils of the inductance is higher than the voltage on the capacitors and it is possible to overestimate the voltage on the clamps of the entire lance (by 10 times). Therefore, the resonance during the last connection of the elements is called the resonance of the voltage.
The voltage resonance mode can be subtracted from the changeable frequency of the dzherel voltage at the same parameters of the elements of the bellow circuit, or by changing the parameters of the elements of the bellow circuit.
In electric power outbuildings in the majority of the voltage fluctuations, the resonance of the voltage is not a phenomenon, it is associated with unsustainable faults of the overvoltage, that is the voltage, operating voltage installations, moreover, the fuses do not protect against overvoltages.
Strum resonance. In an electric lance, with two wires connected in parallel, if the R 1 and L elements are included in one wire, and in the other R 2 and C, the strum resonance mode can be set, with which the strum in the non-decoupled part of the lance will be elastic in phase.
The resonant frequency is indicated by viraz:
0 = (1/LC)1/2 ((L/C - R1 2 )/(L/C - R2 2 ))1/2 .
It is obvious that the resonance of the strums in the lancet can be taken away by changing the frequency of the dzherel or by changing the parameters of the lancer L, C, R1, R2. The vector diagram, which shows the resonance of the strums, may look like:
At the resonance of the streams jet strum flickering in the ring, which is established by inductance and amnistyu, and the dart, which activates the kolyalny circuit from the energy source, and the core itself is more likely to rise from the jet stream.
In the mode of resonance, the streams of the lances, which are looked at, conduct themselves according to the age of life so, nibi wines are composed only of elements of active conduction. In fact, in parallel tubes with reactive elements, streaks can flow, which can be reversed top strum that flows through the life of the dzherel. Ale ci strumi zavzhdi protilezhnі phases one to one. Tse means that through the skin a quarter of the period there is an exchange of energy between the magnetic field of the coil of inductance and the electric field of the capacitor, which is supported by the tension of the body.
At resonance of the strums, the strums near the hairs can reverse the strum at the unbroken part of the lancet, like at resonance, and from the proximity of another. Therefore, the resonance with the parallel connection of the elements is called the resonance of the streams.
Resonance strum_v on vіdmіnu vіd resonance naprugi - a phenomenon, safe for electrical installations. Great strums at the resonances of the strums, the tails are blamed only for the drop, as the creation of large reactive conductivities of the tails - large batteries of capacitors, heavy reactive coils are installed.
