Thermal and dynamic current. Selection and testing of measuring current transformers. thermal current
Current-limiting reactors are tested for electrodynamic and thermal stability conditions, the following test criteria must be met:
- electrodynamic resistance: idin * iud, (3.7)
where idin - electrodynamic resistance at (amplitude value) - see tables 5.14, 5.15; for single (not twin) reactors, only idin is given, and for double reactors, the amplitude value idin and the effective value Idin of the electrodynamic resistance current are given;
taking into account current limitation, is calculated by formulas (2.40) - (2.43);
- thermal resistance:
Iter 2 ter * B, (3.8)
where Iter - thermal resistance at - see table. 5.14, 5.15;
B - thermal current pulse, taking into account the current limitation, is calculated by the formula B = Ip0 * 2(toff + Tae), (3.9)
where toff is the time of switching off by the backup protection; toff = 4 s;
Tae - equivalent time constant of attenuation of the aperiodic component of the short circuit current; Tae = 0.1 - 0.23 s.
The test results are presented in table. 3.5 - 3.7. Checking the electrodynamic and thermal resistance for reactors in the circuit of Fig. 2.1 
The indicated reactors of the RBU 10-1000-0.14U3 type are not sectional, but multi-group, because there are no short-circuit current feeding sources in the section behind the reactor, except for electric motors.
The maximum flows through the reactor at point K2. The corresponding currents, taking into account the current limitation, Ips0 = 13.1 kA and iud.s = 36.2 are calculated in Table 2.6. In terms of electrodynamic resistance, the reactors pass with a large margin - Table 3.5. 
In Table 2.8, the thermal impulse is calculated at B = 86.8 kA2 s after the reactor. Strictly speaking, the indicated thermal impulse takes into account the currents of the engines feeding behind the reactor, which do not actually flow through the reactor at point K2. But, as Table 3.5 shows, even taking into account the overestimation of the thermal impulse, thermal stability is provided with a large margin. Calculation for the SR reactor.
The maximum flows through SR-1 at section C1. The corresponding one, taking into account the current limitation, we calculate through the short circuit calculated in clause 3.2.2 Ip0vg1 = 99.9 kA:
x * (b) \u003d 99.9 1.05 5.78 \u003d 0.061; - from equation (2.31)
Ip0 \u003d 0.061 0.167 1.05 + 5.78 \u003d 26.7 kA, - formula (2.31)
where хр1*(b) = 0.167 is the resistance of the SR reactor.
kud \u003d 1 + exp (-0.01 / 0.1) \u003d 1.905 - formula (2.43)
iud \u003d 2 1.905 26.7 \u003d 71.9 kA - formula (2.42)
B \u003d 71.92 (4 + 0.1) \u003d 2923 kA2 s - formula (3.9)
Calculation for reactor P.
The maximum flows through the reactor P at section 2P.
The corresponding make-up from the system Ip0 = 15.2 kA is calculated in clause 3.2.3. The impact factor remains the same:
isp \u003d 2 1.905 15.2 \u003d 41.0 kA - formula (2.42)
B \u003d 15.22 (4 + 0.1) \u003d 947 kA2 s - formula (3.9) Calculation for the reactor Рres.
The maximum flows through the reactor Рres at directly behind the standby reactor. The calculation in this case completely coincides with the calculation for the working reactor R.
Calculation for the RS reactor.
The maximum flows through the RS reactor at 6.3 kV on group assemblies. The corresponding make-up from the system Ip0 = 13.6 kA is calculated in clause 3.2.4.
iud \u003d 2 1.905 13.6 \u003d 36.6 kA - formula (2.42) 
B \u003d 13.62 (4 + 0.1) \u003d 758 kA2 s - formula (3.9) From Table 3.6 it follows that the determining factor is the verification of reactors for electrodynamic stability. According to thermal resistance, they pass with a large margin, tk. during the flow of the thermal resistance current tter = 8 s significantly exceeds toff = 4 s in formula (3.9).
Checking the electrodynamic and thermal resistance for reactors in the circuit of Fig. 3.2
Read also:
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Busbars are selected according to the allowable heating from the condition ,
where I calc is the rated current, I additional is the long-term permissible current according to the heating condition.
Selected busbar sections must be checked for thermal and electrodynamic resistance.
When short-circuit currents pass in tires and other current-carrying parts, electrodynamic forces arise that create bending moments and stresses in the metal. The criteria for electrodynamic resistance or mechanical strength of tires are the maximum stresses, which should not exceed the values allowed for a given material.
σ r ≤ σ ext, where σ r, σ ext are, respectively, the design and allowable bending stresses of the material.
A busbar fixed on insulators can be considered as a multi-span beam. The greatest stress in the metal during bending
where M is the maximum bending moment, N m; W - moment of resistance of the tire, m 3.
When the tires are on edge, when they are flat.
Here b and h are the width (narrow side) and height (large side) of the tire section, respectively, m.
The expression for the bending moment M, created by the short-circuit shock current, can be obtained if the busbar is considered as a uniformly loaded multi-span beam.
Where l– distance between insulators, m; ζ is a coefficient equal to 10 for the outer spans and 12 for the remaining spans; F is the force of interaction between the conductors when a short-circuit shock current flows through them.
For three-phase tires, the impact current of a three-phase short circuit is taken as the calculated one. Moreover, the calculation of the electrodynamic resistance is carried out for the conductors of the middle phase, since they are affected by highest values EDU.
Here a- the distance between the tires, l is the distance between the phase insulators, K f is the form factor determined from the Dwight curves (usually K f ≈ 1).
Mechanical stresses of conductor materials should not exceed 140 MPa for copper (MT grade) and 70 MPa for aluminum (AT grade).
When calculating the breaking force on the insulator, where K n \u003d 1 when the tires are flat, K n \u003d (h from + b + 0.5h) / h from when the tires are located on the edge. For open switchgear where the insulation electrical apparatus exposed to the action of wind, ice, tension of conductors, in the calculation, a safety factor is introduced K z \u003d 3 (the load on the insulators should be 3 times less than the limiting destructive one). For closed switchgear, the safety factor is reduced to 1.5-1.7.
Tires, like any other system, perform free or natural oscillations in the form of standing waves. If the frequency of forced oscillations under the action of the EDF is close to the frequency of natural oscillations, then mechanical resonance and destruction of the device may occur even with relatively small efforts. Therefore, when calculating the electrodynamic resistance, it is necessary to take into account the possibility of mechanical resonance.
The frequency of natural oscillations of tires located in the same plane can be determined by the expression.
, where 1
- tire span, m; E is the modulus of elasticity of the tire material, Pa; J - moment of inertia cross section tires, m 4; m is the mass of one running meter of the tire, kg/m. The moment of inertia J is determined relative to the section axis perpendicular to the oscillation plane. When the tires are placed on edge, when placed flat
At a natural frequency of more than 200 Hz, the resonance phenomenon is not taken into account. If the frequency f 0< 200 Гц, то для исключения возникновения резонанса изменяют расстояние между опорными изоляторами.
To comply with the conditions of thermal resistance of tires, it is necessary that the short-circuit current passing through them does not cause an increase in temperature above the maximum allowable. The minimum thermally stable section of the busbar or conductor must meet the condition:
where V c is the calculated thermal current impulse. C - thermal coefficient (function), depends on the tire material. For practical calculations V k \u003d I ¥ 2 t pr,
where I ¥ is the effective value of the steady short circuit current; t pr - the reduced time of action of the short-circuit current.
The reduced time is understood as the time during which the steady-state short-circuit current I ¥ releases the same amount of heat as the time-varying short-circuit current during the actual time t.
t pr \u003d t pr.p + t pr.a, where t pr.p, t pr.a are the periodic and aperiodic components of the reduced short circuit time. The periodic component of time t pr.p is determined from the dependence curves t pr.p = f(β ""). Here β"" = I""/I ¥ , where I"" is the effective value of the periodic component of the short circuit current in the initial period (the initial supertransient short circuit current). If the EMF of the source is unchanged, which occurs when powered from a network of unlimited power, then it is considered that I "" = I ¥ and β "" = 1.
Reduced time of the periodic component t pr.a = 0.005β "" 2 . The thermal coefficient C can be analytically determined from the expression C = ,
where A ΘCON, A ΘNACH are thermal functions or values of root-mean-square current pulses corresponding to the final and initial temperature of the bus or conductors during short circuit, A 2 s / mm 4.
Usually, reference books give curves of temperature dependence on the values of the calculated integral A Θ for various materials. The calculation of tires for thermal resistance using these curves is carried out as follows. The allowable temperature of the conductor is set at short circuit and at rated current, then the corresponding values A ΘCON, A ΘNACH are found from the curves. For aluminum tires under nominal conditions, the initial temperature is 70 ° C, the final - permissible - 200 ° C. In this case, the thermal coefficient C \u003d 95.
Thus, for aluminum tires, the minimum thermally resistant section can be analytically found from the expression: .
With the graphic-analytical method of calculation, it is necessary that θ cr ≤ θ add, where θ cr is the temperature of the busbar heating by the short-circuit current; θ add - permissible heating temperature, depending on the tire material.
The heating temperature of the busbar by short-circuit current is determined from curves depending on the initial temperature, busbar material and thermal impulse.
4.4 Checking protective devices for thermal and dynamic resistance
Switch AE 2066MP-100
Ultimate breaking capacity Iab. pr \u003d 9 kA.
Iab. pr=9kA>Isp=3.52kA
Switch AE 2066-100
Ultimate breaking capacity Iab. pr=12 kA.
Iab. pr=12 kA>Isp=11.5 kA
The dynamic withstand for this circuit breaker is fulfilled.
Checking the release according to the condition:
where I p. max - maximum operating current of the press motor.
Fuse PN-2-100-10
U nom = 380V
I off nom > i sp 100kA > 1.94kA
I nom > I slave 100A > 10A
I nom vst > I slave 31.5A > 10A
High-voltage column SF6 circuit breaker
The heating temperature of the contact pad can be determined by the inverted Kukekov formula: , (5.9) where Tk is the maximum allowable contact heating temperature when a short circuit current flows through it ...
Dynamic processes and stability of ship electric power systems
For thermal resistance, cables are checked according to the condition q? qmin, where q is the selective section of the conductor. qmin - kvVk (for the PRC brands accepted in the project, according to Appendix 21.OST5.6181-81, we accept k = 7.3) ...
Evaluation of the correctness of the choice of the number and power of generating sets in the ship electrical network
For thermal resistance, cables are checked according to the condition q? qmin, where q is the selective section of the conductor. qmin - kvVk (for accepted in the project grades of the People's Republic of China in accordance with Appendix 21. OST5.6181-81, we accept k = 7.3) ...
The standard section of 150 mm2, selected for cables a and b in terms of heating and economic current density, should be checked for thermal resistance in short-circuit mode on the busbars of the 8 kA power supply. where is the momentum of the quadratic short-circuit current ...
Calculation of a three-unit traction substation for 10 kV
It is reduced to the determination of mechanical stress in tire materials from the action of electrodynamic forces. The highest mechanical stress in the material of rigid tires should not exceed 0.7 of the tensile strength according to the State Standard ...
Calculation of a three-unit traction substation for 10 kV
To ensure the thermal stability of the busbars during a short circuit, it is necessary that the current flowing through them does not cause an increase in temperature in excess of the maximum allowable during short-term heating, which is 300ºC for copper busbars....
Reconstruction of the power supply system of a residential microdistrict of the city
The cables selected in the normal mode and tested for permissible overload in the post-emergency mode are checked according to the condition (6.10) where SMIN is the minimum cross-section for thermal resistance, mm2; SE - economic section...
Relay protection and automation of control of power supply systems
The condition for the electrodynamic stability of TT TLK-35-50: Substituting the numerical values, we get: Thus, the current transformer TLK-35-50 is suitable according to the condition of electrodynamic stability ...
Agricultural area power supply system
The calculation is made according to the formula: , mm2, (6.13) where С is a constant, which takes the value for SIP - 3 С=; Ta.av - average value of decay time of free short-circuit currents, Ta.av = 0.02 s; - switch operation time, s, for ВВ/ТEL - 10 s...
Power supply of the sinter plant of the metallurgical plant
Let us determine the minimum cable cross-section, according to the conditions of thermal resistance, for the K-2 mm2 point, where C is the thermal function, for 6 kV cables with aluminum conductors and paper insulation C = 85 A. s2 / mm2. Let's determine the minimum cross-section of the cable ...
Electricity supply of a residential building
Checking the thermal resistance of the cable is based on the calculation of the thermal impulse - the amount of heat ...
To test conductors for thermal resistance during a short circuit, the concept of thermal impulse Bk is used, which characterizes the amount of heat ...
Power supply for a polyolefin plant
Point Scalc, kVA n Brand Fprin, mm² Bk, kA mm² qmin, mm² Fcon, mm² 1 2 3 4 5 6 7 8 2 N2XSEY 3Ch25 8.64 21.001 3Ch25 GPP-TP 7,448.98 2 N2XSEY 3Ch25 8.83 21.230 3Ch25 GPP-AD1 1485.00 2 N2XSEY 3Ch25 8.80 21...
Power supply of the mechanical assembly shop
With the passage of short-circuit current. cable, a thermal impulse is generated in the cable. The amount of heat depends on the duration of the protection, the duration of the short-circuit current and the magnitude of the short-circuit current ...
Checking tires for dynamic resistance is reduced to the mechanical calculation of the busbar structure during short circuit. The electrodynamic forces arising during short circuit are oscillatory in nature and have periodic components with a frequency of 50 and 100 Hz. These forces cause tires and insulators, which are a dynamic system, to oscillate. The deformation of structural elements and the corresponding stresses in the material depend on the components of the electrodynamic force and on the natural frequency of the elements brought into oscillation.
Particularly high voltages occur under resonance conditions, when the natural frequencies of the bus system - insulators are close to 50 and 100 Hz. In this case, the stresses in the material of the busbars and insulators can be two to three times higher than the stresses calculated from the maximum electrodynamic force during a short circuit caused by the shock short circuit current. If the natural frequencies of the system are less than 30 or more than 200 Hz, then mechanical resonance does not occur and the tires are checked for electrodynamic resistance under the assumption that the tires and insulators are a static system with a load equal to the maximum electrodynamic force during short circuit.
In most of the used tire designs, these conditions are met, and the EMP does not require checking the tires for electrodynamic resistance, taking into account mechanical vibrations.
In some cases, for example, when designing new designs of switchgear with rigid tires, the frequency of natural oscillations is determined by the following expressions:
for aluminum tires:
for copper bars:
where l - span between insulators, m;
J is the moment of inertia of the tire cross section about the axis perpendicular to the direction of the bending force, cm 4;
S - tire cross-sectional area, cm 2.
By changing the span length and the shape of the tire section, they ensure that mechanical resonance is excluded, i.e. so that v 0 > 200 Hz. If this cannot be achieved, then a special calculation of the tires is made, taking into account the dynamic forces arising from vibrations of the tire structure.
When calculating busbars as a static system, it is assumed that the busbar of each phase is a multi-span beam, freely lying on rigid supports, with a uniformly distributed load. In this case, the bending moment is determined by the expression.
where f is the force per unit length, N/m.
In the most difficult conditions, there is an average phase, which is taken as the calculated one; three-phase is taken as the calculated type of short circuit. The maximum force per unit length of the middle phase in a three-phase short circuit is equal to
where i y - shock short-circuit current, A
a is the distance between the axes of adjacent phases, m.
The stress (in megapascals) that occurs in the tire material is
where W is the moment of resistance of the tire, m 3.
This voltage must be less than the allowable voltage s add (Table 3.3) or equal to it.
The moment of resistance depends on the shape of the section of the tires, their dimensions and relative position (Fig. 3.1, 3.2). For short section bars, the moment of resistance is determined according to the same catalogs as the permissible current.
Table 3.3
Permissible mechanical stresses in the tire material
The selected span should not exceed the largest allowable value l max , determined by the expression
In multi-strip tires, when two or three strips are included in a package, electrodynamic forces arise between the phases and between the strips within the package. Forces between the strips should not lead to their contact. To give the package rigidity and prevent contact between the strips, gaskets made of tire material are installed (Fig. 3.3).
The distance between the gaskets l p is chosen so that the electrodynamic forces during a short circuit do not cause the strips to touch:
where i 2 y - shock current of a three-phase short circuit;
a p is the distance between the axes of the strips, cm;
J p \u003d hb 3 /12 - moment of inertia of the strip, cm 4;
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K f - tire shape factor (Fig. 3.4), taking into account the influence of the transverse dimensions of the conductor on the interaction force.
In order to avoid a sharp increase in the forces in the strips as a result of mechanical resonance, the natural frequency of the system must be greater than 200 Hz.
Based on this, the value of l p is selected according to one more condition:
where m p is the mass of the strip per unit length, kg/m.
The smaller of the two obtained values is taken into account.
The total stress in the tire material consists of two components - s f and s p. The voltage from the interaction of the phases s f is the same as for single-lane tires (W f is taken in accordance with Fig. 3.2). When determining the voltage from the interaction of the strips s p, the following current distribution between the strips is taken: in two-strip - 0.5i y per strip; in three-lane - 0.4i in the extreme and 0.2i in the middle. In this case, the force of interaction between the strips in two-lane tires and the force acting on the extreme strips in three-lane tires are (in newtons per meter), respectively
The strips are considered as a beam with pinned ends and a uniformly distributed load; the maximum bending moment (in newton meters) and s p (in megapascals) are determined by the expressions
The force f p at any arrangement of multi-pole tires acts on the wide edge of the bus and the moment of resistance
The tire mechanical strength condition has the form:
s calc = s f + s p £ s add.
If this condition is not met, then you should reduce s f or s p, which can be done by reducing l f or l p or increasing a or W f.
By solving the equation for s p with respect to l p, you can determine the maximum allowable distance between the gaskets
The final value of l p is taken from design considerations (the length of l p must be a multiple of l).
The mechanical calculation of box-section tires is carried out in the same way as for bipolar tires.
When calculating s f, the following is taken (Table 3.4):
If the tires are located in a horizontal plane and the channels are rigidly connected to each other by welded pads, then W calc = W y0-y0;
In the absence of a rigid connection, W calc = 2W y-y;
When the tires are located in a vertical plane, W calc = 2W x-x.
When determining the force of interaction between the channels that make up the box-section bus, take k f = 1; the distance between the axes of the conductors is taken equal to the size h, and then 
Estimated moment of resistance W p \u003d W y-y.
In a number of switchgear designs, the phase busbars are located so that the busbar sections are the vertices of a triangle - equilateral or rectangular (Table 3.4). When the tires are located at the vertices of an equilateral triangle, the tires of all phases are in the same conditions and the maximum interaction force is equal to the force acting on phase B when the tires are located in a horizontal plane. If the tires are located at the vertices of a right triangle, then the determination of the resulting forces becomes more complicated, since the phases are in different conditions. The definition of s p or l p in box tires is made in this case in the same way as when the tires are located in a horizontal or vertical plane.
Table 3.4
Formulas for calculating tires located at the vertices of a triangle
| Tire arrangement | s f max , MPa | Forces acting on insulators, N |
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Note. In the calculation formulas i y - in amperes, l and a - in meters, W - in cubic meters; F P - tensile, F And - bending and F C - compressive forces.
The mechanical load on the insulators also depends on the span l and the specific load on the busbars f. Therefore, the choice of insulators is made simultaneously with the choice of busbars. Rigid busbars are mounted on support and bushing insulators, which are selected from the conditions
U nom.set £ U nom.out; F calc £ F add,
where U nom.ust and U nom.iz - rated voltages of the installation and insulators;
F calc - force acting on the insulator;
F add - permissible load per insulator head equal to 0.6F res;
F razr - breaking load of the insulator for bending, the value of which for insulators different types are given below (in newtons):
OF-6-375, OF-10-375, OF-20-375, OF-35-375 3,750
OF-6-750, OF-10-750, OF-20-750, OF-35-750 7,500
OF-10-1250 12 500
OF-10-2000, OF-20-2000 20,000
OF-20-3000 30,000
When insulators of all phases are located in a horizontal or vertical plane, the design strength of the support insulators is determined (in newtons) by the expression F calc = f f l f k h, where k h is the correction factor for the height of the busbar, if it is installed “on edge”, k h = H /H of (H = H of + b + h/2).
When the tires are located at the vertices of the triangle F calc = k h F and (Table 3.4).
For bushings F calc = 0.5f f l f. These insulators are also selected according to the allowable current: I max £ I nom.
When choosing devices and conductors in the line circuit, it is necessary to take into account that
a) busbar branching from busbars and bushings between busbars and disconnectors (if there are separating shelves) should be selected based on a short circuit to the reactor;
b) the choice of bus disconnectors, circuit breakers, current transformers, bushings and busbars installed upstream of the reactor should be carried out according to the values of short circuit tones downstream of the reactor.
The calculated type of short circuit when checking the electrodynamic resistance of devices and rigid busbars with their supporting and supporting structures is a three-phase short circuit. Thermal stability should also be checked for a three-phase short circuit. Equipment and conductors used in circuits of generators with a capacity of 60 MW or more, as well as in circuits of generator-transformer blocks of the same power, must be checked for thermal stability, based on an estimated short circuit time of 4 s. Therefore, for the generator circuit, a three-phase and two-phase short circuit should be considered. The breaking capacity of devices in ungrounded or resonantly grounded networks (networks up to 35 kV inclusive) should be checked by the three-phase short circuit current. In effectively grounded networks (networks with a voltage of 110 kV and above), the currents are determined during a three-phase and single-phase short circuit, in order to check the breaking capacity, they do it in a more severe mode, taking into account the conditions for restoring voltage.
Test for electrodynamic resistance.
Surge short-circuit currents can cause damage to electrical apparatus and busbar structures. To prevent this from happening, each type of device is tested at the factory, setting for it the highest allowable short-circuit current (peak value of the total current) i dyn. In the literature, there is another name for this current - the limiting through short-circuit current i pr.skv.
The test condition for electrodynamic resistance has the form
i beats ≤ i dyn,
where i beats- estimated shock current in the circuit..
Thermal stability test.
Conductors and devices during a short circuit should not heat up above the permissible temperature established by the standards for short-term heating.
For the thermal stability of the devices, the condition must be met
where B to - the impulse of the quadratic short circuit current, proportional to the amount of thermal energy released during the short circuit;
I ter - rated current of thermal resistance of the device;
t ter - nominal time of thermal resistance of the device.
The device can withstand the current I ter during the time t ter.
Impulse quadratic short-circuit current
where i t is the instantaneous value of the short circuit current at the moment t;
tc - time from the beginning of the short circuit to its disconnection;
B kp - thermal impulse of the periodic component of the short circuit current;
B k.a - thermal impulse of the aperiodic component of the short circuit current.
The thermal impulse B to is defined differently depending on the location of the short circuit point in the electrical circuit.
Three main cases can be distinguished:
Remote short circuit
short circuit near generators or synchronous compensators,
short circuit near a group of powerful electric motors:
In the first case, the total thermal impulse of the short circuit
where I p.0 - effective value of the periodic component of the initial short circuit current;
T a is the decay time constant of the aperiodic component of the short circuit current.
Determining the thermal impulse Bk for the other two short-circuit cases is rather difficult. For approximate calculations, you can use the above expression B to.
According to the PUE, the trip time t otk is the sum of the time of action of the main relay protection of this circuit t r.z and the total time of the switch off t o.v;
t otk \u003d t r.z + t o.v