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Busbars are selected according to the permissible heating from the condition,
where I calculated is the calculated 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 through busbars and other live parts, electrodynamic forces arise that create bending moments and stresses in the metal. Electrodynamic resistance criteria or mechanical strength tires are the maximum stresses, which should not exceed the permissible values for a given material.
σ р ≤ σ additional, where σ р, σ additional are the calculated and permissible bending stresses of the material, respectively.
A bus mounted on insulators can be considered as a multi-span beam. The highest stress in metal during bending
where M is the maximum bending moment, N m; W – moment of resistance of the tire, m3.
When the tires are placed on edge, when they are placed flat.
Here b and h are the width (narrow side) and height (large side) of the tire section, respectively, m.
An expression for the bending moment M created by the short-circuit shock current can be obtained if we consider the tire as a uniformly loaded multi-span beam.
Where l– distance between insulators, m; ζ – coefficient equal to 10 for outer spans and 12 for other spans; F is the force of interaction between conductors when a short-circuit shock current flows through them.
For three-phase buses, the shock current of a three-phase short circuit is taken as the calculated one. Moreover, the calculation of electrodynamic resistance is carried out for conductors of the middle phase, since they are subject to highest values EDU.
Here A– distance between tires, l– distance between phase insulators, Kf – shape factor determined from Dwight curves (usually Kf ≈ 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 destructive force on an insulator, where Kn = 1 when the busbars are placed flat, Kn = (h out + b + 0.5h)/ h out when the tires are located on the edge. For open distribution devices, where the insulation of electrical devices is exposed to wind, ice, tension of conductors, a safety factor K s = 3 is introduced in the calculation (the load on the insulators should be 3 times less than the maximum destructive load). For closed reactor plants, the safety factor is reduced to 1.5-1.7.
Tires, like any other system, perform free or natural vibrations in the form of standing waves. If the frequency of forced oscillations under the influence of the EDF is close to the frequency of natural oscillations, then mechanical resonance and destruction of the apparatus 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 vibrations of tires located in the same plane can be determined by the expression.
, Where 1
– tire span, m; E – elastic modulus of the tire material, Pa; J – moment of inertia of the tire cross-section, m 4 ; m – mass of one linear meter of tire, kg/m. The moment of inertia J is determined relative to the section axis perpendicular to the plane of vibration. When the tires are placed on the edge, when the tires are placed flat
When the frequency of natural oscillations is more than 200 Hz, the phenomenon of resonance 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 thermal resistance conditions of the busbars, it is necessary that the short-circuit current passing through them does not cause an increase in temperature above the maximum permissible. The minimum thermally stable cross-section of a busbar or conductor must meet the following conditions:
where V k is the calculated thermal current pulse. C – thermal coefficient (function), depends on the tire material. For practical calculations V k = I ¥ 2 t pr,
where I ¥ is the effective value of the steady-state short-circuit current; t pr – reduced short-circuit current action time.
By reduced time we mean 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 =t pr.p + t pr.a, where t pr.p, t pr.a – 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 (initial supertransient short-circuit current). If the emf of the source is constant, which is the case 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. Thermal coefficient C can be analytically determined from the expression C =,
where A ΘKON, A ΘNACH – thermal functions or values of root-mean-square current pulses corresponding to the final and initial temperature of the bus or conductors during a short circuit, A 2 s/mm 4 .
Typically, reference books provide curves of the dependence of temperature on the values of the calculated integral A Θ for various materials. Tires are calculated for thermal resistance using these curves as follows. The permissible conductor temperature during short circuit and at rated current is set, then the corresponding values of A ΘCON, A ΘSTART are found from the curves. For aluminum tires, under nominal conditions, the initial temperature is 70 o C, the final permissible temperature is 200 o C. In this case, the thermal coefficient C = 95.
Thus, for aluminum busbars the minimum thermally resistant section can be analytically found from the expression: .
With the graphic-analytical calculation method, it is necessary that θ cr ≤ θ additional, where θ cr is the temperature of the bus heating by the short-circuit current; θ additional – 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.
The resistance of a current transformer to mechanical and thermal influences is characterized by electrodynamic resistance current and thermal resistance current.
Electrodynamic withstand current I D equal to the largest current amplitude short circuit for the entire duration of its flow, which the current transformer can withstand without damage preventing its further proper operation.
Current I D characterizes the ability of a current transformer to withstand the mechanical (electrodynamic) effects of short circuit current.
Electrodynamic resistance can also be characterized by the multiplicity K D, which is the ratio of the electrodynamic resistance current to the amplitude.
Electrodynamic resistance requirements do not apply to busbar, built-in and detachable current transformers.
Thermal current
Thermal current I tт is equal to the highest effective value of the short circuit current for the period t t, which the current transformer can withstand for the entire period of time without heating the current-carrying parts to temperatures exceeding those permissible for short circuit currents (see below), and without damage preventing its further operation.
Thermal resistance characterizes the ability of a current transformer to withstand the thermal effects of short-circuit current.
To judge the thermal resistance of a current transformer, it is necessary to know not only the values of the current passing through the transformer, but also its duration or, in other words, to know total released heat, which is proportional to the product of the square of the current I tT and its duration t T. This time, in turn, depends on the parameters of the network in which the current transformer is installed, and varies from one to several seconds.
Thermal resistance can be characterized by a factor of K T thermal resistance current, which is the ratio of the thermal resistance current to the effective value of the rated primary current.
In accordance with GOST 7746-78, the following thermal resistance currents are established for domestic current transformers:
- one second I 1T or two seconds I 2T(or their multiplicity K 1T And K 2T in relation to the rated primary current) for current transformers with rated voltages of 330 kV and above;
- one second I 1T or three second I 3T(or their multiplicity K 1T And K 3T in relation to the rated primary current) for current transformers with rated voltages up to 220 kV inclusive.
There should be the following relationships between the electrodynamic and thermal resistance currents:
for current transformers 330 kV and above
for current transformers for rated voltages up to 220 kV
Temperature conditions
The temperature of the current-carrying parts of current transformers at thermal current should not exceed:
- 200 °C for live parts made of aluminum;
- 250 °C for live parts made of copper and its alloys in contact with organic insulation or oil;
- 300 °C for live parts made of copper and its alloys not in contact with organic insulation or oil.
When determining the indicated temperature values, one should proceed from its initial values corresponding to long-term operation of the current transformer at the rated current.
Values of electrodynamic and thermal resistance currents of current transformers state standard are not standardized. However, they must correspond to the electrodynamic and thermal resistance of other devices high voltage, installed in the same circuit with a current transformer. In table 1-2 shows data on the dynamic and thermal resistance of domestic current transformers.
Table 1-2. Data on the electrodynamic and thermal resistance of some types of domestic current transformers
Note. Electrodynamic and thermal resistance depends on the mechanical strength of the insulating and current-carrying parts, as well as on the cross-section of the latter.
Current transformers are designed to reduce the primary current to values most suitable for measuring instruments and relay. (5 A, less often 1 or 2.5 A), as well as for separating control and protection circuits from primary high voltage circuits. Current transformers used in switchgear simultaneously perform the role of a bushing insulator (TPL, TPOL). Complete switchgear systems use support-through (rod) current transformers - TLM. TPLC, TNLM, bus - TSL. in switchgear 35 kV and above - built-in, depending on the type of switchgear and its voltage.
Calculation of current transformers at a substation essentially comes down to checking the current transformer supplied complete with the selected cell. So, the brand of current transformer depends on the type of cell chosen; In addition, current transformers are selected:
1) by voltage;
2) by current (primary and secondary)
It should be borne in mind that the rated secondary current of 1A is used for 500 kV switchgear and powerful 330 kV switchgear; in other cases, a secondary current of 5 A is used. The rated primary current should be as close as possible to the design current of the installation, since the primary winding is underloaded transformer leads to increased errors.
The selected current transformer is tested for dynamic and thermal resistance to short circuit currents. In addition, current transformers are selected according to the accuracy class, which must correspond to the accuracy class of the devices connected to the secondary circuit of the measuring current transformer (ICT) - In order for the current transformer to provide the specified measurement accuracy, the power of the devices connected to it should not be higher than the rated secondary load specified in current transformer data sheet.
The thermal resistance of a current transformer is compared with the thermal impulse Bk:
where is the dynamic stability coefficient.
The load on the secondary circuit of the current transformer can be calculated by the expression:
where is the sum of the resistances of all series-connected windings of devices or relays;
Resistance of connecting wires;
Resistance of contact connections ( = 0.05 Ohm, with 2 – 3 devices: with more than 3 devices = 0.1 Ohm).
The resistance of devices is determined by the formula:
Where - resistivity wires;
l calculation- estimated length of wires;
q- wire cross-section.
The length of the connecting wires depends on the connection diagram of the current transformer:
| , | (6.37) |
Where m- coefficient depending on the switching circuit;
l- length of wires (for substations they take l= 5 m).
When switching on a current transformer in one phase m= 2, when the current transformer is connected to a partial star, , when connected to a star, m =1.
The minimum cross-section of the wires of the secondary circuits of the current transformer should not be less than 2.5 mm 2 (for aluminum) and 1.5 mm 2 (for copper) in terms of mechanical strength. If meters are connected to the current transformer, these sections must be increased by one step.
In the LV substation switchgear, current transformers should be selected (checked) in the following types of cells: input, sectional, outgoing lines, as well as in auxiliary transformer cells. The calculated currents of these cells are determined by expressions (6.21-6.23), and in TSN cells:
 ,
| (6.38) |
Where S ntsn- rated power of TSN.
The calculation results are summarized in table 6.8:
Table 6.8 - Summary table for the selection of current transformers for LV substation:
| Transformer parameter | Selection (check) condition | Cell types | |||
| input | sectioning | outgoing lines | TSN | ||
| Transformer type | determined by the cell series (according to the directory) | ||||
| Rated voltage |  | ||||
| Rated current | |||||
| primary | |||||
| secondary | A | ||||
| Accuracy class | In accordance with the accuracy class of the connected devices | or | |||
| Dynamic stability |  |
||||
| Thermal stability |  |
Example 1
Select a current transformer in the power transformer input cell at the substation. The rated power of the transformer is 6.3 MVA, the transformation ratio is 110/10.5 kV. There are two transformers installed at the substation. The design load of the substation is S max 10.75 MVA. The 10 kV network is not grounded. The surge current on the low voltage side is 27.5 kA. Ammeters and active and reactive power meters must be connected to current transformers. The type of cells in RU-10 kV is KRU-2-10P.
Maximum rated current of the input cell (for the most unfavorable operating mode):
A.
Select the nearest standard current transformer built into the input cell (KRU-2-10P) - TPOL-600/5-0.5/R with two secondary windings: for measuring instruments and relay protection. The rated load of such a current transformer of accuracy class 0.5 is S 2= 10 VA ( r 2= 0.4 Ohm), multiplicity of electrodynamic stability, k din= 81, thermal stability factor, k T= 3 s. These data are indicated in /3, 10/.
The selected current transformer is tested for electrodynamic stability:
,
as well as thermal stability:
,
C from the calculation (table 4.4); T a=0.025 s according to table 4.3;
1105,92 > 121,78.
In ungrounded circuits, it is enough to have current transformers in two phases, for example, in A and C. The loads on the current transformer from the measuring instruments are determined, the data are summarized in Table 6.9:
Table 6.9 – Load of measuring instruments by phases
| Device name | ||||
| A | IN | WITH | ||
| Ammeter | N-377 | 0,1 | ||
| Active energy meter | SAZ-I673 | 2,5 | 2,5 | |
| Reactive energy meter | SRCh-I676 | 2,5 | 2,5 | |
| Total | 5,1 |
The table shows that phase A is the most loaded, its load is VA or r incoming= 
0.204 Ohm. The resistance of the connecting wires made of aluminum with a cross-section is determined q= 4 mm 2, length l= 5 m.
Om,
where = 0.0283 Ohm/m mm 2 for aluminum;
Secondary circuit impedance:
Where r contact= 0.05 Ohm.
Comparing the passport and calculated data on the secondary load of current transformers, we obtain:
Consequently, the selected current transformer passes all parameters.
When choosing devices and conductors in the line circuit, it is necessary to take into account that
a) the busbars of branches from busbars and bushings between busbars and disconnectors (if there are separating shelves) must be selected based on the short circuit to the reactor;
b) the selection of bus disconnectors, switches, current transformers, bushings and busbars installed upstream of the reactor should be made based on the values of the short circuit tones downstream of the reactor.
Calculated type of short circuit when checking the electrodynamic resistance of devices and rigid busbars with related supporting and supporting structures is a three-phase short circuit. Thermal resistance should also be checked against a three-phase short circuit. Equipment and conductors used in generator circuits with a power of 60 MW or more, as well as in generator-transformer block circuits of the same power, must be checked for thermal resistance, based on an estimated short circuit time of 4 s. Therefore, three-phase and two-phase short circuits should be considered for the generator circuit. The breaking capacity of devices in ungrounded or resonantly grounded networks (networks with voltages up to 35 kV inclusive) should be checked by three-phase short circuit current. In effectively grounded networks (networks with voltages of 110 kV and above), currents are determined during three-phase and single-phase short circuits, and the breaking capacity is checked using a more severe mode, taking into account the conditions for voltage restoration.
Electrodynamic resistance test.
Short circuit shock currents can cause breakdowns of electrical devices and busbar structures. To prevent this from happening, each type of device is tested at the factory, setting for it the highest permissible short-circuit current (amplitude value of the total current) i dyn. In the literature there is another name for this current - the maximum through short-circuit current i rms.
The test condition for electrodynamic resistance has the form
i beat ≤ i din,
Where i beat– calculated shock current in the circuit..
Thermal resistance test.
Conductors and devices during a short circuit should not heat up above permissible temperature, established by the standards for short-term heating.
For the thermal resistance of devices, the following condition must be met:
where Bk is the quadratic short circuit current pulse, proportional to the amount of thermal energy released during the short circuit;
I ter - rated current thermal resistance of the device;
t ter - the nominal time of thermal resistance of the device.
The device can withstand current I ter for a time t ter.
Square-wave short-circuit current pulse
where i t is the instantaneous value of the short circuit current at moment t;
t open – time from the beginning of a short circuit to its shutdown;
B kp - thermal impulse of the periodic component of the short circuit current;
Bk.a - thermal impulse of the aperiodic component of the short circuit current.
The thermal impulse Bk 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 is the 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 quite difficult. For approximate calculations You can use the given expression B to.
According to the PUE, the shutdown time t open is the sum of the operating time of the main relay protection of a given circuit t r.z and the total shutdown time of the circuit breaker t o.v;
t open = t r.z + t o.v
