4,523 research outputs found
Active shielding of magnetic field with circular space-time characteristic
Aim. The synthesis of two degree of freedom robust two circuit system of active shielding of magnetic field with circular spacetime characteristic, generated by overhead power lines with "triangle" type of phase conductors arrangements for reducing the magnetic flux density to the sanitary standards level and to reducing the sensitivity of the system to plant parameters uncertainty. Methodology. The synthesis is based on the multi-criteria game decision, in which the payoff vector is calculated on the basis of the Maxwell equations quasi-stationary approximation solutions. The game decision is based on the stochastic particles multiswarm optimization algorithms. The initial parameters for the synthesis by system of active shielding are the location of the overhead power lines with respect to the shielding space, geometry and number of shielding coils, operating currents, as well as the size of the shielding space and magnetic flux density normative value, which should be achieved as a result of shielding. The objective of the synthesis is to determine their number, configuration, spatial arrangementand and shielding coils currents, setting algorithm of the control systems as well as the resulting of the magnetic flux density value at the shielding space. Results. Computer simulation and field experimental research results of two degree of freedom robust two circuit system of active shielding of magnetic field, generated by overhead power lines with Β«triangleΒ» type of phase conductors arrangements are given. The possibility of initial magnetic flux density level reducing and system sensitivity reducing to the plant parameters uncertainty is shown. Originality. For the first time the synthesis, theoretical and experimental research of two degree of freedom robust two -circuit t system of active shielding of magnetic field generated by single-circuit overhead power line with phase conductors triangular arrangements carried out. Practical value. Practical recommendations from the point of view of the practical implementation on reasonable choice of the spatial arrangement of two shielding coils of robust two -circuit system of active shielding of the magnetic field with circular space-time characteristic generated by single-circuit overhead power line with phase conductors triangular arrangements are given.Π¦Π΅Π»Ρ. Π‘ΠΈΠ½ΡΠ΅Π· ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Ρ ΠΊΡΡΠ³ΠΎΠ²ΠΎΠΉ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎ-Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΎΠΉ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ² Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ ΠΈ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ. Π‘ΠΈΠ½ΡΠ΅Π· ΠΎΡΠ½ΠΎΠ²Π°Π½ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ³ΡΡ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π΅ΠΊΡΠΎΡΠ½ΡΠΉ Π²ΡΠΈΠ³ΡΡΡ Π²ΡΡΠΈΡΠ»ΡΠ΅ΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°ΠΊΡΠ²Π΅Π»Π»Π° Π² ΠΊΠ²Π°Π·ΠΈΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ³ΡΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΡΠ»ΡΡΠΈΠ°Π³Π΅Π½ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΌΡΠ»ΡΡΠΈΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ. ΠΡΡ
ΠΎΠ΄Π½ΡΠΌΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ Π΄Π»Ρ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π»ΡΡΡΡΡ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ Π²ΡΡΠΎΠΊΠΎΠ²ΠΎΠ»ΡΡΠ½ΠΎΠΉ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΏΠΎ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΊ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠΌΡ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Ρ, Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ°Π·ΠΌΠ΅ΡΡ, ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ² ΠΈ ΡΠ°Π±ΠΎΡΠΈΠ΅ ΡΠΎΠΊΠΈ Π»ΠΈΠ½ΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ°Π·ΠΌΠ΅ΡΡ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΈ Π½ΠΎΡΠΌΠ°ΡΠΈΠ²Π½ΠΎΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΠΊΠΎΡΠΎΡΠΎΠ΅ Π΄ΠΎΠ»ΠΆΠ½ΠΎ Π±ΡΡΡ Π΄ΠΎΡΡΠΈΠ³Π½ΡΡΠΎ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΠ°Π΄Π°ΡΠ΅ΠΉ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π°, ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠΎΠΊΠΎΠ² ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ, Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° ΡΠ°Π±ΠΎΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π² ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΈ ΠΏΠΎΠ»Π΅Π²ΡΡ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ². ΠΠΎΠΊΠ°Π·Π°Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΈΡΡ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΈ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΡΡΡ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Ρ ΡΠΈΠ½ΡΠ΅Π·, ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ². ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅Π½Π½ΠΎΡΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΌΡ Π²ΡΠ±ΠΎΡΡ Ρ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ Π΄Π²ΡΡ
ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Ρ ΠΊΡΡΠ³ΠΎΠ²ΠΎΠΉ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎ-Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΎΠΉ, ΡΠΎΠ·Π΄Π°Π²Π°Π΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ²
New boundary conditions for integrable lattices
New boundary conditions for integrable nonlinear lattices of the XXX type,
such as the Heisenberg chain and the Toda lattice are presented. These
integrable extensions are formulated in terms of a generic XXX Heisenberg
magnet interacting with two additional spins at each end of the chain. The
construction uses the most general rank 1 ansatz for the 2x2 L-operator
satisfying the reflection equation algebra with rational r-matrix. The
associated quadratic algebra is shown to be the one of dynamical symmetry for
the A1 and BC2 Calogero-Moser problems. Other physical realizations of our
quadratic algebra are also considered.Comment: 22 pages, latex, no figure
High voltage power lines magnetic field system of active shielding with compensation coildifferent spatial arrangement
Aim. The synthesis of single-circuit system of active shielding of magnetic field, generated by group of high voltage power lines,
with different spatial arrangement of shielding coil. Methodology. The synthesis isbased on the decisionof a multi-criteria
stochastic game, in which the vector payoff is calculated on the basis of the Maxwell equations solutions in the quasi-stationary
approximation. The game decision is based on the stochastic multiagent optimization algorithms by multiswarm particles. The
initial parameters for the synthesis of active shielding system are the location of the high voltage power lines with respect to the
shielding space, geometry and number of shielding coils, operating currents, as well as the size of the shielding space and
normative value magnetic flux density, which should be achieved as a result of shielding. The objective of the synthesis of the
active shielding system is to determine their number, configuration, spatial arrangement, wiring diagrams and shielding coils
currents, setting algorithm of the control systems as well as the resulting of the magnetic flux density value at the points ofthe
shielding space. Results. Three variant of single-circuit robust system of active shielding with different spatial arrangement of
shielding coil synthesis results for reduction of a magnetic field generated by group of high voltagepower lines is given. The
possibility of a significant reduction in the level of magnetic flux density of the magnetic field source within and reducing the
sensitivity of the system to uncertainty ofthe plant parameters is given. Originality. For the first time carried out the synthesis,
theoretical and experimentalresearch of the robust system of active shielding of magnetic field generated by group of high
voltage power lines with differentspatial arrangement of compensation coil. Practical value. Practical recommendations from the
point of view of the practical implementation on reasonable choice of the spatial arrangement of shielding coil of robust single-circuit system of active shielding of the magnetic field generated by the group of high voltage power lines is given.Π¦Π΅Π»Ρ. Π‘ΠΈΠ½ΡΠ΅Π· ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΡΠΎΠ·Π΄Π°Π²Π°Π΅ΠΌΠΎΠ³ΠΎ Π³ΡΡΠΏΠΏΠΎΠΉ
Π²ΡΡΠΎΠΊΠΎΠ²ΠΎΠ»ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ, Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΡΠΌ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ΠΌ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠ΅ΠΉ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ.
ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ. Π‘ΠΈΠ½ΡΠ΅Π· ΠΎΡΠ½ΠΎΠ²Π°Π½ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ³ΡΡ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π΅ΠΊΡΠΎΡΠ½ΡΠΉ Π²ΡΠΈΠ³ΡΡΡ Π²ΡΡΠΈΡΠ»ΡΠ΅ΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°ΠΊΡΠ²Π΅Π»Π»Π° Π² ΠΊΠ²Π°Π·ΠΈΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ³ΡΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΡΠ»ΡΡΠΈΠ°Π³Π΅Π½ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΌΡΠ»ΡΡΠΈΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ. ΠΡΡ
ΠΎΠ΄Π½ΡΠΌΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ Π΄Π»Ρ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π»ΡΡΡΡΡ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ Π²ΡΡΠΎΠΊΠΎΠ²ΠΎΠ»ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΏΠΎ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΊ Π·Π°ΡΠΈΡΠ°Π΅ΠΌΠΎΠΌΡ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Ρ, Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ°Π·ΠΌΠ΅ΡΡ, ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ² ΠΈ ΡΠ°Π±ΠΎΡΠΈΠ΅ ΡΠΎΠΊΠΈ Π»ΠΈΠ½ΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ°Π·ΠΌΠ΅ΡΡ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΈ Π½ΠΎΡΠΌΠ°ΡΠΈΠ²Π½ΠΎΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΠΊΠΎΡΠΎΡΠΎΠ΅ Π΄ΠΎΠ»ΠΆΠ½ΠΎ Π±ΡΡΡ Π΄ΠΎΡΡΠΈΠ³Π½ΡΡΠΎ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. Π¦Π΅Π»ΡΡ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π°, ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ, ΡΡ
Π΅ΠΌ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠΈΡΠ°Π½ΠΈΡ ΠΈ ΡΠΎΠΊΠΎΠ² ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠ΅ΠΉ ΠΎΠ±ΠΌΠΎΡΠΎΠΊ, Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° ΡΠ°Π±ΠΎΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π² ΡΠΎΡΠΊΠ°Ρ
ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π°. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΡΠ΅Ρ
Π²Π°ΡΠΈΠ°Π½ΡΠΎΠ² ΡΠΈΠ½ΡΠ΅Π·Π° ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΡΠΌ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ΠΌ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠ΅ΠΉ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ Π΄Π»Ρ ΡΠΌΠ΅Π½ΡΡΠ΅Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΡΠΎΠ·Π΄Π°Π²Π°Π΅ΠΌΠΎΠ³ΠΎ Π³ΡΡΠΏΠΏΠΎΠΉ Π²ΡΡΠΎΠΊΠΎΠ²ΠΎΠ»ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ. ΠΠΎΠΊΠ°Π·Π°Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΈΡΡ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΈ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΡΠΈΡΡΠ΅ΠΌΡ. ΠΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΡΡΡ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Ρ ΡΠΈΠ½ΡΠ΅Π·, ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΡΠΎΠ·Π΄Π°Π²Π°Π΅ΠΌΡΡ
Π³ΡΡΠΏΠΏΠΎΠΉ Π²ΡΡΠΎΠΊΠΎΠ²ΠΎΠ»ΡΡΠ½ΡΠΌΠΈ Π»ΠΈΠ½ΠΈΡΠΌΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°Ρ Π² ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π°, Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΡΠΌ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ΠΌ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠ΅ΠΉ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ. ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅Π½Π½ΠΎΡΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΌΡ Π²ΡΠ±ΠΎΡΡ Ρ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠ΅ΠΉ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΡΠΎΠ·Π΄Π°Π²Π°Π΅ΠΌΠΎΠ³ΠΎ Π³ΡΡΠΏΠΏΠΎΠΉ Π²ΡΡΠΎΠΊΠΎΠ²ΠΎΠ»ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°Ρ
STRUCTURAL-PARAMETRIC SYNTHESIS OF ROLLING MILLS MULTI-MOTOR ELECTRIC DRIVES
Aim. Improving of control accuracy by rolling strip thickness and tension and reducing of sensitivity to changes of plant parameters based on structural-parametric synthesis of robust control by rolling mills multi-motor electric drives with parametric uncertainty. Methodology. The method of structural-parametric synthesis of robust control by rolling mills multi-motor electric drives with parametric uncertainty which improves control accuracy by rolling strip thickness and tension and reducing of sensitivity to changes of plant parameters is developed. The method based on the multi-criteria game decision in which payoff vectors are dispersions of longitudinal thickness and tension of the rolled. The calculation of the payoff vector associated with modeling of the synthesized system with different input signals and for various values of the plant parameters for various modes of operation of the system. The multi criterion game solution is calculated based on particles multiswarm optimization algorithms. Results. The results of the structural-parametric synthesis of robust control by 740 three-stand cold rolling mills multi-motor electric drives are presented. Comparisons of the strip thickness and tension accuracy of the synthesized robust system with the existing system are completed. It is showed that the use of synthesized robust controllers allowed to improve strip thickness and tension accuracy and reduce the sensitivity of the system to changes of plant parameters in comparison with the existing system. Originality. For the first time the method of structural-parametric synthesis of robust control by rolling mills multi-motor electric drives with parametric uncertainty based on multi-criteria game decision and particles multiswarm optimization algorithms to improve the control accuracy by rolling strip thickness and tension and to reduce of sensitivity to changes of plant parameters is developed. Practical value. Practical recommendations on reasonable choice of the structure and parameters of robust control by 740 three-stand cold rolling mills multi-motor electric drives to improving of control accuracy by rolling strip thickness and tension and reducing of sensitivity to changes of plant parameters are given.Β Π¦Π΅Π»Ρ. ΠΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π³ΡΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΠ»ΡΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΡΠΎΠΊΠ°ΡΡΠ²Π°Π΅ΠΌΠΎΠΉ ΠΏΠΎΠ»ΠΎΡΡ ΠΈ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΠ΅ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΠΊ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΡΡΠΊΡΡΡΠ½ΠΎ-ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΌΠ½ΠΎΠ³ΠΎΠ΄Π²ΠΈΠ³Π°ΡΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΡΠΈΠ²ΠΎΠ΄Π°ΠΌΠΈ ΠΏΡΠΎΠΊΠ°ΡΠ½ΡΡ
ΡΡΠ°Π½ΠΎΠ² Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΡ. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΡΡΡΡΠΊΡΡΡΠ½ΠΎ-ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΌΠ½ΠΎΠ³ΠΎΠ΄Π²ΠΈΠ³Π°ΡΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΡΠΈΠ²ΠΎΠ΄Π°ΠΌΠΈ ΠΏΡΠΎΠΊΠ°ΡΠ½ΡΡ
ΡΡΠ°Π½ΠΎΠ² Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΡ, ΠΊΠΎΡΠΎΡΡΠΉ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΏΠΎΠ²ΡΡΠΈΡΡ ΡΠΎΡΠ½ΠΎΡΡΡ ΡΠ΅Π³ΡΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΠ»ΡΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΡΠΎΠΊΠ°ΡΡΠ²Π°Π΅ΠΌΠΎΠΉ ΠΏΠΎΠ»ΠΎΡΡ ΠΈ ΡΠ½ΠΈΠ·ΠΈΡΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΡ ΠΊ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΠ΅ΡΠΎΠ΄ ΠΎΡΠ½ΠΎΠ²Π°Π½ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΠΈΠ³ΡΡ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π΅ΠΊΡΠΎΡΠΎΠΌ Π²ΡΠΈΠ³ΡΡΡΠ° ΡΠ²Π»ΡΡΡΡΡ Π΄ΠΈΡΠΏΠ΅ΡΡΠΈΠΈ ΠΏΡΠΎΠ΄ΠΎΠ»ΡΠ½ΠΎΠΉ ΡΠΎΠ»ΡΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΡΠΎΠΊΠ°ΡΡΠ²Π°Π΅ΠΌΠΎΠΉ ΠΏΠΎΠ»ΠΎΡΡ. ΠΡΡΠΈΡΠ»Π΅Π½ΠΈΠ΅ Π²Π΅ΠΊΡΠΎΡΠ° Π²ΡΠΈΠ³ΡΡΡΠ° ΡΠ²ΡΠ·Π°Π½ΠΎ Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΠΈΠ½ΡΠ΅Π·ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ ΠΏΡΠΈ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
Π²Ρ
ΠΎΠ΄Π½ΡΡ
ΡΠΈΠ³Π½Π°Π»Π°Ρ
, Π΄Π»Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΈ Π² ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΡΠ΅ΠΆΠΈΠΌΠ°Ρ
ΡΠ°Π±ΠΎΡΡ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΠΈΠ³ΡΡ ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΎ Π½Π° Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°Ρ
ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΡΡΡΠΊΡΡΡΠ½ΠΎ-ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΌΠ½ΠΎΠ³ΠΎΠ΄Π²ΠΈΠ³Π°ΡΠ΅Π»ΡΠ½ΡΠΌ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΡΠΈΠ²ΠΎΠ΄ΠΎΠΌ ΡΡΠ΅Ρ
ΠΊΠ»Π΅ΡΡΠ΅Π²ΠΎΠ³ΠΎ ΡΡΠ°Π½Π° Ρ
ΠΎΠ»ΠΎΠ΄Π½ΠΎΠΉ ΠΏΡΠΎΠΊΠ°ΡΠΊΠΈ 740. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π³ΡΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΠ»ΡΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΠΎΠ»ΠΎΡΡ Π² ΡΠΈΠ½ΡΠ΅Π·ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ ΠΈ Π² ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠ΅ΠΉ ΡΠΈΡΡΠ΅ΠΌΠ°Ρ
. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΡΠΈΠ½ΡΠ΅Π·ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠ³ΠΎ ΡΠ΅Π³ΡΠ»ΡΡΠΎΡΠ° ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΎ ΠΏΠΎΠ²ΡΡΠΈΡΡ ΡΠΎΡΠ½ΠΎΡΡΡ ΡΠ΅Π³ΡΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΠ»ΡΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΠΎΠ»ΠΎΡΡ ΠΈ ΡΠ½ΠΈΠ·ΠΈΡΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΏΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Ρ ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠ΅ΠΉ ΡΠΈΡΡΠ΅ΠΌΠΎΠΉ. ΠΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΡΡΡ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΡΡΡΡΠΊΡΡΡΠ½ΠΎ-ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΌΠ½ΠΎΠ³ΠΎΠ΄Π²ΠΈΠ³Π°ΡΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΡΠΈΠ²ΠΎΠ΄Π°ΠΌΠΈ ΠΏΡΠΎΠΊΠ°ΡΠ½ΡΡ
ΡΡΠ°Π½ΠΎΠ² Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΠΈΠ³ΡΡ ΠΈ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ Π΄Π»Ρ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π³ΡΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΠ»ΡΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΡΠΎΠΊΠ°ΡΡΠ²Π°Π΅ΠΌΠΎΠΉ ΠΏΠΎΠ»ΠΎΡΡ ΠΈ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΠΊ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅Π½Π½ΠΎΡΡΡ. ΠΠ°Π½Ρ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΌΡ Π²ΡΠ±ΠΎΡΡ ΡΡΡΡΠΊΡΡΡΡ ΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΡΡΠ΅Ρ
ΠΊΠ»Π΅ΡΡΠ΅Π²ΡΠΌ ΡΡΠ°Π½ΠΎΠΌ Ρ
ΠΎΠ»ΠΎΠ΄Π½ΠΎΠΉ ΠΏΡΠΎΠΊΠ°ΡΠΊΠΈ 740 Π΄Π»Ρ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π³ΡΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΠ»ΡΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΡΠΎΠΊΠ°ΡΡΠ²Π°Π΅ΠΌΠΎΠΉ ΠΏΠΎΠ»ΠΎΡΡ ΠΈ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΠ΅ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΠΊ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ.
SIMPLIFIED MATHEMATICAL MODEL OF GROUP OF OVERHEAD POWER LINES MAGNETIC FIELD
Aim. The method for design of simplified mathematical model of the group of overhead power lines magnetic field allowing to reduce the number of conductors which are taken into account in the model and field and allowing to reduce the sensitivity of the model to plant parameters uncertainty is developed. Methodology. The method based on the multi-criteria game decision, in which the payoff vector is calculated on the basis of the Maxwell equations quasi-stationary approximation solutions. The game decision based on the stochastic particles multiswarm optimization algorithms. The implementation of the method is carried out when determining the number, configuration, spatial arrangement and currents in conductors based on simplified mathematical model of the group of overhead power line magnetic field in a given space area. Results. Computer simulation and field experimental research results of simplified mathematical model on the example of the group of four overhead power lines magnetic field including 21 conductors where based on the developed simplified mathematical model of the magnetic field, the number of conductors taken into account in the model is reduced to 6, and the modeling error does not exceed 4 %. Originality. For the first time the method for design of simplified mathematical model of the group of overhead power lines magnetic field based on the stochastic particles multiswarm optimization algorithms, which allows to significantly simplify the simulation by reducing the number of conductors that are taken into account in the model and to reduce the sensitivity of the model to plant parameters uncertainty, and at the same time limit the modeling error at the engineering level to 5-10 %. Practical value. Practical recommendations on reasonable choice of the minimal number, configuration, spatial arrangement and currents in conductors for the simplified mathematical model of the group of overhead power line magnetic field.Β Π¦Π΅Π»Ρ. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΡΠΏΡΠΎΡΠ΅Π½Π½ΠΎΠΉ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π³ΡΡΠΏΠΏΡ Π²ΠΎΠ·Π΄ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠΉ ΡΠΌΠ΅Π½ΡΡΠΈΡΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊΠΎΠ², ΠΊΠΎΡΠΎΡΡΠ΅ ΡΡΠΈΡΡΠ²Π°ΡΡΡΡ Π² ΠΌΠΎΠ΄Π΅Π»ΠΈ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ. ΠΠ΅ΡΠΎΠ΄ ΠΎΡΠ½ΠΎΠ²Π°Π½ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ³ΡΡ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π΅ΠΊΡΠΎΡΠ½ΡΠΉ Π²ΡΠΈΠ³ΡΡΡ Π²ΡΡΠΈΡΠ»ΡΠ΅ΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°ΠΊΡΠ²Π΅Π»Π»Π° Π² ΠΊΠ²Π°Π·ΠΈΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ³ΡΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΡΠ»ΡΡΠΈΠ°Π³Π΅Π½ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΌΡΠ»ΡΡΠΈΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ. Π Π΅Π°Π»ΠΈΠ·Π°ΡΠΈΡ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΠ΅ΡΡΡ ΠΏΡΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΈ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π°, ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠΎΠΊΠΎΠ² Π² ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊΠ°Ρ
Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠΏΡΠΎΡΠ΅Π½Π½ΠΎΠΉ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π³ΡΡΠΏΠΏΡ Π²ΠΎΠ·Π΄ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π² Π·Π°Π΄Π°Π½Π½ΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π°. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΠΏΠΎΠ»Π΅Π²ΡΡ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ Π³ΡΡΠΏΠΏΡ ΠΈΠ· ΡΠ΅ΡΡΡΠ΅Ρ
Π²ΠΎΠ·Π΄ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ, ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠ΅ΠΉ 21ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊ, Π³Π΄Π΅ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π½ΠΎΠΉ ΡΠΏΡΠΎΡΠ΅Π½Π½ΠΎΠΉ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΠΈΡΡΠ²Π°Π΅ΠΌΡΡ
Π² ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊΠΎΠ² ΡΠΌΠ΅Π½ΡΡΠ΅Π½ΠΎ Π΄ΠΎ 6, Π° ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈ ΡΡΠΎΠΌ Π½Π΅ ΠΏΡΠ΅Π²ΡΡΠ°Π΅Ρ 4 %. ΠΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΡΡΡ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΡΠΏΡΠΎΡΠ΅Π½Π½ΠΎΠΉ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π³ΡΡΠΏΠΏΡ Π²ΠΎΠ·Π΄ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΡΠ»ΡΡΠΈΠ°Π³Π΅Π½ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΌΡΠ»ΡΡΠΈΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠΉ ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ ΡΠΏΡΠΎΡΡΠΈΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π·Π° ΡΡΠ΅Ρ ΡΠΌΠ΅Π½ΡΡΠ΅Π½ΠΈΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊΠΎΠ², ΠΊΠΎΡΠΎΡΡΠ΅ ΡΡΠΈΡΡΠ²Π°ΡΡΡΡ Π² ΠΌΠΎΠ΄Π΅Π»ΠΈ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ, ΠΈ ΠΏΡΠΈ ΡΡΠΎΠΌ ΠΎΠ³ΡΠ°Π½ΠΈΡΠΈΡΡ ΠΏΠΎΠ³ΡΠ΅ΡΠ½ΠΎΡΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π° ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎΠΌ ΡΡΠΎΠ²Π½Π΅ 5-10 %. ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅Π½Π½ΠΎΡΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΌΡ Π²ΡΠ±ΠΎΡΡ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π°, ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠΎΠΊΠΎΠ² Π² ΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΈΠΊΠ°Ρ
ΡΠΏΡΠΎΡΠ΅Π½Π½ΠΎΠΉ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΡΠΎΠ·Π΄Π°Π²Π°Π΅ΠΌΠΎΠ³ΠΎ Π³ΡΡΠΏΠΏΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ
The effectiveness of active shielding of magnetic field with circular spacetime characteristic and with different shielding coils spatial positions
Computer simulation and field experimental research results of two degree of freedom robust two circuit system of active shielding of magnetic field, generated by overhead power lines with Β«triangleΒ» type of phase conductors arrangements and with different shielding coils spatial positions are given. The possibility of initial
magnetic flux density level reducing and system sensitivity to the plant parameters uncertainty reducing is shown.ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΠΏΠΎΠ»Π΅Π²ΡΡ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ², ΠΈ Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΡΠΌ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ΠΌ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ. ΠΠΎΠΊΠ°Π·Π°Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΈΡΡ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΈ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ
EffectiveSan: Type and Memory Error Detection using Dynamically Typed C/C++
Low-level programming languages with weak/static type systems, such as C and
C++, are vulnerable to errors relating to the misuse of memory at runtime, such
as (sub-)object bounds overflows, (re)use-after-free, and type confusion. Such
errors account for many security and other undefined behavior bugs for programs
written in these languages. In this paper, we introduce the notion of
dynamically typed C/C++, which aims to detect such errors by dynamically
checking the "effective type" of each object before use at runtime. We also
present an implementation of dynamically typed C/C++ in the form of the
Effective Type Sanitizer (EffectiveSan). EffectiveSan enforces type and memory
safety using a combination of low-fat pointers, type meta data and type/bounds
check instrumentation. We evaluate EffectiveSan against the SPEC2006 benchmark
suite and the Firefox web browser, and detect several new type and memory
errors. We also show that EffectiveSan achieves high compatibility and
reasonable overheads for the given error coverage. Finally, we highlight that
EffectiveSan is one of only a few tools that can detect sub-object bounds
errors, and uses a novel approach (dynamic type checking) to do so.Comment: To appear in the Proceedings of 39th ACM SIGPLAN Conference on
Programming Language Design and Implementation (PLDI2018
Reduction of magnetic field level in residential old buildings from overhead power lines by means of active screening
Aim. Reduction of the magnetic field induction to the level of modern sanitary standards by means of active screening in residential old buildings which are located near existing typical overhead power lines are considered. Active shielding of the magnetic field inside a single-storey and multi-storey building is considered. During the design the number, configurations, spatial arrangement of the shielding windings, as well as the currents in the shielding windings were determined. Methodology. The design problem for the system of active shielding reduced to solving the minimax vector optimization problem. The vector of objective function in this minimax problem is calculated based on Biot-Savart's law. The solution of this problem is based on multi-agent optimization algorithms. Results. The results of theoretical and experimental studies of the systems of active shielding of the magnetic field generated by various overhead power lines inside a single and multi-storey building are presented. Originality. The possibility of reducing the induction of the initial magnetic field inside the shielded space to the level of sanitary standards is shown. Practical value. From the point of view of the practical implementation for a reasonable choice of the number and spatial arrangement of shielding windings of systems for active shielding of the magnetic field generated by various overhead power lines inside residential buildings of different storeyβs are given.ΠΠ΅ΡΠ°. Π ΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ Π·Π½ΠΈΠΆΠ΅Π½Π½Ρ ΡΠ½Π΄ΡΠΊΡΡΡ ΠΌΠ°Π³Π½ΡΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π΄ΠΎ ΡΡΠ²Π½Ρ ΡΡΡΠ°ΡΠ½ΠΈΡ
ΡΠ°Π½ΡΡΠ°ΡΠ½ΠΈΡ
Π½ΠΎΡΠΌ Π·Π° ΡΠ°Ρ
ΡΠ½ΠΎΠΊ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π΅ΠΊΡΠ°Π½ΡΠ²Π°Π½Π½Ρ Π² ΠΆΠΈΡΠ»ΠΎΠ²ΠΈΡ
Π±ΡΠ΄ΠΈΠ½ΠΊΠ°Ρ
ΡΡΠ°ΡΠΎΡ Π·Π°Π±ΡΠ΄ΠΎΠ²ΠΈ, ΡΠΎΠ·ΡΠ°ΡΠΎΠ²Π°Π½ΠΈΡ
ΠΏΠΎΠ±Π»ΠΈΠ·Ρ ΡΡΠ½ΡΡΡΠΈΡ
ΡΠΈΠΏΠΎΠ²ΠΈΡ
ΠΏΠΎΠ²ΡΡΡΡΠ½ΠΈΡ
Π»ΡΠ½ΡΠΉ Π΅Π»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΡ. Π ΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ Π°ΠΊΡΠΈΠ²Π½Π΅ Π΅ΠΊΡΠ°Π½ΡΠ²Π°Π½Π½Ρ ΠΌΠ°Π³Π½ΡΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²ΡΠ΅ΡΠ΅Π΄ΠΈΠ½Ρ ΠΎΠ΄Π½ΠΎΠΏΠΎΠ²Π΅ΡΡ
ΠΎΠ²ΠΎΠ³ΠΎ Ρ Π±Π°Π³Π°ΡΠΎΠΏΠΎΠ²Π΅ΡΡ
ΠΎΠ²ΠΎΠ³ΠΎ Π±ΡΠ΄ΠΈΠ½ΠΊΡ. ΠΡΠΈ ΠΏΡΠΎΠ΅ΠΊΡΡΠ²Π°Π½Π½Ρ Π²ΠΈΠ·Π½Π°ΡΠ°Π»ΠΈΡΡ ΠΊΡΠ»ΡΠΊΡΡΡΡ, ΠΊΠΎΠ½ΡΡΠ³ΡΡΠ°ΡΡΡ, ΠΏΡΠΎΡΡΠΎΡΠΎΠ²Π΅ ΡΠΎΠ·ΡΠ°ΡΡΠ²Π°Π½Π½Ρ Π΅ΠΊΡΠ°Π½ΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ, Π° ΡΠ°ΠΊΠΎΠΆ ΡΡΡΡΠΌΠΈ Π² Π΅ΠΊΡΠ°Π½ΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΊΠ°Ρ
. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΡΡ. ΠΠ°Π²Π΄Π°Π½Π½Ρ ΠΏΡΠΎΠ΅ΠΊΡΡΠ²Π°Π½Π½Ρ ΡΠΈΡΡΠ΅ΠΌΠΈ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π΅ΠΊΡΠ°Π½ΡΠ²Π°Π½Π½Ρ Π·Π²ΠΎΠ΄ΠΈΡΡΡΡ Π΄ΠΎ Π²ΠΈΡΡΡΠ΅Π½Π½Ρ Π·Π°Π΄Π°ΡΡ ΠΌΡΠ½ΡΠΌΠ°ΠΊΡΠ½ΠΎΡ Π²Π΅ΠΊΡΠΎΡΠ½ΠΎΡ ΠΎΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ. ΠΠ΅ΠΊΡΠΎΡ ΡΡΠ»ΡΠΎΠ²ΠΎΡ ΡΡΠ½ΠΊΡΡΡ Π² ΡΡΠΉ ΠΌΡΠ½ΡΠΌΠ°ΠΊΡΠ½ΡΠΉ Π·Π°Π΄Π°ΡΡ ΠΎΠ±ΡΠΈΡΠ»ΡΡΡΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Ρ Π·Π°ΠΊΠΎΠ½Ρ ΠΡΠΎ-Π‘Π°Π²Π°ΡΠ°. ΠΠΈΡΡΡΠ΅Π½Π½Ρ ΡΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠΈ Π³ΡΡΠ½ΡΡΡΡΡΡΡ Π½Π° Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°Ρ
Π±Π°Π³Π°ΡΠΎΠ°Π³Π΅Π½ΡΠ½ΠΎΡ ΠΎΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ½ΠΈΡ
Ρ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΈΡ
Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Ρ ΡΠΈΡΡΠ΅ΠΌ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π΅ΠΊΡΠ°Π½ΡΠ²Π°Π½Π½Ρ ΠΌΠ°Π³Π½ΡΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΡΠΎ ΡΡΠ²ΠΎΡΡΡΡΡΡΡ ΡΡΠ·Π½ΠΈΠΌΠΈ ΠΏΠΎΠ²ΡΡΡΡΠ½ΠΈΠΌΠΈ Π»ΡΠ½ΡΡΠΌΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΡ Π²ΡΠ΅ΡΠ΅Π΄ΠΈΠ½Ρ ΠΎΠ΄Π½ΠΎ- Ρ Π±Π°Π³Π°ΡΠΎΠΏΠΎΠ²Π΅ΡΡ
ΠΎΠ²ΠΎΠ³ΠΎ Π±ΡΠ΄ΠΈΠ½ΠΊΡ. ΠΡΠΈΠ³ΡΠ½Π°Π»ΡΠ½ΡΡΡΡ. ΠΠΎΠΊΠ°Π·Π°Π½Π° ΠΌΠΎΠΆΠ»ΠΈΠ²ΡΡΡΡ Π·Π½ΠΈΠΆΠ΅Π½Π½Ρ ΡΠ½Π΄ΡΠΊΡΡΡ ΠΏΠΎΡΠ°ΡΠΊΠΎΠ²ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΡΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²ΡΠ΅ΡΠ΅Π΄ΠΈΠ½Ρ ΠΏΡΠΎΡΡΠΎΡΡ, ΡΠΎ Π΅ΠΊΡΠ°Π½ΡΡΡΡΡΡ, Π΄ΠΎ ΡΡΠ²Π½Ρ ΡΠ°Π½ΡΡΠ°ΡΠ½ΠΈΡ
Π½ΠΎΡΠΌ. ΠΡΠ°ΠΊΡΠΈΡΠ½Π° ΡΡΠ½Π½ΡΡΡΡ. Π ΡΠΎΡΠΊΠΈ Π·ΠΎΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΎΡ ΡΠ΅Π°Π»ΡΠ·Π°ΡΡΡ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΡ Π΄Π»Ρ ΠΎΠ±Π³ΡΡΠ½ΡΠΎΠ²Π°Π½ΠΎΠ³ΠΎ Π²ΠΈΠ±ΠΎΡΡ ΠΊΡΠ»ΡΠΊΠΎΡΡΡ Ρ ΠΏΡΠΎΡΡΠΎΡΠΎΠ²ΠΎΠ³ΠΎ ΡΠΎΠ·ΡΠ°ΡΡΠ²Π°Π½Π½Ρ Π΅ΠΊΡΠ°Π½ΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ ΡΠΈΡΡΠ΅ΠΌ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π΅ΠΊΡΠ°Π½ΡΠ²Π°Π½Π½Ρ ΠΌΠ°Π³Π½ΡΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΡΠΎ ΡΡΠ²ΠΎΡΡΡΡΡΡΡ ΡΡΠ·Π½ΠΈΠΌΠΈ ΠΏΠΎΠ²ΡΡΡΡΠ½ΠΈΠΌΠΈ Π»ΡΠ½ΡΡΠΌΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°Ρ Π²ΡΠ΅ΡΠ΅Π΄ΠΈΠ½Ρ ΠΆΠΈΡΠ»ΠΎΠ²ΠΈΡ
Π±ΡΠ΄ΠΈΠ½ΠΊΡΠ² ΡΡΠ·Π½ΠΎΡ ΠΏΠΎΠ²Π΅ΡΡ
ΠΎΠ²ΠΎΡΡΡ
Overhead power lines magnetic field reducing in multi-story building by active shielding means
Aim. Reducing of magnetic flux density of magnetic field in multi-storey building, generated by overhead power lines to the sanitary standards level by active shielding means. The tasks of the work are the synthesis, computer simulation and experimental research of three-circuits system of active shielding, which includes three shielding coils. Methodology. When synthesizing the system of active shielding of magnetic field, are determined their number, configuration, spatial arrangement and of shielding coils as well as the shielding coils currents and resulting magnetic flux density value in the shielding space. The synthesis is based on the multi-criteria game decision, in which the payoff vector is calculated on the basis on quasi-stationary approximation solutions of the Maxwell equations. The game decision is based on the stochastic particles multiswarm optimization algorithms. Results. Computer simulation and experimental research of three-circuit system of active shielding of magnetic field, generated by overhead power lines with phase conductors triangle arrangements in multi-storey building are given. The possibility of initial magnetic flux density level reducing in multi-storey building to the sanitary standards level is shown. Originality. For the first time to reducing of magnetic flux density of magnetic field in multi-storey building the synthesis, computer simulation and experimental research of three-circuit system of active shielding of magnetic field generated by single-circuit overhead power line with phase conductors triangular arrangements carried out. Practical value. Practical recommendations from the point of view of the practical implementation on reasonable choice of the spatial arrangement of three shielding coils of three-circuit system of active shielding of the magnetic field generated by single-circuit overhead power line with phase conductors triangular arrangements in multi-storey building are given.Π¦Π΅Π»Ρ. Π‘Π½ΠΈΠΆΠ΅Π½ΠΈΠ΅ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ°, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΡΠ΅ΠΏΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ. ΠΠ°Π΄Π°ΡΠ°ΠΌΠΈ ΡΠ°Π±ΠΎΡΡ ΡΠ²Π»ΡΡΡΡΡ ΡΠΈΠ½ΡΠ΅Π·, ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠ΅ΠΉ ΡΡΠΈ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΠ΅ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ. ΠΡΠΈ ΡΠΈΠ½ΡΠ΅Π·Π΅ ΡΠΈΡΡΠ΅ΠΌΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ β ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ, ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΡ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠΎΠΊΠΈ Π² ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΊΠ°Ρ
ΠΈ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠΈΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π² ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. Π‘ΠΈΠ½ΡΠ΅Π· ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΎΡΠ½ΠΎΠ²Π°Π½ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ³ΡΡ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π΅ΠΊΡΠΎΡΠ½ΡΠΉ Π²ΡΠΈΠ³ΡΡΡ Π²ΡΡΠΈΡΠ»ΡΠ΅ΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°ΠΊΡΠ²Π΅Π»Π»Π° Π² ΠΊΠ²Π°Π·ΠΈΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ³ΡΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΡΠ»ΡΡΠΈΠ°Π³Π΅Π½ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΌΡΠ»ΡΡΠΈΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ°, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ. ΠΠΎΠΊΠ°Π·Π°Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΈΡΡ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ° Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ. ΠΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΡΡΡ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ° Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ, ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Ρ ΡΠΈΠ½ΡΠ΅Π·, ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΡΠ΅ΠΏΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ². ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅Π½Π½ΠΎΡΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΌΡ Π²ΡΠ±ΠΎΡΡ, Ρ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΡΡΠ΅Ρ
ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΠΎΡ Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ° ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ²
Overhead power lines magnetic field reducing in multi-story building by active shielding means
Aim. Reducing of magnetic flux density of magnetic field in multi-storey building, generated by overhead power lines to the sanitary standards level by active shielding means. The tasks of the work are the synthesis, computer simulation and experimental research of three-circuits system of active shielding, which includes three shielding coils. Methodology. When synthesizing the system of active shielding of magnetic field, are determined their number, configuration, spatial arrangement and of shielding coils as well as the shielding coils currents and resulting magnetic flux density value in the shielding space. The synthesis is based on the multi-criteria game decision, in which the payoff vector is calculated on the basis on quasi-stationary approximation solutions of the Maxwell equations. The game decision is based on the stochastic particles multiswarm optimization algorithms. Results. Computer simulation and experimental research of three-circuit system of active shielding of magnetic field, generated by overhead power lines with phase conductors triangle arrangements in multi-storey building are given. The possibility of initial magnetic flux density level reducing in multi-storey building to the sanitary standards level is shown. Originality. For the first time to reducing of magnetic flux density of magnetic field in multi-storey building the synthesis, computer simulation and experimental research of three-circuit system of active shielding of magnetic field generated by single-circuit overhead power line with phase conductors triangular arrangements carried out. Practical value. Practical recommendations from the point of view of the practical implementation on reasonable choice of the spatial arrangement of three shielding coils of three-circuit system of active shielding of the magnetic field generated by single-circuit overhead power line with phase conductors triangular arrangements in multi-storey building are given.Π¦Π΅Π»Ρ. Π‘Π½ΠΈΠΆΠ΅Π½ΠΈΠ΅ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ°, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΡΠ΅ΠΏΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ. ΠΠ°Π΄Π°ΡΠ°ΠΌΠΈ ΡΠ°Π±ΠΎΡΡ ΡΠ²Π»ΡΡΡΡΡ ΡΠΈΠ½ΡΠ΅Π·, ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠ΅ΠΉ ΡΡΠΈ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΠ΅ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ. ΠΡΠΈ ΡΠΈΠ½ΡΠ΅Π·Π΅ ΡΠΈΡΡΠ΅ΠΌΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ β ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ, ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΡ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠΎΠΊΠΈ Π² ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΊΠ°Ρ
ΠΈ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠΈΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π² ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. Π‘ΠΈΠ½ΡΠ΅Π· ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΎΡΠ½ΠΎΠ²Π°Π½ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ³ΡΡ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π΅ΠΊΡΠΎΡΠ½ΡΠΉ Π²ΡΠΈΠ³ΡΡΡ Π²ΡΡΠΈΡΠ»ΡΠ΅ΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°ΠΊΡΠ²Π΅Π»Π»Π° Π² ΠΊΠ²Π°Π·ΠΈΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ³ΡΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΡΠ»ΡΡΠΈΠ°Π³Π΅Π½ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΌΡΠ»ΡΡΠΈΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ°, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ. ΠΠΎΠΊΠ°Π·Π°Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΈΡΡ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ° Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ. ΠΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΡΡΡ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ° Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ, ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Ρ ΡΠΈΠ½ΡΠ΅Π·, ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΡΠ΅ΠΏΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ². ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅Π½Π½ΠΎΡΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΌΡ Π²ΡΠ±ΠΎΡΡ, Ρ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΡΡΠ΅Ρ
ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ ΡΡΠ΅Ρ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΠΎΡ Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ Π²Π½ΡΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΡΡΠ°ΠΆΠ½ΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ° ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ²
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