Готман В.И. Короткие замыкания и несимметричные режимы в электроэнергетических системах

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Ɋɢɫ. 10.1. ɋɯɟɦɵ ɜɵɞɚɱɢ ɦɨ

30–100 Ɇȼɬ; ɛ



ɛɥɨɱɧɵɟ ɫ

ɫɬɚɧɰɢ

ɗɮɮɟɤɬɢɜɧɵɦ ɫɯɟɦ

ɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɜ ɪɚɫɩɪɟɞ

ɧɚɩɪɹɠɟɧɢɣ ɹɜɥɹɟɬɫɹ ɨɩɬ

ɧɢɹ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɪɟɚɥɢ

ɫɟɬɟɣ. Ɉɧɨ ɩɪɢɦɟɧɹɟɬɫɹ ɞ

ɩɪɹɠɟɧɢɹ, ɩɪɢɧɚɞɥɟɠɚɳ

ɋɜɹɡɶ ɷɬɢɯ ɫɟɬɟɣ ɱɟɪɟɡ ɫɟ

ɡɜɨɥɹɟɬ ɫɧɢɡɢɬɶ ɭɪɨɜɟɧɶ ɬ

Ɋɢɫ. 10.2. Ɉɩɬɢɦɢɡɚɰ

ɢ ɛ –

ɟɫɬ

Ɇɟɫɬɧɨɟ, ɢɥɢ ɩɨɩɟɪ

ɷɥɟɤɬɪɨɫɧɚɛɠɟɧɢɟ ɟɞɢɧɨɝ

ɩɪɟɞɟɥɢɬɟɥɶɧɵɦɢ ɫɟɬɹɦɢ

ɡɶɸ ɱɟɪɟɡ ɫɟɬɶ ɩɨɜɵɲɟɧɧ

ɫɬɚɛɢɥɢɡɢɪɨɜɚɬɶ ɭɪɨɜɟɧɶ

ɨɫɬɟ ɷɥɟɤɬɪɨɩɨɬɪɟɛɥɟɧɢɹ.

221

ɧɨɫɬɢ ɷɥɟɤɬɪɨɫɬɚɧɰɢɣ:



Ɍɗɐ ɫ ɝɟɧɟ

ɚɧɰɢɢ ɫ ɝɟɧɟɪɚɬɨɪɚɦɢ 100–300 Ɇȼɬ; ɜ



ɫ ɝɟɧɟɪɚɬɨɪɚɦɢ 500–1200 Ɇȼɬ

ɵɦ ɪɟɲɟɧɢɟɦ ɩɨ ɨɝɪɚɧɢɱɟɧɢɸ ɬɨɤɨ

ɥɢɬɟɥɶɧɵɯ ɫɟɬɹɯ ɫɪɟɞɧɟɝɨ ɢ ɧɢɡɲɟɝ

ɦɢɡɚɰɢɹ ɫɬɪɭɤɬɭɪɵ ɫɢɫɬɟɦɵ ɷɥɟɤɬɪ

ɭɸɬ ɩɟɪɢɮɟɪɢɣɧɨɟ (ɩɪɨɞɨɥɶɧɨɟ) ɪɚ

ɹ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯ ɫɟɬɟɣ ɨɞɧɨɝɨ ɤ

ɯ ɪɚɡɥɢɱɧɵɦ ɬɟɪɪɢɬɨɪɢɚɥɶɧɵɦ

ɶ ɩɨɜɵɲɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ (ɪɢɫ. 10.

ɤɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ.

ɹ ɫɬɪɭɤɬɭɪɵ ɫɟɬɢ: ɚ –

ɩɟɪɢɮɟɪɢɣɧɨɟ (ɩɪ

ɨɟ (ɩɨɩɟɪɟɱɧɨɟ) ɪɚɡɞɟɥɟɧɢɟ ɫɟɬɢ

ɟɱɧɨɟ, ɪɚɡɞɟɥɟɧɢɟ ɫɟɬɟɣ (ɪɢɫ. 10.2,

ɬɟɪɪɢɬɨɪɢɚɥɶɧɨɝɨ ɪɚɣɨɧɚ ɞɜɭɦɹ ɢ ɛ

ɞɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɤɥɚɫɫɚ ɧɚɩɪɹɠɟɧɢɹ

ɨɝɨ ɧɚɩɪɹɠɟɧɢɹ. Ⱦɚɧɧɨɟ ɪɟɲɟɧɢɟ ɩ

ɨɤɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɩɪɢ ɡɧɚɱ

ɚɬɨɪɚɦɢ

ɨɱɧɵɟ

ɤɨɪɨɬ-

ɨ ɤɥɚɫɫɚ

ɫɧɚɛɠɟ-

ɞɟɥɟɧɢɟ

ɚɫɫɚ ɧɚ-

ɚɣɨɧɚɦ.

2, ɚ) ɩɨ-

ɞɨɥɶɧɨɟ)

ɛ) – ɷɬɨ

ɥɟɟ ɪɚɫ-

ɢɯ ɫɜɹ-

ɡɜɨɥɹɟɬ

ɬɟɥɶɧɨɦ

10.3. Ɍɭɛɱɣɩɨɛɫɨ

Ⱦɟɥɟɧɢɟ ɫɟɬɢ ɩɪɢɦɟ

ɫɹ ɨɝɪɚɧɢɱɢɬɶ ɭɪɨɜɧɢ ɬɨɤ

ɬɢ ɫɬɚɰɢɨɧɚɪɧɨɟ (ɋȾɋ) ɢ ɚ

ɋɬɚɰɢɨɧɚɪɧɨɟ ɞɟɥɟɧ

ɫ ɩɨɦɨɳɶɸ ɫɟɤɰɢɨɧɧɵɯ,

ɬɟɥɟɣ. Ɉɧɨ ɩɪɨɢɡɜɨɞɢɬɫɹ

ɜɵɲɚɟɬ ɞɨɩɭɫɬɢɦɵɟ ɡɧɚɱɟ

ɜɚɧɢɹ. ɉɪɢɦɟɪ ɞɟɥɟɧɢɹ ɫ

ɬɟɥɶɧɵɦɢ ɭɫɬɪɨɣɫɬɜɚɦɢ ɩ

Ⱦɟɥɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ

ɦɟɠɞɭ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵ

ɋȾɋ ɨɤɚɡɵɜɚɟɬ ɫɭɳ

ɧɚɞɟɠɧɨɫɬɶ ɪɚɛɨɬɵ ɷɥɟɤɬ

ɫɬɢ ɜ ɫɟɬɹɯ.

Ɋɢɫ. 10.3. ɋɬɚɰɢɨɧɚɪ

ɩɨɜɵɲɟɧɧɨɝɨ ɧɚɩ

ɚɜɬɨɬɪɚɧɫɮɨɪɦɚɬ

ȺȾɋ ɩɪɨɢɡɜɨɞɢɬɫɹ

ɤɨɦɦɭɬɚɰɢɨɧɧɵɯ ɚɩɩɚɪɚɬ

ɲɢɧɨɫɨɟɞɢɧɢɬɟɥɶɧɵɯ ɜɵɤ

ɩɪɢɫɨɟɞɢɧɟɧɢɣ. ɉɪɢ ɚɜɬɨ

ɤɚɫɤɚɞɧɨɝɨ ɨɬɤɥɸɱɟɧɢɹ ɬ

ɬɵɜɚɬɶ, ɱɬɨ ȺȾɋ ɢɦɟɟɬ ɧɟ

1) ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɹ

ɧɵɯ ɧɟɛɚɥɚɧɫɨɜ ɦɨɳɧɨɫɬ

ɱɚɫɬɹɯ ɫɟɬɢ;

2) ɭɜɟɥɢɱɟɧɢɟ ɜɪɟɦɟ

222

ɠ ɣɦɣ ɛɝɭɩɧɛɭɣɲɠɬɥɩɠ ɟɠɦɠɨɣɠ ɬɠɭɣ

ɹɸɬ ɜ ɩɪɨɰɟɫɫɟ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɤɨɝɞɚ

ɜ ɄɁ ɩɪɢ ɟɟ ɪɚɡɜɢɬɢɢ. Ɋɚɡɥɢɱɚɸɬ ɞɟ

ɜɬɨɦɚɬɢɱɟɫɤɨɟ (ȺȾɋ).

ɟ ɫɟɬɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɧɨɪɦɚɥɶɧɨ

ɢɧɨɫɨɟɞɢɧɢɬɟɥɶɧɵɯ ɢɥɢ ɥɢɧɟɣɧɵɯ ɜ

ɨɝɞɚ, ɤɨɝɞɚ ɭɪɨɜɟɧɶ ɬɨɤɚ ɄɁ ɜ ɭɡɥɟ ɫ

ɢɹ ɞɥɹ ɩɚɪɚɦɟɬɪɨɜ ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ

ɬɢ ɧɚ ɷɥɟɤɬɪɨɫɬɚɧɰɢɢ ɫ ɞɜɭɦɹ ɪɚɫ

ɜɵɲɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɩɨɤɚɡɚɧ ɧɚ

ɫɪɟɞɫɬɜɨɦ ɪɚɡɪɵɜɚ ɬɪɚɧɫɮɨɪɦɚɬɨɪɧ

ɢ ɭɫɬɪɨɣɫɬɜɚɦɢ 220 ɢ 110 ɤȼ.

ɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɪɟɠɢɦɵ, ɭɫɬɨɣɱ

ɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ, ɚ ɬɚɤɠɟ ɧɚ ɩɨɬɟɪɢ

ɨɟ ɞɟɥɟɧɢɟ ɫɟɬɢ ɧɚ ɷɥɟɤɬɪɨɫɬɚɧɰɢɢ ɫ ɞ

ɹɠɟɧɢɹ:

ɚ – ɢɫɯɨɞɧɚɹ ɫɯɟɦɚ; ɛ – ɪɚɡɪɵɜ

ɪɧɨɣ ɫɜɹɡɢ ɦɟɠɞɭ Ɋɍ ɞɜɭɯ ɤɥɚɫɫɨɜ ɧɚɩɪɹɠ

ɚɜɚɪɢɣɧɨɦ ɪɟɠɢɦɟ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢ

ɜ. Ɉɧɨ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɧɚ ɫɟɤɰɢɨɧ

ɸɱɚɬɟɥɹɯ, ɢɧɨɝɞɚ ɧɚ ɜɵɤɥɸɱɚɬɟɥɹɯ

ɚɬɢɱɟɫɤɨɦ ɞɟɥɟɧɢɢ ɫɟɬɢ ɨɛɪɚɡɭɟɬɫɹ

ɤɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ, ɨɞɧɚɤɨ ɧ

ɨɫɬɚɬɤɢ:

ɥɟɧɢɹ ɜ ɩɨɫɥɟɚɜɚɪɢɣɧɨɦ ɪɟɠɢɦɟ ɡɧ

ɣ ɢɫɬɨɱɧɢɤɨɜ ɢ ɧɚɝɪɭɡɤɢ ɜ ɪɚɡɞɟɥ

ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɧɨɪɦɚɥɶɧɨɝɨ ɪɟɠɢ

ɪɟɛɭɟɬ-

ɟɧɢɟ ɫɟ-

ɪɟɠɢɦɟ

ɤɥɸɱɚ-

ɟɬɢ ɩɪɟ-

ɛɨɪɭɞɨ-

ɪɟɞɟɥɢ-

ɪɢɫ. 8.3.

ɣ ɫɜɹɡɢ

ɜɨɫɬɶ ɢ

ɦɨɳɧɨ-

ɭɦɹ Ɋɍ

ɧɢɣ

ɪɚɛɨɬɵ

ɵɯ ɢɥɢ

ɦɨɳɧɵɯ

ɫɢɫɬɟɦɚ

ɞɨ ɭɱɢ-

ɱɢɬɟɥɶ-

ɜɲɢɯɫɹ

ɚ.

ɇɟɫɦɨɬɪɹ ɧɚ ɷɬɨ, ɭɫ

ɫɢɫɬɟɦɚɯ, ɩɨɫɤɨɥɶɤɭ ɞɟɲɟ

10.4. ɍɩɥ

Ɍɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳ

ɮɭɧɤɰɢɸ – ɨɝɪɚɧɢɱɟɧɢɟ

ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɯɟɦɵ ɢ ɩ

ɜɥɢɹɬɶ ɧɚ ɧɨɪɦɚɥɶɧɵɣ ɪɟ

Ɍɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳɢ

ɜ ɷɧɟɪɝɨɫɢɫɬɟɦɚɯ, ɹɜɥɹɸɬ

ɪɚɤɬɟɪɢɫɬɢɤɭ. ȼ ɫɟɬɹɯ 6 (

ɛɟɬɨɧɧɵɟ ɪɟɚɤɬɨɪɵ, ɚ ɜ ɫ

ɦɚɫɥɹɧɵɦ ɨɯɥɚɠɞɟɧɢɟɦ.

ɉɚɫɩɨɪɬɧɵɦɢ ɩɚɪɚɦ

ɩɪɹɠɟɧɢɟ

ɧɨɦ

; ɧɨɦɢɧɚɥ

(ɜ Ɉɦɚɯ ɢɥɢ ɩɪɨɰɟɧɬɚɯ)

ȼɨɡɦɨɠɧɵɟ ɫɯɟɦɵ ɜ

Ɋɢɫ. 1

ɚ –

ɢɧɟ

Ʌɢɧɟɣɧɵɣ ɪɟɚɤɬɨɪ,

ɫɨɟɞɢɧɟɧɢɟ), ɨɝɪɚɧɢɱɢɜɚɟ

ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɵɫɨɤɢɣ ɭɪ

ɜɤɥɸɱɟɧɧɨɣ ɫɟɬɢ. ɉɨɫɥɟɞ

ɤɥɸɱɟɧɧɵɯ ɩɨ ɜɵɫɲɟɣ ɫɬ

ɟɠɢɦɟ ɢɦɟɸɬ ɦɟɫɬɨ ɩɨɬɟ

ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ.

ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɪɟɚɤ

ɢɥɢ ɦɨɳɧɨɫɬɢ ɤɨɪɨɬɤɨɝɨ

ɧɢɱɢɜɚɸɳɟɟ ɞɟɣɫɬɜɢɟ ɪɟ

223

ɪɨɣɫɬɜɚ ȺȾɋ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ

ɵ, ɩɪɨɫɬɵ ɢ ɧɚɞɟɠɧɵ.

ɩɞɫɛɨɣɲɣɝɛɹɴɣɠ ɮɬɭɫɩɤɬɭɝɛ

ɟ ɭɫɬɪɨɣɫɬɜɚ, ɜɵɩɨɥɧɹɹ ɫɜɨɸ ɨ

ɨɤɨɜ ɄɁ, ɢɦɟɸɬ ɫɬɚɛɢɥɶɧɵɟ ɯɚɪɚɤɬ

ɪɚɦɟɬɪɨɜ ɪɟɠɢɦɚ ɢ ɧɟ ɞɨɥɠɧɵ ɫɭɳ

ɢɦ ɪɚɛɨɬɵ ɫɟɬɢ.

ɪɟɚɤɬɨɪɵ, ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɧɚɫɬɨɹɳ

ɹ ɧɟɪɟɝɭɥɢɪɭɟɦɵɦɢ ɢ ɢɦɟɸɬ ɥɢɧɟ

0) ɤȼ ɩɪɢɦɟɧɹɸɬɫɹ ɨɞɢɧɚɪɧɵɟ ɢ ɫɞ

ɬɹɯ ɧɚɩɪɹɠɟɧɢɟɦ 35…220 ɤȼ – ɨɞɢ

ɬɪɚɦɢ ɪɟɚɤɬɨɪɨɜ ɹɜɥɹɸɬɫɹ: ɧɨɦɢɧɚɥ

ɶɧɵɣ ɬɨɤ

ɧɨɦ

; ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨ

ɥɸɱɟɧɢɹ ɪɟɚɤɬɨɪɨɜ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢ

.4. ɋɯɟɦɵ ɜɤɥɸɱɟɧɢɹ ɪɟɚɤɬɨɪɨɜ:

ɧɨɝɨ; ɛ – ɫɟɤɰɢɨɧɧɨɝɨ; ɜ – ɫɞɜɨɟɧɧɨɝɨ

ɤɥɸɱɚɟɦɵɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜ ɥɢɧ

ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɢ ɩɨɞɞ

ɜɟɧɶ ɨɫɬɚɬɨɱɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɜ ɭɡɥ

ɟɟ ɨɱɟɧɶ ɜɚɠɧɨ ɞɥɹ ɷɥɟɤɬɪɨɩɪɢɟɦɧɢ

ɪɨɧɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ. Ɉɞɧɚɤɨ ɜ ɧɨɪ

ɢ ɚɤɬɢɜɧɨɣ ɢ ɪɟɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɟɣ

ɨɪɚ ɜɵɛɢɪɚɟɬɫɹ ɩɨ ɠɟɥɚɟɦɨɦɭ ɭɪɨ

ɚɦɵɤɚɧɢɹ ɡɚ ɥɢɧɟɣɧɵɦ ɪɟɚɤɬɨɪɨɦ. Ɍ

ɤɬɨɪɚ ɫɧɢɠɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɟɝ

ɷɧɟɪɝɨ-

ɧɨɜɧɭɸ

ɪɢɫɬɢɤɢ

ɫɬɜɟɧɧɨ

ɟ ɜɪɟɦɹ

ɧɭɸ ɯɚ-

ɜɨɟɧɧɵɟ

ɚɪɧɵɟ ɫ

ɶɧɨɟ ɧɚ-

ɢɜɥɟɧɢɟ

. 10.4.

ɸ (ɩɪɢ-

ɪɠɢɜɚɟɬ

ɯ ɩɪɟɞ-

ɨɜ, ɩɨɞ-

ɚɥɶɧɨɦ

ɚ ɬɚɤɠɟ

ɧɸ ɬɨɤɚ

ɤɨɨɝɪɚ-

ɨ ɧɨɦɢ-

ɧɚɥɶɧɨɝɨ ɬɨɤɚ, ɤɨɬɨɪɵɣ ɞ

ɟɦɧɢɤɨɜ.

ɋɟɤɰɢɨɧɧɵɟ ɪɟɚɤɬɨ

ɫɛɨɪɧɵɯ ɲɢɧɚɯ ɢ ɩɪɢɫɨɟɞ

ɪɚɦɢ ɨɧɢ ɨɤɚɡɵɜɚɸɬ ɦɟɧɶ

ɫɥɨɜɥɟɧɨ ɬɟɦ, ɱɬɨ ɫɟɤɰɢɨ

ɧɨɦɢɧɚɥɶɧɵɟ ɬɨɤɢ, ɤɨɬɨɪ

ɧɨɪɦɚɥɶɧɨɝɨ ɪɟɠɢɦɚ.

ȼ ɨɬɧɨɲɟɧɢɢ ɩɨɬɟɪɶ

ɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɨɛ

ɟɠɢɦɟ ɦɚɝɧɢɬɧɚɹ ɫɜɹɡɶ

ɧɚɩɪɹɠɟɧɢɹ ɜ ɧɟɦ ɛɟɡ ɫɧɢ

ɷɮɮɢɰɢɟɧɬ ɫɜɹɡɢ ɱɚɫɬɟɣ ɪ

ɧɢɟɦ

ɝɞɟ Ɇ – ɜɡɚɢɦɧɚɹ ɢɧɞɭɤɬɢ

ɢɧɞɭɤɬɢɜɧɨɫɬɢ ɜɟɬɜɟɣ.

ɂɫɯɨɞɧɚɹ ɫɯɟɦɚ ɫɞɜ

«ɡɜɟɡɞɭ» (ɪɢɫ. 10.5).

Ɋɢɫ. 10.5. Ɋɟɠɢɦɵ ɪɚ



ɩɪɨɞɨ

ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɯ

ɥɢɱɧɵɯ ɩɨ ɬɨɤɨɨɝɪɚɧɢɱɟɧ

ɪɭɸɳɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ:

ɜ ɨɞɧɨɰɟɩɧɨɦ ɪɟɠɢɦ



ɜ ɩɪɨɞɨɥɶɧɨɦ ɪɟɠɢɦ

224

ɥɠɟɧ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɦɨɳɧɨɫɬɢ ɷɥɟ

ɵ ɨɝɪɚɧɢɱɢɜɚɸɬ ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵ

ɧɟɧɢɹɯ. ɉɨ ɫɪɚɜɧɟɧɢɸ ɫ ɥɢɧɟɣɧɵɦ

ɟɟ ɬɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳɟɟ ɞɟɣɫɬɜɢɟ.

ɧɵɟ ɪɟɚɤɬɨɪɵ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɧɚ

ɟ ɩɪɨɬɟɤɚɸɬ ɦɟɠɞɭ ɫɟɤɰɢɹɦɢ ɩɪɢ ɧɚ

ɧɚɩɪɹɠɟɧɢɹ ɢ ɪɟɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬ

ɚɞɚɸɬ ɫɞɜɨɟɧɧɵɟ ɪɟɚɤɬɨɪɵ. ȼ ɧɨɪ

ɟɠɞɭ ɜɟɬɜɹɦɢ ɪɟɚɤɬɨɪɚ ɭɦɟɧɶɲɚɟɬ

ɟɧɢɹ ɬɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳɟɣ ɫɩɨɫɨɛɧ

ɚɫɳɟɩɥɟɧɧɨɣ ɨɛɦɨɬɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ

ɜ 12 ɧɨɦ

MLL Ɇ x

ɧɨɫɬɶ ɜɟɬɜɟɣ ɨɛɦɨɬɤɢ; L

, L

– ɫɨɛ

ɟɧɧɨɝɨ ɪɟɚɤɬɨɪɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɬɪɟɯ

ɨɬɵ ɫɞɜɨɟɧɧɨɝɨ ɪɟɚɤɬɨɪɚ

: ɚ



ɨɞɧɨɰɟɩɧ

ɶɧɵɣ; ɜ



ɞɜɭɯɰɟɩɧɨɣ (ɫɤɜɨɡɧɨɣ)

ɦɵ ɜɤɥɸɱɟɧɢɹ ɬɚɤɨɣ ɪɟɚɤɬɨɪ ɪɚɛɨɬɚ

ɸ ɪɟɠɢɦɚɯ, ɬ. ɤ. ɢɦɟɟɬ ɪɚɡɥɢɱɧɵɟ ɪ

ɟ (ɪɢɫ. 10.5, ɚ)

ɫɜ ɧɨɦ ɫɜ ɧɨɦ ɧɨɦ

)kx kx x

;

(ɪɢɫ. 10.5, ɛ)

Ɋɫɜɧɨɦ

2(1 )

kx 

;

ɬɪɨɩɪɢ-

ɚɧɢɹ ɧɚ

ɪɟɚɤ

ɨ-

ɬɨ ɨɛɭ-

ɨɥɶɲɢɟ

ɭɲɟɧɢɢ

ɥɭɱɲɢ-

ɚɥɶɧɨɦ

ɩɨɬɟɪɸ

ɫɬɢ.

ɨ-

ɜɵɪɚɠɟ-

ɬɜɟɧɧɵɟ

ɭɱɟɜɭɸ

ɣ;

ɟɬ ɜ ɪɚɡ-

ɟɡɭɥɶɬɢ-

225

ɜ ɫɤɜɨɡɧɨɦ (ɞɜɭɯɰɟɩɧɨɦ) ɪɟɠɢɦɟ (ɫɦ. ɪɢɫ. 10.5, ɜ)

Ɋɧɨɦɫɜɧɨɦ ɫɜɧɨɦ

(1 )xx kx kx  

ɇɟɞɨɫɬɚɬɤɨɦ ɫɞɜɨɟɧɧɵɯ ɪɟɚɤɬɨɪɨɜ ɹɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɜɵ-

ɲɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɥɚɛɨ ɧɚɝɪɭɠɟɧɧɨɣ ɜɟɬɜɢ ɩɪɢ ɪɚɛɨɬɟ ɜ ɨɞɧɨɰɟɩ-

ɧɨɦ ɢ ɫɤɜɨɡɧɨɦ ɪɟɠɢɦɚɯ (ɫɦ. ɪɢɫ. 10.5, ɚ, ɜ) ɡɚ ɫɱɟɬ ɦɚɝɧɢɬɧɨɣ ɫɜɹɡɢ

ɱɚɫɬɟɣ ɨɛɦɨɬɤɢ ɪɟɚɤɬɨɪɚ.

Ɋɟɚɤɬɨɪɵ ɫ ɧɟɥɢɧɟɣɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ. Ʉ ɷɬɨɣ ɝɪɭɩɩɟ ɨɬɧɨɫɹɬ-

ɫɹ ɭɩɪɚɜɥɹɟɦɵɟ ɢ ɧɚɫɵɳɚɸɳɢɟɫɹ ɪɟɚɤɬɨɪɵ.

ɍɩɪɚɜɥɹɟɦɵɣ ɪɟɚɤɬɨɪ – ɷɬɨ ɪɟɝɭɥɢɪɭɟɦɵɣ

ɪɟɚɤɬɨɪ ɫɨ ɫɬɚɥɶɸ, ɢɡ-

ɦɟɧɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɨɬɨɪɨɝɨ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨɞɦɚɝɧɢɱɢɜɚɧɢɟɦ

ɦɚɝɧɢɬɨɩɪɨɜɨɞɚ ɩɨɥɟɦ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ȼ ɧɨɪɦɚɥɶɧɨɦ ɪɟɠɢɦɟ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɟ ɪɟɚɤɬɨɪɚ ɫɧɢɠɚɟɬɫɹ ɡɚ ɫɱɟɬ ɩɨɞɦɚɝɧɢɱɢɜɚɧɢɹ. ɉɪɢ ɄɁ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɟ ɪɟɚɤɬɨɪɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ. ɗɬɨ ɭɜɟɥɢɱɟɧɢɟ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨ-

ɷɮɮɢɰɢɟɧɬɨɦ ɬɨɤɨɨɝɪɚɧɢɱɟɧɢɹ, ɤɨɬɨɪɵɣ ɫɨɫɬɚɜɥɹɟɬ 4…7 ɟɞɢɧɢɰ.

ɇɚɫɵɳɚɸɳɢɣɫɹ ɪɟɚɤɬɨɪ – ɷɬɨ ɧɟɭɩɪɚɜɥɹɟɦɵɣ ɪɟɚɤɬɨɪ ɫɨ ɫɬɚɥɶ-

ɧɵɦ ɦɚɝɧɢɬɨɩɪɨɜɨɞɨɦ. Ɉɧ ɢɦɟɟɬ ɧɟɥɢɧɟɣɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ





xFI , ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɚɫɵɳɟɧɢɟɦ ɦɚɝɧɢɬɨɩɪɨɜɨɞɚ ɩɨɥɟɦ

ɨɛɦɨɬɤɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ. ɗɤɜɢɜɚɥɟɧɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɟɚɤɬɨɪɚ ɜɨɡ-

ɪɚɫɬɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɬɨɤɚ; ɷɬɨ ɫɜɨɣɫɬɜɨ ɪɟɚɤɬɨɪɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɨɝ-

ɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ.

Ɍɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳɢɟ ɤɨɦɦɭɬɚɰɢɨɧɧɵɟ ɚɩɩɚɪɚɬɵ ɨɝɪɚɧɢɱɢɜɚɸɬ

ɬɨɤ ɄɁ ɜ ɬɟɱɟɧɢɟ ɩɟɪɜɨɝɨ ɩɨɥɭɩɟɪɢɨɞɚ ɟɝɨ ɩɨɹɜɥɟɧɢɹ ɢ ɞɚɥɟɟ ɨɬɤɥɸɱɚ-

ɸɬ ɤɨɪɨɬɤɨɟ ɡɚɦɵɤɚɧɢɟ. Ʉ ɧɢɦ ɨɬɧɨɫɹɬɫɹ ɬɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳɢɟ ɩɪɟɞɨ-

ɯɪɚɧɢɬɟɥɢ

ɢ ɨɝɪɚɧɢɱɢɬɟɥɢ ɭɞɚɪɧɨɝɨ ɬɨɤɚ ɜɡɪɵɜɧɨɝɨ ɞɟɣɫɬɜɢɹ.

Ɍɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳɢɟ ɩɪɟɞɨɯɪɚɧɢɬɟɥɢ ɢɡɝɨɬɚɜɥɢɜɚɸɬɫɹ ɧɚ ɧɚ-

ɩɪɹɠɟɧɢɟ 3…35 ɤȼ. Ɉɧɢ ɨɬɥɢɱɚɸɬɫɹ ɩɪɨɫɬɨɬɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɢ ɧɟɛɨɥɶ-

ɲɨɣ ɫɬɨɢɦɨɫɬɶɸ. Ɉɞɧɚɤɨ ɨɧɢ ɢɦɟɸɬ ɪɹɞ ɫɭɳɟɫɬɜɟɧɧɵɯ ɧɟɞɨɫɬɚɬɤɨɜ:

x ɨɞɧɨɪɚɡɨɜɨɟ ɞɟɣɫɬɜɢɟ, ɱɬɨ ɡɚɬɪɭɞɧɹɟɬ ɩɪɢɦɟɧɟɧɢɟ ɚɜɬɨɦɚɬɢɱɟ-

ɫɤɨɝɨ ɩɨɜɬɨɪɧɨɝɨ ɜɤɥɸɱɟɧɢɹ (Ⱥɉȼ);

x ɧɟɫɬɚɛɢɥɶɧɨɫɬɶ ɬɨɤɨɜɪɟɦɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ;

x ɧɟɭɩɪɚɜɥɹɟɦɨɫɬɶ ɫɨ ɫɬɨɪɨɧɵ ɜɧɟɲɧɢɯ ɭɫɬɪɨɣɫɬɜ (ɪɟɥɟɣɧɨɣ ɡɚ-

ɳɢɬɵ), ɜ ɫɜɹɡɢ ɫ ɱɟɦ ɩɪɟɞɨɯɪɚɧɢɬɟɥɢ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɜ ɰɟɩɹɯ ɦɟɧɟɟ

ɨɬɜɟɬɫɬɜɟɧɧɵɯ ɩɨɬɪɟɛɢɬɟɥɟɣ.

Ɉɝɪɚɧɢɱɢɬɟɥɢ ɭɞɚɪɧɨɝɨ ɬɨɤɚ ɜɡɪɵɜɧɨɝɨ ɞɟɣɫɬɜɢɹ – ɷɬɨ ɫɜɟɪɯɛɵ-

ɫɬɪɨɞɟɣɫɬɜɭɸɳɢɟ ɭɩɪɚɜɥɹɟɦɵɟ ɤɨɦɦɭɬɚɰɢɨɧɧɵɟ ɚɩɩɚɪɚɬɵ ɨɞɧɨɪɚɡɨɜɨ-

ɝɨ ɞɟɣɫɬɜɢɹ. Ʉɨɧɫɬɪɭɤɬɢɜɧɨ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɝɟɪɦɟɬɢɡɢɪɨɜɚɧɧɵɣ

ɰɢɥɢɧɞɪ, ɜɧɭɬɪɢ ɤɨɬɨɪɨɝɨ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɬɨɤɨɜɟɞɭɳɢɣ ɩɪɨɜɨɞɧɢɤ ɫ ɩɢ-

ɪɨɩɚɬɪɨɧɨɦ. Ɉɬɤɥɸɱɟɧɢɟ ɰɟɩɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɪɚɡɪɭɲɟɧɢɟɦ ɬɨɤɨɜɟɞɭ-

ɳɟɝɨ ɩɪɨɜɨɞɧɢɤɚ. ɋɢɝɧɚɥ ɧɚ ɫɪɚɛɚɬɵɜɚɧɢɟ ɩɨɫɬɭɩɚɟɬ ɨɬ

ɭɫɬɪɨɣɫɬɜɚ ɪɟ-

ɥɟɣɧɨɣ ɡɚɳɢɬɵ, ɤɨɧɬɪɨɥɢɪɭɸɳɟɝɨ ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɢ ɟɝɨ ɩɟɪ-

ɜɭɸ ɩɪɨɢɡɜɨɞɧɭɸ (ɫɤɨɪɨɫ

ɝɚɟɬɫɹ ɡɚ ɜɪɟɦɹ ɩɨɪɹɞɤɚ 0

ɥɹɟɬ ɨɤɨɥɨ 5 ɦɫ, ɬ. ɟ.

Ɍɪɚɧɫɮɨɪɦɚɬɨɪɵ ɢ

ɨɬɤɨɣ ɧɢɡɲɟɝɨ ɧɚɩɪɹɠɟ

ɬɹɯ ɧɢɡɤɨɝɨ ɧɚɩɪɹɠɟɧɢɹ.

ɮɨɪɦɚɬɨɪɵ ɫ ɪɚɫɳɟɩɥɟɧɧ

ɸɬɫɹ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭ

ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ (Ƚɗɋ), ɚ

ɷɧɟɪɝɨɫɢɫɬɟɦ ɢ ɩɪɨɦɵɲɥ

ɦɚɬɨɪɵ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ

ɬɟɩɥɨɜɵɯ ɢ ɚɬɨɦɧɵɯ ɷɥɟɤ

ɭɤɚɡɚɧɧɵɯ ɬɪɚɧɫɮɨɪɦɚɬɨɪ

Ɋɢɫ. 10.6. Ɍɢɩɨɜɵɟ ɫɯɟɦɵ

ɫ ɪɚɫɳɟɩɥɟɧɧɨɣ ɨɛɦɨɬɤɨɣ

ɬɪɚɧɫɮɨɪɦɚɬɨɪ

ɏɚɪɚɤɬɟɪɧɵɦɢ ɩɚɪɚ

ɦɨɬɤɢ ɇɇ ɧɚ ɞɜɟ ɹɜɥɹɸɬɫɹ

– ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪ

ɦɟɠɞɭ ɜɵɜɨɞɚɦɢ ɇɇ1–ɇɇ

– ɫɤɜɨɡɧɨɟ ɫɨɩɪɨɬɢ

ɜɵɜɨɞɚɦɢ ȼɇ ɢ ɨɛɴɟɞɢ

ɇɇ1//ɇɇ2;

– ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫ

ɧɢɸ

226

ɶ ɧɚɪɚɫɬɚɧɢɹ ɬɨɤɚ). Ɉɝɪɚɧɢɱɟɧɢɟ ɬɨ

5 ɦɫ; ɩɨɥɧɨɟ ɜɪɟɦɹ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩ

ɪɢɨɞɚ ɩɪɨɦɵɲɥɟɧɧɨɣ ɱɚɫɬɨɬɵ.

ɚɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ɫ ɪɚɫɳɟɩɥɟ

ɢɹ ɩɪɢɦɟɧɹɸɬɫɹ ɞɥɹ ɫɧɢɠɟɧɢɹ ɬɨɤɚ

ɉɨɜɵɲɚɸɳɢɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ɢ ɚɜ

ɣ ɨɛɦɨɬɤɨɣ ɧɢɡɲɟɝɨ ɧɚɩɪɹɠɟɧɢɹ ɢ

ɪɭɩɧɟɧɧɵɯ ɛɥɨɤɨɜ ɷɥɟɤɬɪɨɫɬɚɧɰɢɣ,

ɩɨɧɢɠɚɸɳɢɟ ɩɪɢɦɟɧɹɸɬɫɹ ɧɚ ɩɨɞ

ɧɧɵɯ ɩɪɟɞɩɪɢɹɬɢɣ. ɉɨɧɢɠɚɸɳɢɟ ɬ

ɚɤɠɟ ɜ ɫɢɫɬɟɦɟ ɫɨɛɫɬɜɟɧɧɵɯ ɧɭɠɞ

ɪɨɫɬɚɧɰɢɣ. ɏɚɪɚɤɬɟɪɧɵɟ ɫɯɟɦɵ ɫɨ

ɜ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 10.6.

ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ɢ ɚɜɬɨɬɪɚɧɫɮɨɪɦɚ

ɇ:

ɚ – ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ; ɛ – ɫɯɟɦɚ ɡɚ

; ɜ ɢ ɝ – ɬɨ ɠɟ ɚɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɚ

ɟɬɪɚɦɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɫ ɪɚɫɳɟɩɥɟ

(ɪɢɫ. 10.6, ɛ):

ɫɳɟɩɥɟɧɢɹ (

ɪɚɫɳ

), ɪɚɜɧɨɟ ɫɨɩɪɨɬ

;

ɥɟɧɢɟ (

ɫɤɜ

), ɪɚɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢ

ɟɧɧɵɦɢ ɜɵɜɨɞɚɦɢ ɪɚɫɳɟɩɥɟɧɧɨɣ

ɟɩɥɟɧɢɹ (

ɪɚɫɳ

), ɨɩɪɟɞɟɥɹɟɦɵɣ ɩɨ

ɪɚɫɳ ɪɚɫɳ ɫɤɜ

kxx

;

ɚ ɞɨɫɬɢ-

ɫɨɫɬɚɜ-

ɧɨɣ ɨɛ-

ɄɁ ɜ ɫɟ-

ɨɬɪɚɧɫ-

ɩɨɥɶɡɭ-

ɫɨɛɟɧɧɨ

ɬɚɧɰɢɹɯ

ɚɧɫɮɨɪ-

ɦɨɳɧɵɯ

ɞɢɧɟɧɢɹ

ɨɪɨɜ

ɟɳɟɧɢɹ

ɢɟɦ ɨɛ-

ɜɥɟɧɢɸ

ɦɟɠɞɭ

ɨɛɦɨɬɤɢ

ɜɵɪɚɠɟ-

227

– ɧɨɦɢɧɚɥɶɧɚɹ ɦɨɳɧɨɫɬɶ (

ɧɨɦ

), ɧɨɦɢɧɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ

(

(ȼ)ɧɨɦ

(ɇ )ɧɨɦ

) ɢ ɧɚɩɪɹɠɟɧɢɹ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ (

(ȼ-ɇ)K

(ɇ 1-ɇ 2)K

Ʉɪɨɦɟ ɜɵɲɟɭɩɨɦɹɧɭɬɵɯ, ɢɡɜɟɫɬɧɵ ɢ ɞɪɭɝɢɟ ɬɨɤɨɨɝɪɚɧɢɱɢɜɚɸɳɢɟ

ɭɫɬɪɨɣɫɬɜɚ: ɪɟɡɨɧɚɧɫɧɨɝɨ, ɬɪɚɧɫɮɨɪɦɚɬɨɪɧɨɝɨ, ɪɟɚɤɬɨɪɧɨɝɨ-ɜɟɧɬɢɥɶɧɨɝɨ

ɬɢɩɨɜ ɢ ɞɪ. ɉɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɷɬɢɯ ɭɫɬɪɨɣɫɬɜ ɨɩɢɫɚɧ ɜ ɪɚɛɨɬɚɯ [3,14].

10.5. ɉɪɭɣɧɣɢɛɱɣɺ ɫɠɡɣɧɛ ɢɛɢɠɧɦɠɨɣɺ ɨɠɤɭɫɛɦɠɤ

ɝ ɸɦɠɥɭɫɣɲɠɬɥɣɰ ɬɠɭɺɰ

ȼɟɥɢɱɢɧɚ ɬɨɤɨɜ ɩɪɢ ɤɨɪɨɬɤɢɯ ɡɚɦɵɤɚɧɢɹɯ ɧɚ ɡɟɦɥɸ ɫɭɳɟɫɬɜɟɧɧɨ

ɡɚɜɢɫɢɬ ɨɬ ɪɟɡɭɥɶɬɢɪɭɸɳɟɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɯɟɦɵ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚ-

ɬɟɥɶɧɨɫɬɢ (

0Ȉ

). ɍɜɟɥɢɱɟɧɢɟ ɷɬɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶ-

ɲɟɧɢɸ ɭɤɚɡɚɧɧɵɯ ɬɨɤɨɜ. ɉɪɚɤɬɢɱɟɫɤɢ ɜɟɥɢɱɢɧɚ

0Ȉ

ɨɩɪɟɞɟɥɹɟɬɫɹ

ɤɨɥɢɱɟɫɬɜɨɦ ɢ ɦɟɫɬɨɦ ɪɚɫɩɨɥɨɠɟɧɢɹ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ɢ ɚɜɬɨɬɪɚɧɫ-

ɮɨɪɦɚɬɨɪɨɜ ɫ ɡɚɡɟɦɥɟɧɧɨɣ ɧɟɣɬɪɚɥɶɸ. Ɋɚɡɡɟɦɥɟɧɢɟ ɧɟɣɬɪɚɥɟɣ ɜɫɟɯ

ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ

0Ȉ

, ɚ

ɬɨɤɢ ɄɁ ɧɚ ɡɟɦɥɸ – ɧɚɢɦɟɧɶɲɢɦɢ. Ɉɞɧɚɤɨ ɪɟɠɢɦ ɧɟɣɬɪɚɥɢ ɬɪɚɧɫɮɨɪ-

ɦɚɬɨɪɨɜ ɨɩɪɟɞɟɥɹɟɬ ɭɫɥɨɜɢɹ ɪɚɛɨɬɵ ɢɡɨɥɹɰɢɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ɩɪɢ

ɤɨɦɦɭɬɚɰɢɨɧɧɵɯ ɢ ɚɬɦɨɫɮɟɪɧɵɯ ɩɟɪɟɧɚɩɪɹɠɟɧɢɹɯ, ɚ ɬɚɤɠɟ ɩɪɢ ɜɨɡ-

ɧɢɤɧɨɜɟɧɢɢ ɜ ɫɟɬɢ ɄɁ ɧɚ ɡɟɦɥɸ. ɉɨɷɬɨɦɭ ɜɨɡɦɨɠɧɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɪɟ-

ɠɢɦɚ ɡɚɡɟɦɥɟɧɢɹ ɧɟɣɬɪɚɥɟɣ ɨɝɪɚɧɢɱɟɧɚ ɪɹɞɨɦ ɭɫɥɨɜɢɣ.

1. ɉɪɢ ɄɁ ɧɚ ɡɟɦɥɸ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɟɩɨɜɪɟɠɞɟɧɧɵɯ ɮɚɡɚɯ

ɨɬɧɨ-

ɫɢɬɟɥɶɧɨ ɡɟɦɥɢ ɜɨɡɪɚɫɬɚɟɬ. ɋɬɟɩɟɧɶ ɭɜɟɥɢɱɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɯɚɪɚɤɬɟɪɢ-

ɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɡɚɡɟɦɥɟɧɢɹ ɫɟɬɢ

ɡɮ-ɡɧɨɦ

KU U

, ɝɞɟ

ɮ-ɡ

–

ɧɚɩɪɹɠɟɧɢɟ ɮɚɡɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɡɟɦɥɢ. ɋ ɰɟɥɶɸ ɫɧɢɠɟɧɢɹ ɫɬɨɢɦɨɫɬɢ

ɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ɧɚɩɪɹɠɟɧɢɟɦ 110 ɤȼ ɢ ɜɵɲɟ ɞɟɥɚɸɬ ɫ ɨɫɥɚɛɥɟɧɧɨɣ

ɢɡɨɥɹɰɟɣ ɧɟɣɬɪɚɥɢ. ɂɡ ɷɬɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɫɟɬɢ 110 ɤȼ ɢ ɜɵɲɟ ɞɨɥɠɧɵ

ɛɵɬɶ ɷɮɮɟɤɬɢɜɧɨ ɡɚɡɟɦɥɟɧɵ, ɬ. ɟ. ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɧɚɩɪɹɠɟɧɢɟ ɧɚ

ɧɟɩɨɜɪɟɠɞɟɧɧɵɯ ɮɚɡɚɯ ɩɪɢ ɤɨɪɨɬɤɨɦ ɡɚɦɵɤɚɧɢɢ ɧɚ ɡɟɦɥɸ ɜ ɥɸɛɨɣ ɬɨɱ-

ɤɟ ɧɟ ɩɪɟɜɵɲɚɥɨ 80

% ɥɢɧɟɣɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɫɟɬɢ (1,4

ɮ.ɧɨɦ

). ɗɬɨ ɭɫ-

ɥɨɜɢɟ ɫɜɹɡɚɧɨ ɫ ɭɫɬɚɧɨɜɤɨɣ ɜ ɫɟɬɹɯ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ 80 %-ɯ ɪɚɡɪɹɞɧɢɤɨɜ.

Ɉɧɨ ɜɵɩɨɥɧɹɟɬɫɹ, ɬ. ɟ.

ɡɮ-ɡɧɨɦ

KU U

d 0,8, ɟɫɥɢ ɭɞɨɜɥɟɬɜɨɪɹɟɬɫɹ ɭɫ-

ɥɨɜɢɟ

d 4; 5.

2. ɉɨ ɭɫɥɨɜɢɹɦ ɪɚɛɨɬɵ ɜɵɤɥɸɱɚɬɟɥɟɣ ɠɟɥɚɬɟɥɶɧɨ, ɱɬɨɛɵ ɬɨɤɢ ɨɞ-

ɧɨɮɚɡɧɨɝɨ ɢ ɞɜɭɯɮɚɡɧɨɝɨ ɤɨɪɨɬɤɢɯ ɡɚɦɵɤɚɧɢɣ ɧɚ ɡɟɦɥɸ ɜ ɥɸɛɨɣ ɬɨɱɤɟ

ɫɟɬɢ ɧɟ ɩɪɟɜɵɲɚɥɢ ɬɨɤɚ ɬɪɟɯɮɚɡɧɨɝɨ ɄɁ ɜ ɷɬɨɣ ɠɟ ɬɨɱɤɟ. ɗɬɨ ɬɪɟɛɨɜɚ-

ɧɢɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɟɫɥɢ ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɪɟɚɤɬɢɜɧɨɫɬɶ ɫɯɟɦɵ ɧɭɥɟɜɨɣ

228

ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɛɨɥɶɲɟ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɪɟɚɤɬɢɜɧɨɫɬɢ ɫɯɟɦɵ ɩɪɹ-

ɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ (

t 1).

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɜɵɛɨɪɟ ɪɟɠɢɦɚ ɡɚɡɟɦɥɟɧɢɹ ɧɟɣɬɪɚɥɟɣ ɫɢɥɨ-

ɜɵɯ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ɧɚɩɪɹɠɟɧɢɟɦ 110 ɤȼ ɢ ɜɵɲɟ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥ-

ɧɹɬɶ ɫɥɟɞɭɸɳɢɟ ɭɫɥɨɜɢɹ:



  

31.13

1, 1;

KKK

II I Idd

ɡɮ-ɡɧɨɦ

0,8,KU U d

ɝɞɟ

– ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɡɟɦɥɟɧɢɹ ɫɟɬɢ;

ɞɨɩNN

UUd , ɝɞɟ

ɞɨɩN

U – ɞɨɩɭɫɬɢɦɨɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɟɣɬɪɚɥɢ

ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ;

ɢɦɩ ɢɦɩ.ɞɨɩ

UUd

ɝɞɟ

ɢɦɩ.ɞɨɩN

– ɢɦɩɭɥɶɫɧɨɟ ɞɨɩɭɫɬɢɦɨɟ

ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɟɣɬɪɚɥɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɩɪɢ ɄɁ ɜ ɫɟɬɢ.

ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɭɫɥɨɜɢɣ ɨɝɪɚɧɢɱɢɬɶ ɬɨɤ ɄɁ ɧɚ

ɡɟɦɥɸ ɦɨɠɧɨ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɨ ɩɭɬɟɦ ɪɚɡɡɟɦɥɟɧɢɹ ɧɟɣɬɪɚɥɟɣ ɧɟɫɤɨɥɶ-

ɤɢɯ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ɫɟɬɢ. Ɉɝɪɚɧɢɱɟɧɢɹ ɬɨɤɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ

ɦɨɠɧɨ ɞɨɛɢɬɶɫɹ ɢ ɜɤɥɸɱɟɧɢɟɦ ɜ ɧɟɣɬɪɚɥɢ ɫɢɥɨɜɵɯ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ

ɪɟɚɤɬɨɪɨɜ ɢɥɢ ɪɟɡɢɫɬɨɪɨɜ. ɉɪɢ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɫɨɩɪɨɬɢɜɥɟɧɢɢ

ɪɟɚɤɬɨ-

ɪɵ ɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨ ɨɝɪɚɧɢɱɢɜɚɸɬ ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ, ɱɟɦ ɪɟ-

ɡɢɫɬɨɪɵ. Ɉɞɧɚɤɨ ɪɟɚɤɬɨɪɵ ɭɬɹɠɟɥɹɸɬ ɭɫɥɨɜɢɹ ɪɚɛɨɬɵ ɢɡɨɥɹɰɢɢ ɧɟɣ-

ɬɪɚɥɢ ɩɪɢ ɚɬɦɨɫɮɟɪɧɵɯ ɩɟɪɟɧɚɩɪɹɠɟɧɢɹɯ. Ɋɟɡɢɫɬɨɪɵ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ

ɪɟɚɤɬɨɪɚɦɢ, ɨɛɟɫɩɟɱɢɜɚɸɬ ɛɨɥɶɲɭɸ ɫɤɨɪɨɫɬɶ ɡɚɬɭɯɚɧɢɹ ɚɩɟɪɢɨɞɢɱɟ-

ɫɤɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɬɨɤɚ ɄɁ.

10.6. Ʌɩɩɫɟɣɨɛɱɣɺ ɮɫɩɝɨɠɤ ɭɩɥɩɝ Ʌɂ

Ʉɨɨɪɞɢɧɚɰɢɹ ɭɪɨɜɧɟɣ ɬɨɤɨɜ ɄɁ – ɷɬɨ ɫɨɝɥɚɫɨɜɚɧɢɟ ɢɯ ɡɧɚɱɟɧɢɣ ɜ

ɪɚɡɥɢɱɧɵɯ ɭɡɥɚɯ ɷɧɟɪɝɨɫɢɫɬɟɦɵ ɢ ɩɪɢɜɟɞɟɧɢɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɫ ɩɚɪɚ-

ɦɟɬɪɚɦɢ ɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹ. ɇɟɨɛɯɨɞɢɦɨɫɬɶ ɤɨɨɪɞɢɧɚɰɢɢ ɜɨɡɧɢɤɚɟɬ

ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɷɥɟɤɬɪɨɭɫɬɚɧɨɜɨɤ (ɫɬɚɧɰɢɣ, ɩɨɞɫɬɚɧɰɢɣ, ɥɢɧɢɣ

ɷɥɟɤɬɪɨɩɟɪɟɞɚɱɢ ɢ ɬ. ɞ.) ɢɥɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɷɧɟɪɝɨɫɢɫɬɟɦ.

ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɷɥɟɤɬɪɨɭɫɬɚɧɨɜɤɢ ɰɟɥɶ ɤɨɨɪɞɢɧɚɰɢɢ ɫɨɫɬɨ-

ɢɬ ɜ ɜɵɛɨɪɟ ɟɟ ɨɩɬɢɦɚɥɶɧɨɣ ɫɯɟɦɵ ɢ ɫɜɹɡɟɣ ɫ ɭɡɥɨɜɵɦɢ ɩɨɞɫɬɚɧɰɢɹɦɢ

ɷɧɟɪɝɨɫɢɫɬɟɦɵ. ɉɪɢ ɷɬɨɦ ɞɨɥɠɧɵ ɭɱɢɬɵɜɚɬɶɫɹ ɜɨɡɦɨɠɧɵɟ ɩɚɪɚɦɟɬɪɵ

ɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹ, ɪɟɠɢɦɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ, ɬɪɟɛɨɜɚɧɢɹ ɤ ɭɫɬɨɣɱɢɜɨ-

ɫɬɢ ɢ ɧɚɞɟɠɧɨɫɬɢ ɪɚɛɨɬɵ ɷɥɟɤɬɪɨɭɫɬɚɧɨɜɤɢ. Ⱦɥɹ ɤɨɨɪɞɢɧɚɰɢɢ ɭɪɨɜɧɟɣ

ɬɨɤɨɜ ɄɁ ɢɫɩɨɥɶɡɭɸɬɫɹ ɭɤɚɡɚɧɧɵɟ ɜɵɲɟ ɫɩɨɫɨɛɵ ɫ ɭɱɟɬɨɦ ɤɨɧɤɪɟɬɧɵɯ

ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɨɭɫɬɚɧɨɜɨɤ.

ɉɪɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɷɧɟɪɝɨɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɰɢɹ ɭɪɨɜɧɟɣ ɬɨɤɨɜ

ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɨɩɟɪɚɬɢɜɧɵɦ ɢɡɦɟɧɟɧɢɟɦ ɫɯɟɦɵ,

ɟɠɢɦɨɜ ɪɚɛɨɬɵ ɢ ɩɚɪɚɦɟ

ɧɢɹ. ȼ ɱɚɫɬɧɨɫɬɢ, ɢɫɩɨɥɶɡ

– ɫɬɚɰɢɨɧɚɪɧɨɟ ɢ ɚɜ

ɰɢɨɧɧɵɯ ɢɥɢ ɲɢɧɨɫɨɟɞɢɧ

– ɪɚɡɡɟɦɥɟɧɢɟ ɧɟɣɬɪ

ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ɱɟɪɟɡ ɪɟ

– ɬɨɤɨɨɝɪɚɧɢɱɢɜɚɸ

ɥɟɧɧɨɣ ɨɛɦɨɬɤɨɣ ɇɇ;

– ɤɨɦɦɭɬɚɰɢɨɧɧɵɟ ɚ

Ⱥɧɚɥɢɡ ɤɨɨɪɞɢɧɚɰɢ

ɞɥɹ ɨɛɨɫɧɨɜɚɧɢɹ ɦɨɞɟɪɧɢɡ

ɉɪɢɦɟɪ 10.1

ɋɪɚɜɧɢɬɶ ɪɟɠɢɦɵ

ɮɨɪɦɚɬɨɪɨɜ Ƚɉɉ (ɪɢɫ. 10.

ɤɨɜ ɬɪɟɯɮɚɡɧɨɝɨ ɄɁ ɧɚ ɲɢ

ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ

ɋɢɫɬɟɦɚ ɋ: ɢɫɬɨɱ

= 200 ɆȼȺ – ɦɨɳɧɨɫɬ

Ɍɪɚɧɫɮɨɪɦɚɬɨɪɵ Ɍ1,

ɧɨɦ

= 125 MBA,

= 11

Ɋɢɫ. 10.7. ɋɯɟɦɵ ɤ ɩɪɢɦɟ

Ɋɟɲɟɧɢɟ. ɉɪɢɧɢɦɚ

= 10,5 ɤȼ. ɇɚɯɨɞɢɦ ɛɚɡ

229

ɬɪɨɜ ɨɫɧɨɜɧɵɯ ɷɥɟɦɟɧɬɨɜ ɷɥɟɤɬɪɨɨɛ

ɸɬɫɹ:

ɨɦɚɬɢɱɟɫɤɨɟ ɞɟɥɟɧɢɟ ɫɟɬɢ ɩɨɫɪɟɞɫɬ

ɬɟɥɶɧɵɯ ɜɵɤɥɸɱɚɬɟɥɟɣ;

ɥɟɣ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ, ɡɚɡɟɦɥɟɧɢɟ ɧ

ɢɫɬɨɪɵ ɢɥɢ ɪɟɚɤɬɨɪɵ;

ɢɟ ɪɟɚɤɬɨɪɵ ɢɥɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ɫ

ɩɚɪɚɬɵ ɫ ɭɥɭɱɲɟɧɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬ

ɬɨɤɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɢɫɩɨ

ɚɰɢɢ ɫɭɳɟɫɬɜɭɸɳɟɝɨ ɷɥɟɤɬɪɨɨɛɨɪɭɞ

ɚɪɚɥɥɟɥɶɧɨɣ ɢ ɪɚɡɞɟɥɢɬɟɥɶɧɨɣ ɪɚɛɨ

, ɚ) ɩɨ ɡɧɚɱɟɧɢɹɦ ɧɚɱɚɥɶɧɨɝɨ ɢ ɭɞɚ

ɚɯ ɇɇ ɜ ɬɨɱɤɟ

(3)

ɢɤ ɧɟɢɡɦɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ



ɜ ɬɨɱɤɟ

Ɍ2:

(ȼ)ɧɨɦ (ɇ)ɧɨɦ

= 115/10,5 ɤȼ;

ɭ 10.1:

ɚ – ɢɫɯɨɞɧɚɹ ɫɯɟɦɚ; ɛ – ɫɯɟɦɚ ɡɚɦɟ

ɦ ɛɚɡɢɫɧɵɟ ɭɫɥɨɜɢɹ:

ɛ K

= 20

ɫɧɵɣ ɬɨɤ ɧɚ ɫɬɭɩɟɧɢ ɤɨɪɨɬɤɨɝɨ ɡɚɦ

ɪɭɞɨɜɚ-

ɨɦ ɫɟɤ-

ɣɬɪɚɥɟɣ

ɪɚɫɳɟɩ-

ɤɚɦɢ.

ɶɡɭɟɬɫɹ

ɜɚɧɢɹ.

ɬ ɬɪɚɧɫ-

ɧɨɝɨ ɬɨ-

115 ɤȼ,

ɟɧɢɹ

0 ɆȼȺ,

ɤɚɧɢɹ:

230

2000

110

310,5



ɤȺ.

Ɉɩɪɟɞɟɥɹɟɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɷɥɟɦɟɧɬɨɜ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ

(ɫɦ. ɪɢɫ. 10.7, ɛ) ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ:

2000

;

2* 3*

ɧɨɦ

11 2000

1,76

100 100 125



Ɋɚɫɫɱɢɬɵɜɚɟɦ ɬɨɤɢ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ:

x ɩɪɢ ɩɚɪɚɥɥɟɥɶɧɨɣ ɪɚɛɨɬɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ (ɜɵɤɥɸɱɚɬɟɥɶ ȼ

ɜɤɥɸɱɟɧ)

1* 2*

110

58,5

0,5 1 0,5 1,76



ɤȺ;

yyɩ

2 1,8 2 58,5 149iK I 

ɤȺ;

x ɩɪɢ ɪɚɡɞɟɥɶɧɨɣ ɪɚɛɨɬɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ (ɜɵɤɥɸɱɚɬɟɥɶ ȼ ɨɬ-

ɤɥɸɱɟɧ)

1* 3*

110

36,2

11,76



ɤȺ;

1, 8 2 3 6, 2 9 2, 2i 

ɤȺ.

ɉɟɪɟɯɨɞ ɫ ɪɚɡɞɟɥɶɧɨɣ ɧɚ ɩɚɪɚɥɥɟɥɶɧɭɸ ɪɚɛɨɬɭ ɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ

Ƚɉɉ ɜɵɡɵɜɚɟɬ ɩɨɜɵɲɟɧɢɟ ɬɨɤɨɜ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɧɚ ɲɢɧɚɯ ɇɇ ɧɚ

58,5 36,2

100 62

36,2





ɉɪɢɦɟɪ 10.2

Ⱦɥɹ ɫɯɟɦɵ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 10.8, ɚ, ɜɵɛɪɚɬɶ ɩɚɪɚɦɟɬɪɵ ɪɟ-

ɚɤɬɨɪɚ ɧɚɩɪɹɠɟɧɢɟɦ 10 ɤȼ ɞɥɹ ɨɝɪɚɧɢɱɟɧɢɹ ɦɨɳɧɨɫɬɢ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵ-

ɤɚɧɢɹ ɞɨ 200 ɆȼȺ ɧɚ ɲɢɧɚɯ 10 ɤȼ. Ɇɨɳɧɨɫɬɶ ɄɁ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɫɢɫ-

ɬɟɦɨɣ, ɩɪɢ ɬɪɟɯɮɚɡɧɨɦ ɄɁ ɧɚ ɜɵɫɲɟɣ ɫɬɨɪɨɧɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɜ ɬɨɱɤɟ

ɫɨɫɬɚɜɥɹɟɬ 3000 ɆȼȺ. ɉɚɪɚɦɟɬɪɵ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ:

ɧɨɦ

= 40 ɆȼȺ,

(ȼ)ɧɨɦ (ɇ)ɧɨɦ

= 115/10,5 ɤȼ,

10,4