Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Расчет переходных процессов в электроэнергетических системах методом интеграла Дюамеля. Учебное пособие
.pdf
ɉɪɨɰɟɫɫ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩɢ ɢɦɟɟɬ ɱɟɬɵɪɟ ɷɬɚɩɚ. ɇɚ ɷɬɚɩɚɯ
I ɢ II ɭɫɬɪɨɣɫɬɜɨɦ ɡɚɳɢɬɵ ɮɢɤɫɢɪɭɟɬɫɹ ɬɨɤ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵ-
ɤɚɧɢɹ ɢ ɩɨɫɥɟ ɞɨɫɬɢɠɟɧɢɹ ɢɦ ɭɫɬɚɜɤɢ ɫɪɚɛɚɬɵɜɚɧɢɹ ɭɫɬɪɨɣɫɬɜɨ ɮɨɪɦɢɪɭɟɬ ɢ ɩɨɫɵɥɚɟɬ ɤɨɦɚɧɞɭ ɧɚ ɪɚɫɯɨɠɞɟɧɢɟ ɤɨɧɬɚɤɬɨɜ ɜɵɤɥɸɱɚɬɟɥɹ. ɇɚ ɷɬɚɩɟ III ɩɪɨɢɫɯɨɞɢɬ ɩɪɨɰɟɫɫ
ɧɚɪɚɫɬɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɭɝɟ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɨɝɪɚɧɢɱɟɧɢɸ ɬɨɤɚ ɢ ɫɜɟɞɟɧɢɸ ɟɝɨ
ɤ ɧɭɥɸ. ɗɬɚɩ IV ɜɤɥɸɱɚɟɬ ɫɧɢɠɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɨɧɬɚɤɬɚɯ ɜɵɤɥɸɱɚɬɟɥɹ ɞɨ ɧɚɩɪɹɠɟɧɢɹ
ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ.
ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɞɭɝɟ uɞ(t), ɜɥɢɹɸɳɟɟ ɧɚ ɯɚɪɚɤɬɟɪ ɨɬɤɥɸɱɟɧɢɹ ɜɵɤɥɸɱɚɬɟɥɟɦ ɰɟɩɢ, ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɦɨɠɟɬ ɛɵɬɶ
ɡɚɞɚɧɨ ɜ ɜɢɞɟ ɡɚɪɚɧɟɟ ɢɡɜɟɫɬɧɨɣ ɮɭɧɤɰɢɢ ɜɪɟɦɟɧɢ, ɨɩɪɟɞɟɥɹɟɦɨɣ ɥɢɲɶ ɤɨɧɫɬɪɭɤɬɢɜɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɞɭɝɨɝɚɫɢɬɟɥɶɧɨɣ ɤɚɦɟɪɵ ɜɵɤɥɸɱɚɬɟɥɹ. ɉɨɷɬɨɦɭ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ
ɩɪɨɰɟɫɫɚ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩɢ ɜɵɤɥɸɱɚɬɟɥɟɦ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɚ ɭɫɪɟɞɧɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɭɝɟ
(ɪɢɫ. 2.7), ɩɨɥɭɱɟɧɧɚɹ ɧɚ ɨɫɧɨɜɚɧɢɢ ɨɫɰɢɥɥɨɝɪɚɦɦ ɨɬɤɥɸɱɟɧɢɹ ɢɦ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ (ɪɢɫ. 2.8).
Ɇɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɚ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩɢ ɜɵɤɥɸɱɚɬɟɥɟɦ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɢɧɬɟɝɪɚɥɨɦ Ⱦɸɚɦɟɥɹ, ɝɞɟ
ɬɨɤ ɹɜɥɹɟɬɫɹ ɪɟɚɤɰɢɟɣ ɫɢɫɬɟɦɵ ɧɚ ɜɨɡɞɟɣɫɬɜɢɟ ɜ ɜɢɞɟ
ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɭɝɟ, ɤɨɬɨɪɨɟ ɢɦɟɟɬ ɫɥɨɠɧɭɸ ɮɨɪɦɭ. Ⱦɥɹ
ɷɬɨɝɨ ɧɭɠɧɨ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɰɟɩɶ ɩɪɢɜɟɫɬɢ ɤ ɩɚɫɫɢɜɧɨɣ ɩɭɬɟɦ ɢɡɴɹɬɢɹ ɢɡ ɫɯɟɦɵ ɢɫɬɨɱɧɢɤɨɜ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ,
ɬ. ɟ. ɭɱɟɫɬɶ ɜ ɤɚɱɟɫɬɜɟ ɢɫɬɨɱɧɢɤɚ ɬɨɥɶɤɨ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɞɭɝɟ
uɞ(t), ɨɛɪɚɬɧɨɟ ɩɪɢɥɨɠɟɧɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ Ud.
61
Ɋɢɫ. 2.7
Ɋɢɫ. 2.8
62
ɍɱɟɬ ɬɨɤɚ, ɜɵɡɵɜɚɟɦɨɝɨ ɢɫɬɨɱɧɢɤɚɦɢ ɷɧɟɪɝɢɢ, ɜɯɨɞɹɳɢɦɢ ɜ ɫɨɫɬɚɜ ɚɤɬɢɜɧɨɝɨ ɞɜɭɯɩɨɥɸɫɧɢɤɚ, ɤɨɬɨɪɵɦ ɦɨɠɧɨ
ɡɚɦɟɧɢɬɶ ɪɚɫɫɦɚɬɪɢɜɚɟɦɭɸ ɰɟɩɶ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɧɬɚɤɬɨɜ
ɜɵɤɥɸɱɚɬɟɥɹ, ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧ ɦɟɬɨɞɨɦ ɧɚɥɨɠɟɧɢɹ.
ɉɪɢ ɷɬɨɦ ɬɨɤ ɜ ɰɟɩɢ ɫ ɢɫɬɨɱɧɢɤɨɦ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ U
ɢ ɢɫɬɨɱɧɢɤɨɦ ɬɨɤɚ, ɢɦɢɬɢɪɭɸɳɢɦ ɢɧɞɭɤɬɢɜɧɵɟ ɷɥɟ-
d
ɦɟɧɬɵ ɨɬɤɥɸɱɚɟɦɨɣ ɜɟɬɜɢ ɩɪɢ ɧɚɥɢɱɢɢ ɧɚɱɚɥɶɧɨɝɨ ɬɨɤɚ,
ɧɚɯɨɞɢɬɫɹ ɩɪɢ ɜɤɥɸɱɟɧɧɨɦ ɜɵɤɥɸɱɚɬɟɥɟ ɢ ɧɟɧɭɥɟɜɵɯ
ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɶ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩɢ ɜɵɤɥɸɱɚɬɟɥɟɦ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɚɥɝɟɛɪɚɢɱɟɫɤɨɣ ɫɭɦɦɨɣ ɫɨɫɬɚɜɥɹɸɳɢɯ
ɬɨɤɚ ɨɬ ɤɚɠɞɨɝɨ ɢɫɬɨɱɧɢɤɚ.
ɉɪɢɦɟɧɹɹ ɩɟɪɜɭɸ ɮɨɪɦɭ ɡɚɩɢɫɢ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ
(1.81), ɩɨɥɭɱɢɦ ɜ ɨɛɳɟɦ ɜɢɞɟ ɮɭɧɤɰɢɸ ɬɨɤɚ ɞɥɹ ɧɟɤɨɬɨɪɨɝɨ
n-ɝɨ ɦɨɦɟɧɬɚ ɧɚɛɥɸɞɟɧɢɹ
௧
ᇱ
݅
ሺݐሻ
+ න
= න
௧
మ
݀ݑ
భ
௧
బ
ˇଶ
ሺɒሻ
݀ݑ
ˇଵ
݀ɒ
ሺɒሻ
݄ሺݐെɒሻ݀ɒ
݄ሺݐെɒሻ݀ɒ
+ ڮ
+
݀ɒ
௧
భ
௧
ڮ+ න
ೖ
݀ݑ
ˇ
ሺɒሻ
݄ሺݐെɒሻ݀ɒ
+ ڮ
(2.48)
݀ɒ
௧
ೖషభ
௧
ڮ+ න
݀ݑ
ˇ
ሺɒሻ
݄ሺݐെɒሻ݀߬
,
݀ɒ
௧
షభ
݇=1,2,…,݊,
63
ɝɞɟ u
ɞ1
(IJ), u
(IJ), …, u
ɞ2
(IJ), …, u
ɞk
(IJ) – ɮɭɧɤɰɢɢ ɧɚɩɪɹɠɟ-
ɞn
ɧɢɹ ɧɚ ɞɭɝɟ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ n-ɦ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ;
h(t – IJ) – ɮɭɧɤɰɢɹ, ɜɵɪɚɠɚɸɳɚɹ ɫɬɭɩɟɧɱɚɬɭɸ ɩɟɪɟɯɨɞɧɭɸ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɧɚ ɜɫɟɦ ɜɪɟɦɟɧɧɨɦ ɞɢɚɩɚɡɨɧɟ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɭɝɟ ɧɟ ɢɦɟɟɬ
ɬɨɱɟɤ ɪɚɡɪɵɜɚ (ɪɢɫ. 2.7), ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɜ ɫɨɨɬɧɨɲɟɧɢɢ
(2.48) ɨɬɫɭɬɫɬɜɭɸɬ ɫɥɚɝɚɟɦɵɟ ɢɡ ɥɟɜɨɣ ɱɚɫɬɢ ɜɵɪɚɠɟɧɢɹ
(1.81).
ɇɚɣɞɟɦ ɩɟɪɟɯɨɞɧɭɸ ɫɬɭɩɟɧɱɚɬɭɸ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɰɟɩɢ
ɩɪɢ ɫɬɭɩɟɧɱɚɬɨɦ ɟɞɢɧɢɱɧɨɦ ɫɢɝɧɚɥɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɨɧɬɚɤɬɚɯ ɜɵɤɥɸɱɚɬɟɥɹ, ɢɦɟɸɳɟɦ ɨɛɪɚɬɧɵɣ ɡɧɚɤ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
ሻ
݅ሺݐሻ+ ܮ
ܴ
ʬ
ʬ
݀݅ሺݐ
= െܪሺݐ
݀ݐ
(2.49)
ሻ
,
ɝɞɟ Rɗ ɢ Lɗ – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɷɤɜɢɜɚɥɟɧɬɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
ɢ ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɢɧɞɭɤɬɢɜɧɨɫɬɶ ɰɟɩɢ. Ⱦɚɧɧɨɦɭ ɭɪɚɜɧɟɧɢɸ
ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɩɟɪɚɰɢɨɧɧɨɟ
1
ܴʬ݅ሺሻ+ ܮʬ݅ሺሻ= െ
,
(2.50)
ɨɬɤɭɞɚ ɢɡɨɛɪɚɠɟɧɢɟ ɞɥɹ ɬɨɤɚ
݅ሺሻ= െ
ܮ
ʬ
1
1
ቀ+
.
ܴ
ʬ
ቁ
ܮ
ʬ
(2.51)
64
Ɉɪɢɝɢɧɚɥ ɷɬɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɢɦɟɟɬ ɜɢɞ
ோ
1
݅ሺݐሻ= െ
ܴ
ʬ
ቆ1 െ݁
ʬ
ି
௧
ʬ
ቇ.
(2.52)
Ɍɨɝɞɚ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɟɪɟɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɤɨɝɞɚ
ɩɨɞ ɪɟɚɤɰɢɟɣ ɩɨɧɢɦɚɟɬɫɹ ɬɨɤ ɰɟɩɢ, ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
ோ
ሼݐሽ
1
௨
= െ
݄
ܴ
ʬ
ቆ1 െ݁
ି
ʬ
௧
ʬ
ቇήܪሺݐ
ሻ
.
(2.53)
Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɟɪɟɯɨɞɧɚɹ ɫɬɭɩɟɧɱɚɬɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɛɭ-
ɞɟɬ ɨɞɢɧɚɤɨɜɨɣ ɧɚ ɤɚɠɞɨɦ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɮɭɧɤɰɢɹ, ɜɵɪɚɠɚɸɳɚɹ ɫɬɭɩɟɧɱɚɬɭɸ ɩɟɪɟɯɨɞɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɜ (2.48) ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ
ɜɵɪɚɠɟɧɢɟɦ
݄ሺݐെɒሻ= െ
ܴ
൬
ʬ
1 െ݁
1
ି
௧ିத
த
ʬ
,
൰
(2.54)
ɝɞɟ
ܴ
ɒ
ʬ
=
.
ʬ
(2.55)
ܮ
ʬ
Ɍɨɝɞɚ, ɜ ɨɛɳɟɦ ɜɢɞɟ ɮɭɧɤɰɢɹ ɬɨɤɚ ɞɥɹ ɧɟɤɨɬɨɪɨɝɨ ɦɨɦɟɧɬɚ ɧɚɛɥɸɞɟɧɢɹ ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɮɭɧɤɰɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɭɝɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
65
௧
భ
= െ
1
ܴ
ʬ
1
ܴ
1
න
ܴ
ʬ
௧
బ
௧
మ
݀ݑ
ˇଶ
න
݀ɒ
௧
భ
௧
ೖ
݀ݑ
න
ʬ
௧
ೖషభ
௧
1
݀ݑ
න
ܴ
ʬ
௧
షభ
ᇱ
ሺݐሻ
݅
െ
ڮെ
ڮെ
݀ݑ
ሺɒሻ
ˇ
݀ɒ
ˇଵ
݀ɒ
ሺɒሻ
ˇ
݀ɒ
ሺɒሻ
1 െ݁
൬
൬
ሺɒሻ
1 െ݁
൬
ି
1 െ݁
1 െ݁
൬
௧ିத
த
ି
ʬ
௧ିத
த
ି
൰
ʬ
ି
݀ɒ
൰
௧ିத
த
௧ିத
த
ʬ
݀ɒ
ʬ
൰
െڮ
െڮ
݀ɒ
൰
݀ɒ
െ
(2.56)
,
݇= 1,2,…,݊.
ɂɡɦɟɧɟɧɢɟ ɬɨɤɚ ɜ ɰɟɩɢ ɫ ɜɤɥɸɱɟɧɧɵɦ ɜɵɤɥɸɱɚɬɟɥɟɦ ɢ
ɩɪɢ ɧɚɥɢɱɢɢ ɜ ɧɟɣ ɧɚɱɚɥɶɧɨɝɨ ɬɨɤɚ, ɜɵɡɜɚɧɧɨɟ ɬɨɥɶɤɨ ɜɯɨɞɧɵɦ ɧɚɩɪɹɠɟɧɢɟɦ Ud, ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
ᇱᇱ
ሺݐሻ
ܴʬ݅
ᇱᇱ
ሺݐሻ
+ ܮ
݀݅
ʬ
݀ݐ
= ܷ
.
ௗ
(2.57)
ɋɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɟɦɭ ɨɩɟɪɚɰɢɨɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
ܷ
ᇱᇱ
ሺሻ
ܴʬ݅
+ ܮʬ݅
ᇱᇱ
ሺሻ
=
ௗ
+ ܮʬ݅
ሺ0ሻ
,
(2.58)
ɨɬɤɭɞɚ
ܷ
=
ௗ
ܮ
ʬ
ᇱᇱ
ሺሻ
݅
ή
ቀ+
1
ሺ0ሻ
+ ݅
ܴ
ʬ
ቁ
ܮ
ʬ
+
1
.
ܴ
ʬ
ܮ
ʬ
(2.59)
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɨɛɳɟɦ ɜɢɞɟ ɢɡɦɟɧɟɧɢɟ ɬɨɤɚ ɜ ɰɟɩɢ ɫ
ɢɫɬɨɱɧɢɤɨɦ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ Ud ɢ ɩɪɢ ɧɟɧɭɥɟɜɵɯ
ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ, ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɨ ɜ ɨɛɳɟɦ ɜɢɞɟ ɞɥɹ
ɤɚɠɞɨɝɨ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ
66
௧ି௧
ܷ
=
ܴ
ௗ
൬
ʬ
1 െ݁
ᇱᇱ
ሺݐሻ
݅
షభ
ି
த
ʬ
ᇱᇱ
ሺ
+ ݅
൰
ݐ
ିଵ
௧ି௧
షభ
ି
த
ሻ
ʬ
(2.60)
݁
.
ɂɬɚɤ, ɚɥɝɟɛɪɚɢɱɟɫɤɚɹ ɫɭɦɦɚ ɫɨɫɬɚɜɥɹɸɳɢɯ ɬɨɤɚ ɨɬ ɤɚɠɞɨɝɨ ɢɫɬɨɱɧɢɤɚ, ɩɪɟɞɫɬɚɜɥɹɸɳɚɹ ɫɨɛɨɣ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ
ɦɨɞɟɥɶ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩɢ ɜɵɤɥɸɱɚɬɟɥɟɦ, ɩɪɢɧɢɦɚɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ
ሺݐሻ
݅
= ݅
ᇱ
ሺݐሻ
+ ݅
ᇱᇱ
ሺݐሻ
,
(2.61)
ɢɥɢ
௧ି௧
ܷ
ሺɒሻ
ି
ܴ
1
ܴ
ି
ܴ
=
ሺɒሻ
த
ʬ
ʬ
௧
த
ʬ
ˇ
݀ɒ
௧
ʬ
௧
ʬ
ܴ
݁
௧
න
ೖషభ
௧
ሺɒሻ
݁
த
ೖషభ
௧
ೖ
షభ
ௗ
ʬ
த
த
ʬ
௧
න
௧
න
1 െ݁
൬
த
ʬ
݀ɒ
݀ɒ
ೖ
݀ݑ
݀ݑ
݀ݑ
݀ɒ
ˇ
݀ɒ
െ
െ
ˇ
݀ɒ
ሺɒሻ
ˇ
݀ɒ
+ ݅
ሺݐሻ
݅
௧
௧
భ
ି
த
ʬ
+
+
݁
ܴ
௧
ି
த
݁
ܴ
ʬ
݀ݑ
ˇଵ
න
ʬ
௧
ʬ
න
݀ɒ
௧
బ
మ
݀ݑ
ˇଶ
݀ɒ
௧
భ
݁
ڮ+
െ
݁
ڮ+
௧
1
െ
ܴ
݀ݑ
න
ʬ
௧
షభ
ି
1
ܴ
ሺɒሻ
ሺɒሻ
ᇱᇱ
1
ܴ
ʬ
݀ɒ
షభ
த
ʬ
+
൰
௧
భ
න
ʬ
௧
బ
௧
మ
݀ݑ
න
݀ݑ
ˇଶ
ˇଵ
݀ɒ
ሺɒሻ
ሺɒሻ
݀ɒ
݀ɒ
+
+ ڮ
݀ɒ
௧
భ
த
த
ʬ
݀ɒ
െ
(2.62)
݁
+ ڮ
த
த
ʬ
݁
݀ɒ
െ
௧ି௧
షభ
ି
த
ሺ
ሻ
ݐ
ିଵ
ʬ
݁
,
݇= 1,2,…,݊.
67
ɂɬɚɤ, ɜɵɪɚɠɟɧɢɟ (2.62) ɩɨɡɜɨɥɹɟɬ ɩɨɥɧɨɫɬɶɸ ɪɚɫɫɱɢɬɚɬɶ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩɢ ɩɪɢ ɥɸɛɵɯ ɮɨɪɦɚɯ
ɜɫɬɪɟɱɧɵɯ ɧɚɩɪɹɠɟɧɢɣ, ɜɜɨɞɢɦɵɯ ɜ ɰɟɩɶ ɜɵɤɥɸɱɚɬɟɥɹɦɢ ɜ ɪɟɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɩɨɫɨɛɚɯ ɢɯ ɚɩɩɪɨɤɫɢɦɚɰɢɢ.
Ɏɭɧɤɰɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɭɝɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɤɪɢɜɨɣ
ɧɚ ɪɢɫ. 2.7, ɨɩɢɫɵɜɚɟɬɫɹ ɧɚ ɤɚɠɞɨɦ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ
ɭɪɚɜɧɟɧɢɟɦ
ሺݐሻ
ˇ
= ܽ
ݑ
ˇ
ݐ
,
(2.63)
ɝɞɟ aɞn – ɤɨɷɮɮɢɰɢɟɧɬ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɫɤɨɪɨɫɬɶ ɧɚɪɚɫɬɚɧɢɹ ɜɫɬɪɟɱɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ, ȼ/ɫ. Ɉɬɤɭɞɚ ɩɪɨɢɡɜɨɞɧɚɹ ɷɬɨɣ
ɮɭɧɤɰɢɢ ɜ ɜɵɪɚɠɟɧɢɢ (2.62) ɪɚɜɧɚ
ሺ߬ሻ
݀ݑ
ˇ
݀߬
= ܽ
(2.64)
.
ˇ
ɉɨɞɫɬɚɜɥɹɹ (2.64) ɜ ɜɵɪɚɠɟɧɢɟ (2.62), ɞɥɹ ɤɚɠɞɨɝɨ ɪɚɫɱɟɬɧɨɝɨ ɢɧɬɟɪɜɚɥɚ ɜ ɨɛɳɟɦ ɜɢɞɟ ɧɚɯɨɞɢɦ
௧ି௧
ܷ
ି
௧
த
ି
த
ି
ିଵ
=
௧
த
ʬ
௧
ʬ
த
ܴ
ʬ
න݁
௧
బ
௧
మ
න݁
௧
భ
௧
න݁
௧
ೖషభ
௧
ʬ
௧
ሻ
݁
ௗ
൬
ʬ
௧
భ
த
த
ೖ
௧
න݁
షభ
௧ି௧
ି
1 െ݁
த
த
ʬ
݀ɒ
ʬ
݀ɒ
த
த
ʬ
݀ɒ
த
த
ʬ
షభ
த
ʬ
݀ɒ
ሺݐሻ
݅
ܽ
ˇଵ
݁
+
ܴ
ʬ
ܽ
ି
ˇଶ
݁
+
ܴ
ʬ
ܽ
ˇ
ڮ+
ڮ+
ܴ
+݅
݁
ʬ
ܽ
ˇ
݁
ܴ
ʬ
ᇱᇱ
ሺ
ݐ
షభ
ି
த
ʬ
+
൰
௧
భ
ܽ
ˇଵ
െ
െ
െ
ܽ
ܴ
െ
ܴ
ˇଶ
ʬ
ܽ
ܴ
න݀ɒ
ʬ
௧
௧
න݀ɒ
௧
భ
ˇ
ʬ
௧
ܽ
ˇ
ܴ
ʬ
బ
మ
௧
ೖ
න݀ɒ
ೖషభ
௧
න݀ɒ
௧
షభ
+ ڮ
, ݇=1,2,…,݊,
+
(2.65)
+ ڮ
+
68
ɢɥɢ, ɜɵɩɨɥɧɢɜ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ
௧ି௧
൰
െܽ
ೖ
ି
െܽ
െ݁
ˇଶ
த
ି
షభ
ʬ
ˇଵ
ܴ
௧ି௧
൰
1
ܴ
1
ʬ
த
+
ሺ
ݐ
ʬ
ሺ
ݐଶെݐ
ೖషభ
ʬ
൰
ଵെݐ
ଵ
െ
ሻ
ሻ
+
+ ڮ
(2.66)
ܷ
ሺݐሻ
݅
+ܽ
ܮ
ˇଵ
ܴ
ʬ
ܮ
ˇଶ
ʬ
ܴ
ʬ
ଶ
ڮ+ ܽ
+ܽ
௧ି௧
ି
ʬ
݁
൬
ଶ
௧ି௧
ି
த
݁
൬
ˇ
ௗ
=
భ
த
ʬ
మ
ʬ
ܮ
ܴ
ܴ
െ݁
െ݁
ʬ
ଶ
ʬ
ʬ
ି
݁
൬
1 െ݁
൬
௧ି௧
ି
த
௧ି௧
భ
த
ʬ
௧ି௧
ି
த
బ
ʬ
൰
ʬ
1
ڮ+ ܽ
ˇ
ܴ
+݅
ˇ
ሻ
ܴ
݁
ሺ
ʬ
௧ି௧
ି
௧ି௧
ି
ݐെݐ
షభ
த
ʬ
షభ
த
ʬ
െܽ
ܮ
ʬ
1 െ݁
൬
ଶ
ʬ
ᇱᇱ
ሺ
ݐ
ିଵ
ሻ
+ ڮ
ିଵ
1
ˇ
ሺ
ݐെݐ
ܴ
ʬ
൰
െܽ
, ݇=1,2,…,݊.
ିଵ
ሻ
+
ɂɬɚɤ, ɧɚ ɤɚɠɞɨɦ ɷɬɚɩɟ ɩɪɨɰɟɫɫɚ ɨɬɤɥɸɱɟɧɢɹ ɰɟɩɢ ɮɭɧɤɰɢɹ ɬɨɤɚ ɢɦɟɟɬ ɜɢɞ:
– ɧɚ ɷɬɚɩɟ I ɜ ɢɧɬɟɪɜɚɥɟ 0 t t
1
ܷ
=
ܴ
ௗ
ʬ
1 െ݁
൬
ሺݐሻ
݅
ଵ
௧
ି
ఛ
ʬ
+ ܫ݁
൰
௧
ି
த
ʬ
,
(2.67)
ɝɞɟ I0 – ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ i1(t) (ɩɪɢ t = 0) ɜ ɤɨɪɨɬɤɨɡɚɦɤɧɭɬɨɣ ɰɟɩɢ.
– ɧɚ ɷɬɚɩɟ II ɜ ɢɧɬɟɪɜɚɥɟ t1 t t
2
௧ି௧
ܷ
=
ܴ
ௗ
ʬ
1 െ݁
൬
ሺݐሻ
݅
ଶ
భ
ି
த
ʬ
ᇱᇱ
ሺ
+ ݅
൰
ଶ
௧ି௧
భ
ି
த
ʬ
ሻ
ݐ
݁
ଵ
,
(2.68)
69
ɝɞɟ
௧
ܷ
ᇱᇱ
ሺ
݅
ݐ
ଵ
ଶ
ᇱᇱ
=
ሺ
݅
ݐ
ଵ
ଵ
ሻ
ௗ
ሻ
=
ܴ
ʬ
1 െ݁
൬
భ
ି
த
ʬ
+ ܫ݁
൰
௧
భ
ି
த
ʬ
.
(2.69)
– ɧɚ ɷɬɚɩɟ III ɜ ɢɧɬɟɪɜɚɥɟ t
ܷ
=
ௗ
+ ܽ
ቈ
ܴ
ʬ
ሺݐሻ
݅
ଷ
ˇଷ
2
ܮ
ʬ
ଶ
ܴ
ʬ
1
െܽ
ˇଷ
ሺ
ܴ
ʬ
ݐെݐ
ሻ
+ ݅
ଶ
ɝɞɟ
ܷ
ᇱᇱ
ሺ
݅
ݐ
ଷ
ᇱᇱ
=
ሺ
݅
ݐ
ଶ
ଶ
ሻ
ଶ
ᇱᇱ
+݅
ଶ
ௗ
ሻ
=
ܴ
ʬ
ି
ሺ
ሻ
ݐ
݁
ଵ
– ɧɚ ɷɬɚɩɟ IV ɜ ɢɧɬɟɪɜɚɥɟ t3 t t
ܷ
=
ˇଷ
ௗ
+ ܽ
ቈ
ܴ
ʬ
ܮ
ʬ
ଶ
ܴ
ʬ
ሺݐሻ
݅
ସ
+ܽ
ܮ
ʬ
ˇସ
ଶ
ܴ
ʬ
௧ି௧
య
ି
த
ʬ
݁
൬
1
െܽ
ˇଷ
ܴ
ሺ
ʬ
ݐଷെݐ
+݅
ሻ
െܽ
ଶ
ᇱᇱ
ሺ
ሻ
ݐ
݁
ଷ
ସ
t t
1 െ݁
൬
ᇱᇱ
ሺ
ଷ
1 െ݁
൬
௧
మି௧భ
த
ʬ
1 െ݁
൬
െ݁
ˇସ
ܴ
௧ି௧
య
ି
த
ʬ
ݐ
ି
1
ଶ
.
௧ି௧
ʬ
,
3
ି
ି
ሻ
݁
௧
ି
4
ି
మ
த
ʬ
ሺ
ݐെݐ
௧ି௧
த
௧ି௧
த
మି௧భ
த
ʬ
௧ି௧
த
െ
൰
మ
ʬ
െ
൰
(2.70)
మ
ʬ
,
+
൰
య
ʬ
+
൰
(2.72)
ሻ
+
ଷ
(2.71)
ɝɞɟ
௧
ܷ
ᇱᇱ
ሺ
݅
ݐ
ସ
ᇱᇱ
=
ሺ
݅
ݐ
ଷ
ଷ
ᇱᇱ
+݅
ଷ
ሻ
ଷ
ௗ
ሻ
=
ሺ
ݐ
1 െ݁
൬
ܴ
ʬ
௧
యି௧మ
ି
த
ʬ
ሻ
݁
ଶ
యି௧మ
ି
த
ʬ
+
൰
(2.73)
.
70
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]