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تغیر مسیر یافته از - پریونیت
زمان تقریبی مطالعه: 6 دقیقه
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سیستم پریونیت

در مهندسی برق و به خصوص مهندسی برق-قدرت برای بیان مقادیر از سیستم پریونیت (انگلیسی: Per-unit system) استفاده می‌شود.

پریونیت که به نام در-واحدی نیز شناخته می‌شود اینگونه است که به جای بیان اندازهٔ کمیت، اندازه را بر مقدار پایه تقسیم می‌کنند و عدد حاصل را که بدون واحد است به عنوان مقدار پریونیت استفاده می‌کنند.

اهداف

استفاده از این سیستم چندین مزیت دارد که می‌توان به موارد زیر اشاره کرد:

  • دستگاه‌های مشابه مقادیر پریونیت مشابهی دارند. یعنی با وجود اینکه ژنراتورها، موتورها و... مقادیر توان و امپدانس متفاوتی دارند ولی این مقادیر در مقیاس پریونیت تقریباً یکسانند و به همین دلیل بررسی خطا تسهیل می‌شود.
  • تولیدکنندگان معمولاً امپدانس را بر حسب پریونیت بیان می‌کنند.
  • با نرمالیزه کردن مقادیر با مقدار مبنا محاسبات بسیار راحتتر می‌شود. چراکه معمولاً مقدار مبنا بزرگترین مقدار موجود در شبکه انتخاب می‌شود و لذا مقادیر پریونیت کوچکتر از یک خواهد بود.

روابط ریاضی

Equation
Base number selection {\displaystyle {\text{Base number selection}}}
Arbitrarily selecting from ohm's law the two base numbers: base voltage and base current {\displaystyle {\text{Arbitrarily selecting from ohm's law the two base numbers: base voltage and base current}}}
1 {\displaystyle 1}
We have, Z = E I {\displaystyle {\text{We have, Z}}={\frac {E}{I}}}
2 {\displaystyle 2}
Base ohms = base volts base amperes {\displaystyle {\text{Base ohms}}={\frac {\text{base volts}}{\text{base amperes}}}}
3 {\displaystyle 3}
Per-unit volts = volts base volts {\displaystyle {\text{Per-unit volts}}={\frac {\text{volts}}{\text{base volts}}}}
4 {\displaystyle 4}
Per-unit amperes = amperes base amperes {\displaystyle {\text{Per-unit amperes}}={\frac {\text{amperes}}{\text{base amperes}}}}
5 {\displaystyle 5}
Per-unit ohms = ohms base ohms {\displaystyle {\text{Per-unit ohms}}={\frac {\text{ohms}}{\text{base ohms}}}}
Alternatively, choosing base volts and base kva values, we have, {\displaystyle {\text{Alternatively, choosing base volts and base kva values, we have,}}}
in single-phase systems: {\displaystyle {\text{in single-phase systems:}}}
6 {\displaystyle 6}
Base amperes  = base kva * 1000 base volts {\displaystyle {\text{Base amperes }}={\frac {\text{base kva * 1000}}{\text{base volts}}}}
7 {\displaystyle 7}
Base amperes  = base kva base kv L − L {\displaystyle {\text{Base amperes }}={\frac {\text{base kva}}{{\text{base kv}}_{L-L}}}}
8 {\displaystyle 8}
Base ohms  = base volts base amperes {\displaystyle {\text{Base ohms }}={\frac {\text{base volts}}{\text{base amperes}}}}
and in three-phase systems: {\displaystyle {\text{and in three-phase systems:}}}
9 {\displaystyle 9}
Base amperes  = base kva * 1000 3 ∗ base volts {\displaystyle {\text{Base amperes }}={\frac {\text{base kva * 1000}}{{\sqrt {3}}*{\text{base volts}}}}}
10 {\displaystyle 10}
Base amperes  = base kva 3 ∗ base kv L − L {\displaystyle {\text{Base amperes }}={\frac {\text{base kva}}{{\sqrt {3}}*{\text{base kv}}_{L-L}}}}
11 {\displaystyle 11}
Base ohms  = base volts 3 ∗ base amperes {\displaystyle {\text{Base ohms }}={\frac {\text{base volts}}{{\sqrt {3}}*{\text{base amperes}}}}}
Working out for convenience per-unit ohms directly, we have {\displaystyle {\text{Working out for convenience per-unit ohms directly, we have}}}
for single-phase and three-phase systems: {\displaystyle {\text{for single-phase and three-phase systems:}}}
12 {\displaystyle 12}
Base ohms  = ohms * base kva k v L − L 2 ∗ 1000 {\displaystyle {\text{Base ohms }}={\frac {\text{ohms * base kva}}{kv_{L-L}^{2}*1000}}}
Short-Circuit Calculation Formulas {\displaystyle {\text{Short-Circuit Calculation Formulas}}}
Ohms conversions: {\displaystyle {\text{Ohms conversions:}}}
13 {\displaystyle 13}
Per-unit ohms reactance = ohms reactance *  kva base k v L − L 2 ∗ 1000 {\displaystyle {\text{Per-unit ohms reactance}}={\frac {{\text{ohms reactance * }}{\text{kva base}}}{kv_{L-L}^{2}*1000}}}
14 {\displaystyle 14}
Ohms reactance = %  reactance ∗ k v L − L 2 ∗ 10 kva base {\displaystyle {\text{Ohms reactance}}={\frac {\%{\text{ reactance}}*kv_{L-L}^{2}*10}{\text{kva base}}}}
15 {\displaystyle 15}
Per-unit ohms reactance = per cent ohms reactance 100 {\displaystyle {\text{Per-unit ohms reactance}}={\frac {\text{per cent ohms reactance}}{100}}}
Changing ohms from one kva base to another: {\displaystyle {\text{Changing ohms from one kva base to another:}}}
16 {\displaystyle 16}
%  ohms reactance on kva base 2 = kva base 2 kva base 1 ∗ %  ohms reactance on base 1 {\displaystyle \%{\text{ ohms reactance on kva base}}_{2}={\frac {{\text{kva base}}_{2}}{{\text{kva base}}_{1}}}*\%{\text{ ohms reactance on base}}_{1}}
17 {\displaystyle 17}
0/1 ohms reactance on kva base 2 = kva base 2 kva base 1  * 0/1 ohms reactance on base 1 {\displaystyle {\text{0/1 ohms reactance on kva base}}_{2}={\frac {{\text{kva base}}_{2}}{{\text{kva base}}_{1}}}{\text{ * 0/1 ohms reactance on base}}_{1}}
Changing incoming system reactance: {\displaystyle {\text{Changing incoming system reactance:}}}
a. If system reactance is given in percent, use Eq. 16 to change from one kva base to another. {\displaystyle {\text{a. If system reactance is given in percent, use Eq. 16 to change from one kva base to another.}}}
b. If system reactance is given in short-circuit symmetrical rms kva or current, convert to per-unit as follows: {\displaystyle {\text{b. If system reactance is given in short-circuit symmetrical rms kva or current, convert to per-unit as follows:}}}
18 {\displaystyle 18}
0/1 reactance = kva base used in reactance in studied calculation system short-circuit kva {\displaystyle {\text{0/1 reactance}}={\frac {\text{kva base used in reactance in studied calculation}}{\text{system short-circuit kva}}}}
19 {\displaystyle 19}
0/1 reactance = kva base used in reactance in studied calculation system short-circuit current *  3  * system kv L − L {\displaystyle {\text{0/1 reactance}}={\frac {\text{kva base used in reactance in studied calculation}}{{\text{system short-circuit current * }}{\sqrt {3}}{\text{ * system kv}}_{L-L}}}}
Calculating approximate motor kva base: {\displaystyle {\text{Calculating approximate motor kva base:}}}
a. For induction motors and 0.8 power factor synchronous motors {\displaystyle {\text{a. For induction motors and 0.8 power factor synchronous motors}}}
20 {\displaystyle 20}
kva base ≈  horsepower rating {\displaystyle {\text{kva base}}\approx {\text{ horsepower rating}}}
b. For unity power factor synchronous motors {\displaystyle {\text{b. For unity power factor synchronous motors}}}
21 {\displaystyle 21}
kva base ≈  0.8 * horsepower rating {\displaystyle {\text{kva base}}\approx {\text{ 0.8 * horsepower rating}}}
Converting ohms from one voltage to another: {\displaystyle {\text{Converting ohms from one voltage to another:}}}
22 {\displaystyle 22}
Ohms on basis of voltage 1 = ( voltage 1 voltage 2 ) 2  * ohms on basis of voltage 2 {\displaystyle {\text{Ohms on basis of voltage}}_{1}=({\frac {{\text{voltage}}_{1}}{{\text{voltage}}_{2}}})^{2}{\text{ * ohms on basis of voltage}}_{2}}
Short-circuit kva and current calculations {\displaystyle {\text{Short-circuit kva and current calculations}}}
Symmetrical short circuit kva: {\displaystyle {\text{Symmetrical short circuit kva:}}}
23 {\displaystyle 23}
= 100 * kva base %  X {\displaystyle ={\frac {\text{100 * kva base}}{\%{\text{ X}}}}}
24 {\displaystyle 24}
= kva base 0/1 X {\displaystyle ={\frac {\text{kva base}}{\text{0/1 X}}}}
25 {\displaystyle 25}
= 3 ∗ Voltage L − N 2 ohms reactance  * 1000 {\displaystyle =3*{\frac {{\text{Voltage}}_{L-N}^{2}}{{\text{ohms reactance}}{\text{ * 1000}}}}}
26 {\displaystyle 26}
= kv L − L 2  * 1000 ohms reactance {\displaystyle ={\frac {{\text{kv}}_{L-L}^{2}{\text{ * 1000}}}{\text{ohms reactance}}}}
Symmetrical short circuit current: {\displaystyle {\text{Symmetrical short circuit current:}}}
27 {\displaystyle 27}
= 100 * kva base %  X ∗ 3 ∗ kv L − L {\displaystyle ={\frac {\text{100 * kva base}}{\%{\text{ X}}*{\sqrt {3}}*{\text{kv}}_{L-L}}}}
28 {\displaystyle 28}
= kva base 0/1 X ∗ 3 ∗ kv L − L {\displaystyle ={\frac {\text{kva base}}{{\text{0/1 X}}*{\sqrt {3}}*{\text{kv}}_{L-L}}}}
29 {\displaystyle 29}
= kv L − L  * 1000 3 ∗ ohms reactance {\displaystyle ={\frac {{\text{kv}}_{L-L}{\text{ * 1000}}}{{\sqrt {3}}*{\text{ohms reactance}}}}}
Asymmetrical short-circuit current and kva: {\displaystyle {\text{Asymmetrical short-circuit current and kva:}}}
30 {\displaystyle 30}
Asymmetrical short-circuit current = symmetrical current * X/R factor  {\displaystyle {\text{Asymmetrical short-circuit current = symmetrical current * X/R factor }}}
31 {\displaystyle 31}
Asymmetrical short-circuit kva = symmetrical kva * X/R factor  {\displaystyle {\text{Asymmetrical short-circuit kva = symmetrical kva * X/R factor }}}

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