A cikin farkon da za su shafi karkashin kasa. Shafin karkashin kasa shi ne tattalin yadda ake tsara kasa wajen wasu gudanarwa da ke faru, kuma wannan ya faru da hanyoyin doka (ON da OFF). A cikin sistem na karkashin kasa, halin masana'antar da take sanya ya iya samun matsalolin da suka faru saboda waɗannan gudanarwa. Binciken waɗannan matsaloli a cikin shafin karkashin kasa suna nufin shafin karkashin kasa ta hanyar zamani da kuma shafin karkashin kasa ta hanyar zamani mai zurfi. Shafin karkashin kasa ta hanyar zamani yana nuna idan an yi daidaita ko ba a cikin sistem bayan an kara waɗannan gudanarwa mai yawa. Shafin karkashin kasa ta hanyar zamani mai zurfi yana nuna idan an yi daidaita ko ba a cikin sistem bayan an kara waɗannan gudanarwa mai zurfi.
Waɗannan gudanarwa zai iya kasance gudanarwar da take faru, amfani da ko rashin mutum mai yawa, ko kuma rashin kayayyakin. Matukar wannan bincike shine in samun idan takarda mai kasa yake ci abin daidai bayan an kara waɗannan gudanarwa. A cikin haka, an ke tsari kan tushen da ba su linearity. Matsayin Zai Yawanci Tsarin Kasa yana nuna karkashin kasa ta hanyar zamani. Wannan yana nuna hanyar tsarin mai kyau da ake amfani da ita. Ana amfani da shi don bincika karkashin kasa ta hanyar zamani masana'antar da yake da wahid ko kuma masana'atar biyu da yake da bus da maida tsaye.
A cikin kasa mai ba da rawa, karkashin kasa da aka bayarza yana nuna
Sani ma a duba waɗannan gudanarwar a cikin masana'anta da ya yi aiki a cikin hali mai daidai. A cikin haka, karkashin da aka bayarza yana nuna
Don kara waɗannan gudanarwa, circuit breaker a cikin wurin da ya faru ya kamata a buɗe. Wannan yanayi yana lura 5/6 cycles, kuma post-fault transient yana lura wadanda.
Masana'antar da ya bayar karkashin kasa yana sauki da steam turbine. Saboda mass system da turbine, tsarin lokaci yana nuna seconds, kuma saboda karkashin kasa, yana nuna milliseconds. Saboda haka, a lokacin da transients karkashin kasa suka faru, karkashin kasa yana daidai. Binciken karkashin kasa ta hanyar zamani yana nuna yadda sistem na karkashin kasa ya yi daidaita daga gudanarwa da kuma bayar karkashin kasa mai daidai da takarda mai kasa (δ).
An samun kurba na takarda mai kasa da aka nuna a fig.1. Sani a system da ya bayar ‘Pm’ karkashin kasa a takarda δ0 (fig.2) ya yi aiki a cikin hali mai daidai. Bayan an faru waɗannan gudanarwa; circuit breakers suka buɗe, kuma karkashin kasa ya ci zero. Amma Pm yana daidai. Saboda haka, accelerating power,
Yawan karkashin kasa yana nuna rate of change of kinetic energy stored within the rotor masses. Saboda haka, saboda tasirin mai daidai da non-zero accelerating power, rotor ya ci abinci. Saboda haka, takarda mai kasa (δ) ya ci.
A nan, a muke so kuɗi δc da aka buɗe circuit breaker. Karkashin kasa zai ci abin daidai. A lokacin, karkashin kasa zai fiye da karkashin kasa. Amma, accelerating power (Pa) zai ci negative. Saboda haka, masana'anta zai ci yadda. Takarda mai kasa zai ci saboda inertia a cikin rotor masses. Wannan ci akan yiwuƙe da kuma rotor masana'antar zai ci yadda ko kuma daidaita sistem yake ci.
Swings equation yana nuna
Pm → Karkashin kasa mai sauki
Pe → Karkashin kasa mai jirgin
δ → Takarda mai kasa
H → Inertia constant
ωs → Synchronous speed
Muna sanin,
Amfani da equation (2) a cikin equation (1), muna samu
A nan, zabi dt zuwa either side of equation (3) and integrate it among the two arbitrary load angles which are δ0 and δc. Then we get,
Assume the generator is at rest when load angle is δ0. We know that
At the time of occurrence of a fault, the machine will start to accelerate. When the fault is cleared, it will continue to increase speed before it reaches to its peak value (δc). At this point,
So the area of accelerating from equation (4) is
Similarly, the area of deceleration is
Next, we can assume the line to be reclosed at load angle, δc. In this case, the area of acceleration is bigger than area of deceleration. A1 > A2. The load angle of the generator will pass the point δm. Beyond this point, the mechanical power is greater than electrical power and it forces the accelerating power to remain positive. Before slowing down, the generator therefore gets accelerate. Consequently, the system will become unstable.
When A2 > A1, the system will decelerate entirely before getting accelerated again. Here, the rotor inertia will force the successive acceleration and deceleration areas to become smaller than the previous ones. Consequently, the system will reach steady state.
When A2 = A1, the margin of the stability limit is defined by this condition. Here, the clearing angle is given by δcr, the critical clearing angle.
Since, A2 = A1. We get
The critical clearing angle is related to the equality of areas, it is termed as matsayin zai yawanci tsarin kasa. It can be used to find out the utmost limit on the load which the system can acquire without crossing the stability limit.
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