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Department of Electrical Engineering, R H S C O E M S R, Nashik
Gokhale Education Society’s
R. H. Sapat College of Engineering, Management Studies
And Research. Nashik-422005
Department of Electrical Engineering
LABORATORY
MANUAL CUM
JOURNAL
PRACTICAL: POWER SYSTEM OPERATION AND CONTROL
TITLE: To apply equal area criteria for stability analysis under sudden rise in
mechanical power
EXPERIMENT NO. : 01 ISSUE NO:02 ISSUE DATE:15/06/2019
REV. DATE : REV. NO. : 02 DEPT. :ELECTRICAL ENGINEERING
LABORATORY : SOFTWARE LAB SEMESTER:VIII PAGE:19
Department of Electrical Engineering, R H S C O E M S R, Nashik
Department of Electrical Engineering, R H S C O E M S R, Nashik
2𝑑𝛿
𝑑𝑡
𝑑
𝑑𝑡 𝑑𝛿
𝑑𝑡
2
𝑑𝛿
𝑑𝑡
𝑑𝛿
𝑑𝑡
Department of Electrical Engineering, R H S C O E M S R, Nashik
𝑃𝑚1 − 𝑃𝑒 𝑑𝛿 = 𝑎𝑟𝑒𝑎 𝑎𝑏𝑐 = 𝑎𝑟𝑒𝑎 𝐴1
𝛿1
𝛿0
𝑃𝑚1 − 𝑃𝑒 𝑑𝛿 = 𝑎𝑟𝑒𝑎 𝑏𝑑𝑒 = 𝑎𝑟𝑒𝑎 𝐴2
𝛿𝑚𝑎𝑥
𝛿1
Department of Electrical Engineering, R H S C O E M S R, Nashik
Department of Electrical Engineering, R H S C O E M S R, Nashik
𝑃𝑚 𝛿1 − 𝛿0 − 𝑃𝑚𝑎𝑥 𝑠𝑖𝑛𝛿𝑑𝛿 = 𝑃𝑚𝑎𝑥 𝑠𝑖𝑛𝛿𝑑𝛿 − 𝑃𝑚 𝛿𝑚𝑎𝑥 − 𝛿1 𝛿𝑚𝑎𝑥
𝛿1
𝛿1
𝛿0
𝑃𝑚 𝛿𝑚𝑎𝑥 − 𝛿0 = 𝑃𝑚𝑎𝑥 (𝑐𝑜𝑠𝛿0 − 𝑐𝑜𝑠𝛿𝑚𝑎𝑥 )
𝑃𝑚 = 𝑃𝑚𝑎𝑥 𝑠𝑖𝑛𝛿𝑚𝑎𝑥
𝑠𝑖𝑛𝛿𝑚𝑎𝑥 𝛿𝑚𝑎𝑥 − 𝛿0 + 𝑐𝑜𝑠𝛿𝑚𝑎𝑥 = 𝑐𝑜𝑠𝛿0
Department of Electrical Engineering, R H S C O E M S R, Nashik
𝑓 𝑥 = 𝑐𝑜𝑠𝛿0 − 𝑐𝑜𝑠𝛿𝑚𝑎𝑥 − 𝑠𝑖𝑛𝛿𝑚𝑎𝑥 𝛿𝑚𝑎𝑥 − 𝛿0
𝑓′ 𝑥 = 𝑐𝑜𝑠𝛿𝑚𝑎𝑥 𝛿0 − 𝛿𝑚𝑎𝑥
−𝑓(𝑥)
𝑓 ′ (𝑥)
Department of Electrical Engineering, R H S C O E M S R, Nashik
Department of Electrical Engineering, R H S C O E M S R, Nashik
Department of Electrical Engineering, R H S C O E M S R, Nashik
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