Date post: | 16-Jul-2015 |
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Engineering |
Upload: | mathankumar-subramaniam |
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OBJECTIVES
• To perform the OPF analysis considering the line flow limits also.
• To carry out the wheeling transactions.
• To check the transient stability limits.
PROBLEM FORMULATION
The objective of the OPF problem is to minimize the total
Fuel cost of the generator unit
Obj = $/hr …..(1) ∑=
gn
i 1Fi (Pi)
Subject to the equality constraint in real power balance
Pi – PL – PD = 0 …..(2)∑=
gn
i 1
GENERATOR INEQUALITY CONSTRAINTS
Generator real power limits
Pi min ≤ Pi ≤ Pi max .....(3)
Generator reactive power limits
Qi min ≤ Qi ≤ Qi max .....(4)
Bus Voltage magnitude limits
Vi min ≤ Vi ≤ Vi max …..(5)
Bus Voltage angle limits
δi min ≤ δi ≤ δi max …..(6)
Maximum line flow constraints
Lf i ≤ Lf max …..(7)
Transient stability limits
-δ max ≤ δ ≤ δ max …..(8)
LOAD FLOW CONSTRAINTS
MODELING OF WHEELING TRANSACTIONS
Bilateral transactions
Pgi – Pdj = 0 …..(9)
Multilateral transactions
∑k
i
Pgi - ∑k
jPdj = 0 …..(10) k = 1, 2, …….. tk
tk – Total no. of wheeling transactions.
Start
Prepare the line, bus, generator data of the power system
Perform the OPF analysis
Is there any wheeling transactions?Reduce the
Magnitude of power transfer
Compute the feasibility (line flow limits) and perform the transactions
Is there any Transient stability violations?
Print the results
Stop
No
No
Yes
Yes
FLOW CHART
DESCRIPTION OF TEST SYSTEM
IEEE 30 bus system has
• No. of generators: 6
• Tap changing transformers: 4
• Lines: 41
• Base load: 283.4MW
0 0.5 1 1.5-60
-50
-40
-30
-20
-10
0
Time (sec)
Rel
ativ
e ro
tor
angl
es (
Deg
ree)
TWO SIMULTANEOUS BILATERAL TRANSACTIONS
G2
G11
G13
G5
G8
CASE STUDIESTable: 1 Two Simultaneous Bilateral transactionsTable: 1 Two Simultaneous Bilateral transactions
Transactions
Bus No. Magnitude of power transfer (MW)From To
TB1 30 10 15
TB2 20 18 10
Table: 2 Four simultaneous Bilateral transactionsTable: 2 Four simultaneous Bilateral transactions
Transactions
Bus No. Magnitude of power transfer (MW)From To
TB1 30 10 15
TB2 20 18 10
TB3 28 15 20
TB4 24 14 25
Table: 3 Two Simultaneous Multilateral transactionsTable: 3 Two Simultaneous Multilateral transactions
TransactionsBus No. Magnitude of
Power Transfer(MW)
Bus No.
Magnitude of Power
Transfer(MW)From To
TM1
10 20 6 15
20 30 12 15 15 20
Total 50 50
TM2
17 15 28 20
22 20 4 15
25 30 9 15 29 15
Total 65 65
Table: 4 Two Bilateral and two Multilateral transactionsTable: 4 Two Bilateral and two Multilateral transactions
Transactions
Bus No. Magnitude of power transfer (MW)
From To
TB1 27 16 20
TB2 24 14 25
Two multilateral transactions as in case 3.
CONCLUSION
The wheeling transactions are carried out in the OPF problem and
optimal generator settings are obtained. The permitted wheeling
transactions are satisfying the line flow limits and transient stability
limits. The transient response curves are illustrated when a three phase
fault is developed in a transmission line. The developed OPF solution is
capable of giving optimal solution with transient stability limits.
REFERENCES1.H.W. Dommel and W.F. Tinney,” Optimal Power Flow Solutions”, IEEE Trans. Power Apparatus. Syst., Vol. PAS-87, pp. 1866-1876, Oct. 1968.
2.Hadi Saadat, Power system Analysis : Tata McGraw-Hill publishing company Ltd, 2002.
3.K.R. Padiyar, Dynamic and Stability Control : BS publications, II edition, 2002.
4.Xuemin Zhang, Y.H.Song, Quiang Lu, Shengwei Mei,”Dynamic Available Transfer Capability (ATC) Evaluation by Dynamic Constrained Optimization”, IEEE Power Engineering Review, May 2004.
5.Deqinag Gan, Robert J. Thomas, Ray D.Zimmerman, “A Transient Stability Constrained Optimal Power Flow”, Bulk Power System Dynamics and Control IV- Restructuring, Santorini, Greece,pp. 24-28, Aug. 1998.
6.Taiyou Yong, Robert Lasseter, ”Optimal Power Flow Formulation in Market of Retail Wheeling”, PSERC, pp. 99-103, 1999.
7.Jason Yuryevich, kit Po Wong, “Evolutionary Programming Based Optimal Power Flow Algorithm”, IEEE Transactions on Power Systems, Vol. 14, No. 4, Nov. 1999.
8.Yue yuan, Junji Kubokawa, and Hiroshi Sasaki, “A Solution of Optimal Power Flow With Multicontingency Transient Stability Constraints”, IEEE Transactions on Power Systems,Vol.18, No 3,Aug. 2003.
9.Yog Raj Sood, Narayana Prasad Padhy, Hari Om Gupta, “Assessment for Feasibility and Pricing of Wheeling Transactions under Deregulated Environment of Power industry”, Electrical Power and Energy Systems 26, pp. 163-171, 2004.
10.Yue yuan, Junji Kubokawa, and Hiroshi Sasaki, “ Pricing for transient stability”, IEEE DRPT 2004, conference proceedings, Hong kong, pp. 6-8, Apr. 2004.