This document presents an optimal power flow (OPF) analysis that considers transient stability constraints in addition to traditional OPF constraints like generator limits and line flow limits. The OPF formulation is modified to allow for bilateral and multilateral wheeling transactions while respecting stability limits. Test cases are presented applying the approach to the IEEE 30 bus system for various wheeling transaction scenarios. Simulation results demonstrating transient stability are also shown.

1. TRANSIENT STABILITY
CONSTRAINTS FOR
OPTIMAL POWER FLOW
by
MATHANKUMAR.S
VMKVEC

2. OBJECTIVES
• To perform the OPF analysis considering the line flow limits also.
• To carry out the wheeling transactions.
• To check the transient stability limits.

3. PROBLEM FORMULATION
The objective of the OPF problem is to minimize the total
Fuel cost of the generator unit
Obj = $/hr …..(1) ∑=
gn
i 1
Fi (Pi)
Subject to the equality constraint in real power balance
Pi – PL – PD = 0 …..(2)∑=
gn
i 1

4. GENERATOR INEQUALITY CONSTRAINTS
Generator real power limits
Pi min
≤ Pi
≤ Pi max
.....(3)
Generator reactive power limits
Qi min
≤ Qi
≤ Qi max
.....(4)

5. 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

6. MODELING OF WHEELING TRANSACTIONS
Bilateral transactions
Pgi
– Pdj
= 0 …..(9)
Multilateral transactions
∑
k
i
Pgi - ∑
k
j
Pdj = 0 …..(10) k = 1, 2, …….. tk
tk
– Total no. of wheeling transactions.

7. 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

8. DESCRIPTION OF TEST SYSTEM
IEEE 30 bus system has
• No. of generators: 6
• Tap changing transformers: 4
• Lines: 41
• Base load: 283.4MW

9. 0 0.5 1 1.5
-60
-50
-40
-30
-20
-10
0
Time (sec)
Relativerotorangles(Degree)
TWO SIMULTANEOUS BILATERAL TRANSACTIONS
G2
G11
G13
G5
G8

10. CASE STUDIES
Table: 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

11. Table: 3 Two Simultaneous Multilateral transactionsTable: 3 Two Simultaneous Multilateral transactions
Transactions
Bus 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

12. 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.

13. 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.

14. REFERENCES
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Ltd, 2002.
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