TRANSIENT STABILITY CONSTRAINTS FOR

OPTIMAL POWER FLOW

by

 MATHANKUMAR.S

VMKVEC 

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.