1. 1 Identification of Voltage Stability Weak Points in Bulk Power System Tao He, Sujit Mandal, Floyd Galvan Entergy Presented to the NSF Applied Mathematics for Deregulated Electric Power Systems Workshop, Washington DC

2. 2 Entergy System 15,500 miles of Transmission Lines –500 kV, 230 kV, 161 kV, 138 kV, 115 kV, 69 kV 1450 Substations 14 Interfaces with neighboring companies with over 75 tie lines ~22,000 MW of Load ~ 2.4 Million customers in LA, MS, AR and TX ~45,000 MW of available generation by 2005 !!

3. 3 PV Curve Analysis - Disadvantages PV curves are not very helpful to find the weak points in a system PV analysis is scenario-based. If the scenario changes, a new PV curve analysis needs to be performed PV analysis is very time consuming. It is not suited for real-time operation purposes

4. 4 Basic Concepts For simplified two bus system, assuming: –The sending end is infinite bus, i.e. voltage = 1.0 p.u. –The receiving end load increases, keeping Qr/Pr ratio constant For any particular Qr/Pr ratio, the equations for receiving end voltage and power are

5. 5 PV Curves Equations 1 & 2 show that the PV curve can be drawn from Power-Angle and Voltage-Angle curves

6. 6 Power & Voltage at the Knee Point Figure shows the relationship between voltage stability and angle difference between the receiving and sending end buses The analytical equations for P rmax and E rmax at the knee point of the above PV curve can be derived from Equations 1 & 2:

7. 7 VSMI The Voltage Stability Margin Index (VSMI), for any given Qr/Pr ratio, can be defined as Lower values of VSMI indicate closer proximity to voltage collapse Above equations have been tested on simple two bus system

8. 8 Application to Large Scale Power System If a large scale power system can be represented by a simplified two bus system, then VSMI of every branch can be calculated by Equation 6

9. 9 Such an equivalent two bus system can be found, assuming: –Sending end system can be represented by an infinite bus, whose voltage is 1.0 p.u. –The X/R ratio of source impedance is the same as that of the interested branch The VSMI of every branch in the large scale power system can be calculated by repeating the simplification process for every branch The weak points can be found by comparing the VSMIs of every branch Application to Large Scale Power System

10. 10 Downstream of Gypsy Region Downstream of Gypsy region in Entergy system has a voltage stability problem. There are five major 230 kV tie lines and three major units at Ninemile and Michoud

11. 11 Ranking of Critical Lines BRANCHSND_VOLSND_ANGRCV_VOLRCV_ANGMWMVARQ/PINDEX 98555 6GYPSY 230 98557 6SNORCO 230 10.941-0.1610.914-0.228841.5290.90.350.01 98569 6BGATEL 230 98544 6SORR 2 230 10.963-0.0470.958-0.05796.738.60.400.02 98606 69MILE 230 98691 6NAPOL 230 10.884-0.4310.876-0.455266.571.90.270.02 98586 6LABARE 230 98580 6PARIS 230 10.881-0.4180.878-0.427171.142.50.250.03 98606 69MILE 230 98687 6DERBI 230 10.884-0.4310.876-0.458244.261.90.250.03 98626 6KAISER 230 98630 6PACKHM 230 10.865-0.4990.865-0.499131.931.30.240.03 98633 6PACKAI 230 98626 6KAISER 230 10.865-0.4980.865-0.499131.931.30.240.03 98691 6NAPOL 230 98686 6MKTST 230 10.876-0.4550.875-0.461149.336.30.240.03 98504 6DNLDVL 230 98505 6BYVRET 230 10.984-0.0040.978-0.018187.561.60.330.06 98606 69MILE 230 98613 6ESTELL 230 10.884-0.4310.873-0.471219.550.10.230.07 98555 6GYPSY 230 98590 6UCITY 230 10.941-0.1610.895-0.310576.0177.80.310.07 98555 6GYPSY 230 98589 6PONTCH 230 10.941-0.1610.888-0.344584.3176.30.300.07 98545 6SLIDEL 230 50070 FRONTST6 230 10.909-0.3290.900-0.359323.584.90.260.07 98557 6SNORCO 230 98558 6PRSPCT 230 10.914-0.2280.912-0.233756.2180.10.240.08 98613 6ESTELL 230 98614 6PTRSRD 230 10.873-0.4710.870-0.486182.532.00.180.09 98583 6SPORT 230 98655 6JOLIET 230 10.882-0.4310.879-0.444349.864.00.180.10 98558 6PRSPCT 230 98559 6GOODHP 230 10.912-0.2330.911-0.238721.6165.00.230.10

12. 12 VSMI of Gypsy – South Norco 230 kV Line Unit Output (MW)Voltage (p.u.)VSMI (%) 5500.98816.2 4500.98615.4 3500.98113.6 3000.97110.4 2600.9606.87 2100.9410.9

13. 13 Advantages of VSMI VSMI technique is much faster than PV curve technique VSMI will adjust with changing operating conditions automatically VSMI calculation has the potential for being used in real- time operation This new approach can provide very useful information to find the weak points in the system This new approach can estimate the proximity to voltage collapse

14. 14 Future Work VSMI index can be negative for transmission lines which have heavy reactive power flow compared to real power flow Transformer taps and negative impedance, such as series cap compensation are not considered