ECE 476 POWER SYSTEM ANALYSIS

1. ECE 476POWER SYSTEM ANALYSIS Lecture 14Power Flow Professor Tom Overbye Department of Electrical andComputer Engineering

2. Announcements • Homework 7 is 6.46, 6.49, 6.52, 11.19, 11.21, 11.27; due date is October 30 • Potential spring courses: ECE 431 and ECE 398RES (Renewable Electric Energy Systems) • If interested you can still sign up for a power lunch.

3. The N-R Power Flow: 5-bus Example T2 800 MVA 345/15 kV T1 1 5 4 3 520 MVA Line 3 345 kV 50 mi 400 MVA 15 kV 800 MVA 15 kV 400 MVA 15/345 kV 345 kV 100 mi 40 Mvar 80 MW 345 kV 200 mi Line 2 Line 1 2 280 Mvar 800 MW Single-line diagram

4. The N-R Power Flow: 5-bus Example Table 1. Bus input data Table 2. Line input data

5. The N-R Power Flow: 5-bus Example Table 3. Transformer input data Table 4. Input data and unknowns

6. Time to Close the Hood: Let the Computer Do the Math! (Ybus Shown)

7. Ybus Details Elements of Ybus connected to bus 2

8. Here are the Initial Bus Mismatches

9. And the Initial Power Flow Jacobian

10. And the Hand Calculation Details!

11. Five Bus Power System Solved

12. 37 Bus Example Design Case This is Design Case 2 From Chapter 6

13. Good Power System Operation Good power system operation requires that there be no reliability violations for either the current condition or in the event of statistically likely contingencies Reliability requires as a minimum that there be no transmission line/transformer limit violations and that bus voltages be within acceptable limits (perhaps 0.95 to 1.08) Example contingencies are the loss of any single device. This is known as n-1 reliability. North American Electric Reliability Corporation now has legal authority to enforce reliability standards (and there are now lots of them). See http://www.nerc.com for details (click on Standards)

14. Looking at the Impact of Line Outages Opening one line (Tim69-Hannah69) causes an overload. This would not be allowed

15. Contingency Analysis Contingencyanalysis providesan automaticway of lookingat all the statisticallylikely contingencies. Inthis example thecontingency set Is all the single line/transformeroutages

16. Power Flow And Design One common usage of the power flow is to determine how the system should be modified to remove contingencies problems or serve new load In an operational context this requires working with the existing electric grid In a planning context additions to the grid can be considered In the next example we look at how to remove the existing contingency violations while serving new load.

17. An Unreliable Solution Case now has nine separate contingencies with reliability violations

18. A Reliable Solution Previous case was augmented with the addition of a 138 kV Transmission Line

19. Generation Changes and The Slack Bus The power flow is a steady-state analysis tool, so the assumption is total load plus losses is always equal to total generation Generation mismatch is made up at the slack bus When doing generation change power flow studies one always needs to be cognizant of where the generation is being made up Common options include system slack, distributed across multiple generators by participation factors or by economics

20. Generation Change Example 1 Display shows “Difference Flows” between original 37 bus case, and case with a BLT138 generation outage; note all the power change is picked up at the slack

21. Generation Change Example 2 Display repeats previous case except now the change in generation is picked up by other generators using a participation factor approach

22. Voltage Regulation Example: 37 Buses Display shows voltage contour of the power system, demo will show the impact of generator voltage set point, reactive power limits, and switched capacitors

23. Real-sized Power Flow Cases Real power flow studies are usually done with cases with many thousands of buses Buses are usually group in to various balancing authority areas, with each area doing its own interchange control Cases also model a variety of different automatic control devices, such as generator reactive power limits, load tap changing transformers, phase shifting transformers, switched capacitors, HVDC transmission lines, and (potentially) FACTS devices

24. Sparse Matrices and Large Systems Since for realistic power systems the model sizes are quite large, this means the Ybus and Jacobian matrices are also large. However, most elements in these matrices are zero, therefore special techniques, known as sparse matrix/vector methods, can be used to store the values and solve the power flow Without these techniques large systems would be essentially unsolvable.

25. Eastern Interconnect Example Example, which models the Eastern Interconnectcontains about 43,000 buses.

26. Solution Log for 1200 MW Gen Outage In this example wesimulated the lossof a 1200 MWgenerator in NorthernIllinois. This caused a generation imbalancein the associated balancing authorityarea, which wascorrected by a redispatch of localgeneration.

27. “DC” Power Flow • The “DC” power flow makes the most severe approximations: • completely ignore reactive power, assume all the voltages are always 1.0 per unit, ignore line conductance • This makes the power flow a linear set of equations, which can be solved directly

28. Power System Control • A major problem with power system operation is the limited capacity of the transmission system • lines/transformers have limits (usually thermal) • no direct way of controlling flow down a transmission line (e.g., there are no valves to close to limit flow) • open transmission system access associated with industry restructuring is stressing the system in new ways • We need to indirectly control transmission line flow by changing the generator outputs

29. DC Power Flow Example

30. DC Power Flow 5 Bus Example Notice with the dc power flow all of the voltage magnitudes are 1 per unit.

31. Indirect Transmission Line Control What we would like to determine is how a change in generation at bus k affects the power flow on a line from bus i to bus j. The assumption is that the change in generation is absorbed by the slack bus

32. Power Flow Simulation - Before • One way to determine the impact of a generator change is to compare a before/after power flow. • For example below is a three bus case with an overload

33. Power Flow Simulation - After Increasing the generation at bus 3 by 95 MW (and hence decreasing it at bus 1 by a corresponding amount), results in a 31.3 drop in the MW flow on the line from bus 1 to 2.

34. Analytic Calculation of Sensitivities • Calculating control sensitivities by repeat power flow solutions is tedious and would require many power flow solutions. An alternative approach is to analytically calculate these values

35. Analytic Sensitivities

36. Three Bus Sensitivity Example

37. Balancing Authority Areas • An balancing authority area (use to be called operating areas) has traditionally represented the portion of the interconnected electric grid operated by a single utility • Transmission lines that join two areas are known as tie-lines. • The net power out of an area is the sum of the flow on its tie-lines. • The flow out of an area is equal to total gen - total load - total losses = tie-flow

38. Area Control Error (ACE) • The area control error (ace) is the difference between the actual flow out of an area and the scheduled flow, plus a frequency component • Ideally the ACE should always be zero. • Because the load is constantly changing, each utility must constantly change its generation to “chase” the ACE.

39. Automatic Generation Control • Most utilities use automatic generation control (AGC) to automatically change their generation to keep their ACE close to zero. • Usually the utility control center calculates ACE based upon tie-line flows; then the AGC module sends control signals out to the generators every couple seconds.

40. Power Transactions • Power transactions are contracts between generators and loads to do power transactions. • Contracts can be for any amount of time at any price for any amount of power. • Scheduled power transactions are implemented by modifying the value of Psched used in the ACE calculation

41. PTDFs • Power transfer distribution factors (PTDFs) show the linear impact of a transfer of power. • PTDFs calculated using the fast decoupled power flow B matrix

42. Nine Bus PTDF Example Figure shows initial flows for a nine bus power system

43. Nine Bus PTDF Example, cont'd Figure now shows percentage PTDF flows from A to I

44. Nine Bus PTDF Example, cont'd Figure now shows percentage PTDF flows from G to F

45. WE to TVA PTDFs

46. Line Outage Distribution Factors (LODFS) • LODFs are used to approximate the change in the flow on one line caused by the outage of a second line • typically they are only used to determine the change in the MW flow • LODFs are used extensively in real-time operations • LODFs are state-independent but do dependent on the assumed network topology

47. Flowgates • The real-time loading of the power grid is accessed via “flowgates” • A flowgate “flow” is the real power flow on one or more transmission element for either base case conditions or a single contingency • contingent flows are determined using LODFs • Flowgates are used as proxies for other types of limits, such as voltage or stability limits • Flowgates are calculated using a spreadsheet

48. NERC Regional Reliability Councils NERCis theNorthAmericanElectricReliabilityCouncil

49. NERC Reliability Coordinators