Power System Analysis: Two-Bus Newton-Raphson Example

ECE 476 Power System Analysis Lecture 13: Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign overbye@illinois.edu

Announcements Read Chapter 6 H6 is 6.19, 6.30, 6.31, 6.34, 6.38, 6.45. It does not need to be turned in, but will be covered by an in-class quiz on Oct 15 Power and Energy scholarships will be decided on Monday; application on website; apply to Prof. Sauer Grainger Awards due on Nov 1; application on website; apply to Prof. Sauer energy.ece.illinois.edu/ 1

Two Bus Newton-Raphson Example For the two bus power system shown below, use the Newton-Raphson power flow to determine the voltage magnitude and angle at bus two. Assume that bus one is the slack and SBase = 100 MVA. Line Z = 0.1j One 1.000 pu Two 1.000 pu 0 MW 0 MVR 200 MW 100 MVR 10 10 j 10 10 j j j 2 = = x Y bus V 2 2

Two Bus Example, contd General power balance equations n = + = P ( cos sin ) V V G B P P i i k ik ik ik ik Gi Di = 1 k n = = Q ( sin cos ) V V G B Q Q i i k ik ik ik ik Gi Di = 1 k Bus two power balance equations (10sin V V ) 2.0 + = 0 2 1 2 2 ( 10cos + (10) 1.0 + = ) 0 V V V 2 1 2 2 3

Two Bus Example, contd = ) 2.0 + = x P ( ) (10sin 0 V 2 2 2 2 = ( 10cos + (10) 1.0 + = ( ) x ) 0 Q V V 2 2 2 2 Now calculate the power flow Jacobian P ( ) = = P ( ) x x 2 2 V 2 2 x ( ) x J x Q ( ) Q ( ) 2 2 V 2 2 + 10 10 cos sin 10sin V V 2 2 2 20 10cos V 2 2 2 2 4

Two Bus Example, First Iteration 0 1 (0) = = x Set 0, guess v Calculate ) 2.0 + (10sin V 2.0 1.0 2 2 V (0) = = x f( ) 2 ( 10cos + + ) (10) 1.0 + V 2 2 2 10sin 10 10 cos sin V V 10 0 0 2 2 2 20 (0) = = J x ( ) 10cos V 10 2 2 2 2 12.0 1.0 0 1 10 0 0 0.2 0.9 (1) = = x Solve 10 5

Two Bus Example, Next Iterations 0.9(10sin( 0.2)) 2.0 + 0.212 0.279 (1) = = x f( ) 2 + 10 1.0 + 0.9( 10cos( 0.2)) 8.82 1.788 0.9 1.986 8.199 (1) = J x ( ) 1 0.2 0.9 = = 8.82 1.788 1.986 8.199 0.212 0.279 0.236 0.8554 0.233 0.8586 (2) = = x 0.0145 0.0190 0.0000906 0.0001175 (2) (3) = x x f( ) (3) = x f( ) Done! V 0.8554 13.52 2 6

Two Bus Solved Values Once the voltage angle and magnitude at bus 2 are known we can calculate all the other system values, such as the line flows and the generator reactive power output 200.0 MW 168.3 MVR -200.0 MW -100.0 MVR Line Z = 0.1j One 1.000 pu Two 0.855 pu -13.522 Deg 200.0 MW 168.3 MVR 200 MW 100 MVR 7

Two Bus Case Low Voltage Solution This case actually has two solutions! The second "low voltage" is found by using a low initial guess. = = 0 (0) x Set 0, guess v 0.25 Calculate ) 2.0 + (10sin V 2 2 2 V (0) = = x f( ) 2 0.875 ( 10cos + (10) 1.0 + + ) V 2 2 2 10sin 10 10 cos sin V V 2.5 0 0 2 2 2 20 (0) = = J x ( ) 10cos V 5 2 2 2 2 8

Low Voltage Solution, cont'd 1 0.8 0 2.5 0 0 2 (1) = = x Solve 0.875 0.25 1.462 0.534 5 0.075 0.921 0.220 1.42 0.2336 (2) (2) (3) = = = f x x x ( ) Low voltage solution 200.0 MW 831.7 MVR -200.0 MW -100.0 MVR Line Z = 0.1j One 1.000 pu Two 0.261 pu -49.914 Deg 200.0 MW 831.7 MVR 200 MW 100 MVR 9

Two Bus Region of Convergence Slide shows the region of convergence for different initial guesses of bus 2 angle (x-axis) and magnitude (y-axis) Red region converges to the high voltage solution, while the yellow region converges to the low voltage solution 10

PV Buses Since the voltage magnitude at PV buses is fixed there is no need to explicitly include these voltages in x or write the reactive power balance equations the reactive power output of the generator varies to maintain the fixed terminal voltage (within limits) optionally these variations/equations can be included by just writing the explicit voltage constraint for the generator bus |Vi | Vi setpoint = 0 11

Three Bus PV Case Example For this three bus case we have = + + x x ( ) ( ) Q P P P P P P 2 2 2 2 G D = = x ( ) f x 0 3 3 3 Q 3 G + D ( ) x V 2 2 2 D Line Z = 0.1j 0.941 pu -7.469 Deg One 1.000 pu Two 200 MW 100 MVR 170.0 MW 68.2 MVR Line Z = 0.1j Line Z = 0.1j Three 1.000 pu 30 MW 63 MVR 12

Generator Reactive Power Limits The reactive power output of generators varies to maintain the terminal voltage; on a real generator this is done by the exciter To maintain higher voltages requires more reactive power Generators have reactive power limits, which are dependent upon the generator's MW output These limits must be considered during the power flow solution 13

Generator Reactive Limits, cont'd During power flow once a solution is obtained check to make generator reactive power output is within its limits If the reactive power is outside of the limits, fix Q at the max or min value, and resolve treating the generator as a PQ bus this is know as "type-switching" also need to check if a PQ generator can again regulate Rule of thumb: to raise system voltage we need to supply more vars 14

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 Line 2 Line 1 345 kV 200 mi 2 280 Mvar 800 MW Single-line diagram 15

The N-R Power Flow: 5-bus Example V per unit PG per unit QG per unit PL per unit 0 QL per unit 0 QGmax per unit QGmin per unit Bus Type degrees 1 Swing 1.0 0 Table 1. Bus input data 2 Load 0 0 8.0 2.8 3 Constant voltage 1.05 5.2 0.8 0.4 4.0 -2.8 4 5 Load Load 0 0 0 0 0 0 0 0 Maximum MVA per unit R X G B Bus-to- Bus 2-4 2-5 4-5 per unit per unit per unit per unit Table 2. Line input data 0.0090 0.0045 0.00225 0.100 0.050 0.025 0 0 0 1.72 0.88 0.44 12.0 12.0 12.0 16

The N-R Power Flow: 5-bus Example Maximum TAP Setting per unit R per unit X Gc per unit Bm per unit Maximum MVA per unit per unit Table 3. Transformer input data Bus-to- Bus 1-5 0.00150 0.02 0 0 6.0 3-4 0.00075 0.01 0 0 10.0 Bus Input Data Unknowns V1 = 1.0, 1 = 0 1 P1, Q1 V2, 2 2 P2 = PG2-PL2 = -8 Q2 = QG2-QL2 = -2.8 V3 = 1.05 P3 = PG3-PL3 = 4.4 P4 = 0, Q4 = 0 Table 4. Input data and unknowns Q3, 3 3 V4, 4 V5, 5 4 5 P5 = 0, Q5 = 0 17

Time to Close the Hood: Let the Computer Do the Math! (Ybus Shown) 18

Ybus Details Elements of Ybus connected to bus 2 =Y = 0 Y 21 23 + 1 1 + = = = + 0.89276 9.91964 Y j per unit 24 ' ' 0.009 0.1 R jX j 24 24 1 1 + = = = 78552 . 1 + 83932 . 19 Y j per unit 25 + ' ' 0045 . 0 j . 0 05 R jX 25 25 ' ' 1 1 B B = + + + 25 24 Y j j 22 + + ' ' ' ' 2 2 R jX R jX 24 24 25 25 + . 1 j 72 . 0 88 . 0 ( = = . 2 + + 89276 91964 . 9 j 28 ) . 1 ( = 78552 19 j 83932 . 84 ) j 2 2 67828 4590 . 5847 . 28 624 . j per unit 19

Here are the Initial Bus Mismatches 20

And the Initial Power Flow Jacobian 21

And the Hand Calculation Details! = Y Y Y 0 . 8 ) 0 ( 2 ) 0 ( 2 ] 24 ) 0 ( 5 84 cos( ) 0 . 1 ( 5847 . 28 { 0 . 1 95 cos( ) 0 . 1 ( 95972 . 9 + cos( ) 0 . 1 ( 9159 . 19 + 10 89 . 2 ( 0 . 8 = ) 0 ( 1 ) 0 ( 3 ) 0 ( 2 P ( 0 ( 2 V ] 22 ) 0 ( 2 ) 0 ( cos[ 2 ) ){ Y cos[ cos[ ] ] P + + + P V V V x cos[ cos[ P Y V ) 0 ( 4 V 2 2 2 21 1 21 + 22 2 23 3 23 24 4 ]} 25 5 25 624 . = ) 143 . 143 . ) )} 99972 . 7 95 ) = = 4 per unit = ) 0 ( 2 sin[ ) 0 . 1 )( unit per ) 0 ( 4 . 95 ] 1 ) 0 ( 24 ) 0 ( 4 V 95972 . 9 )( 0 . 1 ( = 91964 . 9 = ) 0 ( 2 V sin[ ] J Y 24 24 143 22

Five Bus Power System Solved One Five Four Three A A MVA MVA 395 MW 520 MW A MVA 114 Mvar 337 Mvar slack 1.000 pu 0.000 Deg 0.974 pu -4.548 Deg 1.019 pu -2.834 Deg 80 MW 40 Mvar A A MVA MVA 1.050 pu -0.597 Deg 0.834 pu -22.406 Deg Two 800 MW 280 Mvar 23

37 Bus Example Design Case Metropolis Light and Power Electric Design Case 2 SLA CK345 A MVA A MVA 220 MW 52 Mvar 1.03 pu RA Y345 s l ac k System Losses: 10.70 MW A A A 1.02 pu SLA CK138 TIM345 MVA MVA MVA 1.02 pu RA Y138 A A 1.03 pu A MVA MVA TIM138 33 MW 13 Mvar MVA A 1.00 pu 1.03 pu MVA 15.9 Mvar 18 MW 5 Mvar 1.02 pu RA Y69 A 37 MW A 17 MW 3 Mvar A A MVA PA I69 13 Mvar MVA 1.01 pu MVA MVA 1.02 pu TIM69 1.01 pu GROSS69 A A 23 MW 7 Mvar FERNA 69 MVA MVA 1.01 pu WOLEN69 A 12 MW 3 Mvar A A HISKY69 MVA PETE69 A MVA MVA A 4.9 Mvar A 58 MW 40 Mvar MORO138 A MVA MVA 39 MW 13 Mvar 1.01 pu MVA MVA 1.00 pu BOB138 A 12 MW 5 Mvar HA NNA H69 28.9 Mvar DEMA R69 A A 60 MW 19 Mvar MVA MVA MVA 1.00 pu 20 MW 12 Mvar 1.02 pu BOB69 A 1.00 pu 0.99 pu 14.2 Mvar UIUC69 MVA 1.00 pu 12.8 Mvar 124 MW 45 Mvar 56 MW KYLE69 A A 13 Mvar LYNN138 A MVA 16 MW -14 Mvar MVA MVA A 25 MW 36 Mvar A A 14 MW 4 Mvar MVA BLT138 1.00 pu MVA A MA NDA 69 MVA 0.99 pu A A A 25 MW 10 Mvar SHIMKO69 1.02 pu MVA MVA MVA HOMER69 1.01 pu 7.4 Mvar A A BLT69 MVA 1.01 pu A MVA 15 MW 5 Mvar A 20 MW 3 Mvar MVA HA LE69 55 MW 25 Mvar MVA A A 1.00 pu MVA 36 MW 10 Mvar 1.01 pu MVA A A A 60 MW 12 Mvar 7.3 Mvar A MVA MVA A MVA 1.00 pu 1.00 pu PA TTEN69 MVA 0.0 Mvar MVA A 45 MW 0 Mvar 14 MW ROGER69 MVA 1.01 pu WEBER69 LA UF69 2 Mvar 1.02 pu 23 MW 6 Mvar 22 MW 15 Mvar 10 MW 5 Mvar 14 MW 3 Mvar A A A 20 MW 28 Mvar MVA MVA MVA 1.02 pu JO138 JO345 LA UF138 1.02 pu SA VOY69 38 MW 3 Mvar 1.00 pu 1.01 pu BUCKY138 A MVA A A 150 MW 0 Mvar 1.01 pu SA VOY138 MVA MVA A A MVA MVA 150 MW 0 Mvar A MVA 1.03 pu 1.02 pu A MVA 24

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) 25

Looking at the Impact of Line Outages Metropolis Light and Power Electric Design Case 2 SLA CK345 A MVA A MVA 227 MW 43 Mvar 1.03 pu RA Y345 s l ac k System Losses: 17.61 MW A A A 1.02 pu SLA CK138 TIM345 MVA MVA MVA 1.02 pu RA Y138 A A 1.03 pu A MVA MVA TIM138 33 MW 13 Mvar MVA A 1.01 pu 1.03 pu MVA 16.0 Mvar 18 MW 5 Mvar 1.02 pu RA Y69 A 37 MW A 17 MW 3 Mvar A A MVA PA I69 13 Mvar MVA 1.01 pu MVA MVA 1.02 pu TIM69 1.01 pu GROSS69 A A 23 MW 7 Mvar FERNA 69 MVA MVA 1.01 pu WOLEN69 A 12 MW 3 Mvar A A HISKY69 MVA PETE69 A MVA MVA 4.9 Mvar A 58 MW 40 Mvar MORO138 A MVA 39 MW 13 Mvar 1.01 pu MVA MVA 1.00 pu BOB138 A 12 MW 5 Mvar HA NNA H69 28.9 Mvar DEMA R69 A A 60 MW 19 Mvar MVA MVA MVA 1.00 pu 20 MW 12 Mvar 1.02 pu BOB69 A 1.00 pu 0.90 pu 11.6 Mvar UIUC69 MVA 1.00 pu 12.8 Mvar 124 MW 45 Mvar 56 MW KYLE69 A A 13 Mvar LYNN138 A MVA 16 MW -14 Mvar MVA MVA A 25 MW 36 Mvar A 14 MW 4 Mvar A MVA BLT138 1.00 pu MVA A MA NDA 69 MVA 0.90 pu A A A 110% MVA 25 MW 10 Mvar SHIMKO69 1.02 pu MVA MVA A HOMER69 1.01 pu 7.3 Mvar A BLT69 MVA 1.01 pu A MVA A 15 MW 5 Mvar 135% MVA 20 MW 3 Mvar MVA HA LE69 55 MW 32 Mvar A A 0.94 pu MVA 36 MW 10 Mvar 1.01 pu MVA A A A 60 MW 12 Mvar 7.2 Mvar A MVA MVA A MVA 1.00 pu 1.00 pu PA TTEN69 MVA 0.0 Mvar MVA A 45 MW 0 Mvar 14 MW ROGER69 MVA 1.00 pu WEBER69 LA UF69 2 Mvar 1.01 pu 23 MW 6 Mvar 22 MW 15 Mvar 10 MW 5 Mvar A 14 MW 3 Mvar A A 80% MVA 20 MW 40 Mvar MVA MVA 1.02 pu JO138 JO345 LA UF138 1.01 pu SA VOY69 38 MW 9 Mvar 0.99 pu 1.00 pu BUCKY138 A MVA A A 150 MW 4 Mvar 1.01 pu SA VOY138 MVA MVA A A MVA MVA 150 MW 4 Mvar A MVA 1.03 pu 1.02 pu A MVA Opening one line (Tim69-Hannah69) causes an overload. This would not be allowed 26

Contingency Analysis Contingency analysis provides an automatic way of looking at all the statistically likely contingencies. In this example the contingency set Is all the single line/transformer outages 27

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. 28

An Unreliable Solution Metropolis Light and Power Electric Design Case 2 SLA CK345 A MVA A MVA 269 MW 67 Mvar 1.02 pu RA Y345 s l ac k System Losses: 14.49 MW A A A 1.02 pu SLA CK138 TIM345 MVA MVA MVA 1.01 pu RA Y138 A A 1.03 pu A MVA MVA TIM138 33 MW 13 Mvar MVA A 0.99 pu 1.02 pu MVA 15.9 Mvar 18 MW 5 Mvar 1.02 pu RA Y69 A 37 MW A 17 MW 3 Mvar A A MVA PA I69 13 Mvar MVA 1.01 pu MVA MVA 1.02 pu TIM69 1.01 pu GROSS69 A A 23 MW 7 Mvar FERNA 69 MVA MVA 1.01 pu WOLEN69 A 12 MW 3 Mvar A A HISKY69 MVA PETE69 A MVA A MVA 4.9 Mvar A 96% MVA 58 MW 40 Mvar MORO138 A MVA 39 MW 13 Mvar 1.01 pu MVA MVA 1.00 pu BOB138 A 12 MW 5 Mvar HA NNA H69 28.9 Mvar DEMA R69 A A 60 MW 19 Mvar MVA MVA MVA 1.00 pu 20 MW 12 Mvar 1.02 pu BOB69 A 1.00 pu 0.97 pu 13.6 Mvar UIUC69 MVA 1.00 pu 12.8 Mvar 124 MW 45 Mvar 56 MW KYLE69 A A 13 Mvar LYNN138 A MVA 16 MW -14 Mvar MVA MVA A 25 MW 36 Mvar A 14 MW 4 Mvar A MVA BLT138 1.00 pu MVA MVA 0.97 pu A A A 25 MW 10 Mvar SHIMKO69 1.02 pu MVA MVA MVA A HOMER69 1.01 pu 7.4 Mvar A BLT69 A MA NDA 69 MVA 1.01 pu A MVA 15 MW 5 Mvar A 20 MW 3 Mvar MVA HA LE69 55 MW 28 Mvar MVA A A 0.99 pu MVA 36 MW 10 Mvar 1.01 pu MVA A A A 60 MW 12 Mvar 7.3 Mvar A MVA MVA A MVA 1.00 pu 1.00 pu PA TTEN69 MVA 0.0 Mvar MVA A 45 MW 0 Mvar 14 MW ROGER69 MVA 1.01 pu WEBER69 LA UF69 2 Mvar 1.02 pu 23 MW 6 Mvar 22 MW 15 Mvar 10 MW 5 Mvar 14 MW 3 Mvar A A A 20 MW 40 Mvar MVA MVA MVA 1.02 pu JO138 JO345 LA UF138 1.02 pu SA VOY69 38 MW 4 Mvar 1.00 pu 1.01 pu BUCKY138 A MVA A A 150 MW 1 Mvar 1.01 pu SA VOY138 MVA MVA A A MVA MVA 150 MW 1 Mvar A MVA 1.03 pu 1.02 pu A MVA Case now has nine separate contingencies with reliability violations 29

A Reliable Solution Metropolis Light and Power Electric Design Case 2 SLA CK345 A MVA A MVA 266 MW 59 Mvar 1.02 pu RA Y345 s l ac k System Losses: 11.66 MW A A A 1.02 pu SLA CK138 TIM345 MVA MVA MVA 1.01 pu RA Y138 A A 1.03 pu A MVA MVA TIM138 33 MW 13 Mvar MVA A 1.00 pu 1.03 pu MVA 15.8 Mvar 18 MW 5 Mvar 1.02 pu RA Y69 A 37 MW A 17 MW 3 Mvar A A MVA PA I69 13 Mvar MVA 1.01 pu MVA MVA 1.02 pu TIM69 1.01 pu GROSS69 A A 23 MW 7 Mvar FERNA 69 MVA MVA 1.01 pu WOLEN69 A 12 MW 3 Mvar A A HISKY69 MVA PETE69 A MVA MVA A 4.9 Mvar A 58 MW 40 Mvar MORO138 A MVA MVA 39 MW 13 Mvar 1.01 pu MVA MVA 1.00 pu BOB138 12 MW 5 Mvar A HA NNA H69 28.9 Mvar DEMA R69 A A 60 MW 19 Mvar MVA MVA MVA 20 MW 12 Mvar Kyle138 1.02 pu BOB69 A 0.99 pu 0.99 pu 14.1 Mvar UIUC69 MVA 1.00 pu A 12.8 Mvar 124 MW 45 Mvar 56 MW M VA KYLE69 A A 13 Mvar LYNN138 A MVA MVA 16 MW -14 Mvar MVA A 25 MW 36 Mvar A 14 MW 4 Mvar A MVA BLT138 1.00 pu MVA MVA 0.99 pu A A A 25 MW 10 Mvar SHIMKO69 1.02 pu MVA MVA MVA HOMER69 1.01 pu 7.4 Mvar A A BLT69 A MA NDA 69 MVA 1.01 pu A MVA 15 MW 5 Mvar A 20 MW 3 Mvar MVA HA LE69 55 MW 29 Mvar MVA A A 1.00 pu MVA MVA 36 MW 10 Mvar 1.01 pu A A A 60 MW 12 Mvar 7.3 Mvar A MVA MVA A MVA 1.00 pu 1.00 pu PA TTEN69 MVA 0.0 Mvar MVA A 45 MW 0 Mvar 14 MW ROGER69 MVA 1.01 pu WEBER69 LA UF69 2 Mvar 1.02 pu 23 MW 6 Mvar 22 MW 15 Mvar 10 MW 5 Mvar 14 MW 3 Mvar A A A 20 MW 38 Mvar MVA MVA MVA 1.02 pu JO138 JO345 LA UF138 1.02 pu SA VOY69 38 MW 4 Mvar 1.00 pu 1.01 pu BUCKY138 A MVA A A 150 MW 1 Mvar 1.01 pu SA VOY138 MVA MVA A A MVA MVA 150 MW 1 Mvar A MVA 1.03 pu 1.02 pu A MVA Previous case was augmented with the addition of a 138 kV Transmission Line 30

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 31

Generation Change Example 1 A SLA CK345 MVA A MVA 162 MW 35 Mvar 0.00 pu RA Y345 s l ac k A A A 0.00 pu SLA CK138 TIM345 MVA MVA MVA -0.01 pu RA Y138 A A 0.00 pu A MVA TIM138 MVA 0.00 pu 0 MW 0 Mvar A MVA 0.00 pu -0.1 Mvar 0 MW 0 Mvar MVA A A -0.01 pu RA Y69 0 MW MVA MVA 0 MW 0 Mvar A A 0.00 pu TIM69 PA I69 0 Mvar 0.00 pu MVA MVA A 0 MW 0 Mvar 0.00 pu GROSS69 A A MVA FERNA 69 MVA 0.00 pu WOLEN69 A MVA 0 MW 0 Mvar A MORO138 HISKY69 MVA MVA A A -0.1 Mvar 0 MW 0 Mvar A MVA MVA 0 MW 0 Mvar -0.01 pu MVA -0.03 pu BOB138 A PETE69 A DEMA R69 0.00 pu MVA A A HA NNA H69 0 MW 0 Mvar MVA 0 MW 0 Mvar MVA MVA 0 MW 0 Mvar A 0.00 pu BOB69 -0.2 Mvar UIUC69 0.00 pu MVA -0.1 Mvar 0.00 pu -157 MW -45 Mvar 0 MW -0.1 Mvar A 0 Mvar LYNN138 A MVA 0 MW 0 Mvar A MVA A MVA A 0 MW 0 Mvar 0 MW 0 Mvar A -0.002 pu BLT138 MVA -0.03 pu MVA MVA 0.00 pu A MA NDA 69 A A A SHIMKO69 0.00 pu HOMER69 0 MW 0 Mvar MVA 0.0 Mvar A MVA 0.00 pu MVA A BLT69 MVA -0.01 pu A MVA 0 MW 0 Mvar 0 MW 0 Mvar A MVA HA LE69 0 MW 51 Mvar A 0.00 pu MVA A MVA MVA 0 MW 0 Mvar 0.00 pu A A A 0 MW 0 Mvar 0.0 Mvar A MVA MVA A MVA 0.00 pu 0.00 pu PA TTEN69 MVA 0.0 Mvar MVA A 0 MW 0 Mvar 0 MW ROGER69 MVA 0.00 pu WEBER69 LA UF69 0 Mvar 0.00 pu 0 MW 0 Mvar 0 MW 0 Mvar 0 MW 0 Mvar 0 MW 0 Mvar A A A 0 MW 4 Mvar MVA MVA MVA 0.00 pu JO138 JO345 LA UF138 0.00 pu SA VOY69 0 MW 3 Mvar 0.00 pu 0.00 pu BUCKY138 A A MVA A 0 MW 2 Mvar 0.00 pu SA VOY138 MVA MVA A A MVA MVA 0 MW 2 Mvar A 0.00 pu MVA 0.00 pu A 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 MVA 32

Generation Change Example 2 A SLA CK345 MVA A MVA 0 MW 37 Mvar 0.00 pu RA Y345 s l ac k A A A 0.00 pu SLA CK138 TIM345 MVA MVA MVA -0.01 pu RA Y138 A A 0.00 pu A MVA TIM138 MVA 0.00 pu 0 MW 0 Mvar A MVA 0.00 pu -0.1 Mvar 0 MW 0 Mvar MVA A A 0.00 pu RA Y69 0 MW MVA MVA 0 MW 0 Mvar A A 0.00 pu TIM69 PA I69 0 Mvar 0.00 pu MVA MVA A 0 MW 0 Mvar 0.00 pu GROSS69 A A MVA FERNA 69 MVA 0.00 pu WOLEN69 A MVA 0 MW 0 Mvar A MORO138 HISKY69 MVA MVA A A 0.0 Mvar 0 MW 0 Mvar A MVA MVA 0 MW 0 Mvar 0.00 pu MVA -0.03 pu BOB138 A PETE69 A DEMA R69 0.00 pu MVA A A HA NNA H69 0 MW 0 Mvar MVA 0 MW 0 Mvar MVA MVA 0 MW 0 Mvar A 0.00 pu BOB69 -0.2 Mvar UIUC69 0.00 pu MVA -0.1 Mvar 0.00 pu -157 MW -45 Mvar 0 MW -0.1 Mvar A 0 Mvar LYNN138 A MVA 0 MW 0 Mvar A MVA A MVA A 0 MW 0 Mvar 0 MW 0 Mvar A -0.003 pu BLT138 MVA -0.03 pu MVA MVA 0.00 pu A MA NDA 69 A A A SHIMKO69 0.00 pu HOMER69 0 MW 0 Mvar MVA -0.1 Mvar A MVA -0.01 pu MVA A BLT69 MVA -0.01 pu A MVA 0 MW 0 Mvar 0 MW 0 Mvar A MVA HA LE69 19 MW 51 Mvar A 0.00 pu MVA A MVA MVA 0 MW 0 Mvar 0.00 pu A A A 0 MW 0 Mvar 0.0 Mvar A MVA MVA A MVA 0.00 pu 0.00 pu PA TTEN69 MVA 0.0 Mvar MVA A 0 MW 0 Mvar 0 MW ROGER69 MVA 0.00 pu WEBER69 LA UF69 0 Mvar 0.00 pu 0 MW 0 Mvar 0 MW 0 Mvar 0 MW 0 Mvar 0 MW 0 Mvar A A A 99 MW -20 Mvar MVA MVA MVA 0.00 pu JO138 JO345 LA UF138 0.00 pu SA VOY69 42 MW -14 Mvar 0.00 pu 0.00 pu BUCKY138 A A MVA A 0 MW 0 Mvar 0.00 pu SA VOY138 MVA MVA A A MVA MVA 0 MW 0 Mvar A 0.00 pu MVA 0.00 pu Display repeats previous case except now the change in generation is picked up by other generators using a participation factor approach A MVA 33

Voltage Regulation Example: 37 Buses SLA CK345 A MVA A MVA 219 MW 52 Mvar 1.02 pu RA Y345 System Losses: 11.51 MW s l ac k A A A 1.02 pu SLA CK138 MVA MVA MVA TIM345 1.01 pu RA Y138 A A 1.03 pu A MVA TIM138 MVA MVA 1.00 pu 33 MW 13 Mvar A 1.03 pu 15.9 Mvar 18 MW 5 Mvar MVA A A 1.02 pu RA Y69 37 MW MVA MVA 17 MW 3 Mvar A A 1.02 pu TIM69 PA I69 13 Mvar 1.01 pu MVA MVA A 23 MW 7 Mvar 1.01 pu GROSS69 A A MVA FERNA 69 MVA 1.01 pu WOLEN69 A MVA 21 MW 7 Mvar MORO138 A MVA HISKY69 MVA A A 4.8 Mvar 12 MW 5 Mvar A MVA MVA 20 MW 8 Mvar 1.00 pu MVA 1.00 pu BOB138 A PETE69 A DEMA R69 MVA 1.00 pu A A MVA HA NNA H69 58 MW 40 Mvar MVA MVA 51 MW 15 Mvar 45 MW 12 Mvar 1.02 pu BOB69 A 29.0 Mvar MVA UIUC69 0.99 pu 14.3 Mvar 1.00 pu 157 MW 45 Mvar 56 MW 12.8 Mvar A 13 Mvar LYNN138 A MVA 0 MW 0 Mvar A MVA A A A MVA MVA 58 MW 36 Mvar 14 MW 4 Mvar A MVA 0.997 pu BLT138 MVA 1.00 pu MVA 0.99 pu 33 MW 10 Mvar A MA NDA 69 A A SHIMKO69 1.02 pu A HOMER69 MVA MVA A 0.0 Mvar 7.4 Mvar MVA 1.01 pu BLT69 MVA 1.01 pu A 1.010 pu 15 MW 3 Mvar 15 MW 5 Mvar A MVA HA LE69 92 MW 10 Mvar A MVA 1.00 pu MVA A 36 MW 10 Mvar 1.01 pu A A A 60 MW 12 Mvar 7.2 Mvar MVA A MVA MVA A MVA 1.00 pu 1.00 pu PA TTEN69 MVA 20.8 Mvar MVA A 45 MW 0 Mvar 14 MW ROGER69 MVA 1.00 pu WEBER69 LA UF69 2 Mvar 1.02 pu 23 MW 6 Mvar 22 MW 15 Mvar 0 MW 0 Mvar 14 MW 3 Mvar A A A 20 MW 9 Mvar MVA MVA MVA 1.02 pu JO138 JO345 LA UF138 1.02 pu SA VOY69 38 MW 3 Mvar 1.00 pu 1.01 pu BUCKY138 A MVA A A 150 MW 0 Mvar 1.01 pu SA VOY138 MVA MVA A A MVA MVA 150 MW 0 Mvar A MVA 1.03 pu 1.02 pu A MVA Display shows voltage contour of the power system, demo will show the impact of generator voltage set point, reactive power limits, and switched capacitors 34