Lecture 9: Advanced Power Flow, Gaussian

Elimination, Sparse Systems

ECEN 615Methods of Electric Power Systems Analysis

Prof. Tom Overbye

Dept. of Electrical and Computer Engineering

Texas A&M University

overbye@tamu.edu

Announcements

• Read Chapter 6

• Homework 2 is due on Sept 27

2

Area Interchange Example: Seven Bus, Three Area System

3PowerWorld Case: B7Flat

Example Large System Areas

4

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Each oval

corresponds to a

power flow area

with the size

proportional to

the area’s

generation

Generator Volt/Reactive Control

• Simplest situation is a single generator at a bus

regulating its own terminal

• Either PV, modeled as a voltage magnitude constraint, or as a

PQ with reactive power fixed at a limit value. If PQ the

reactive power limits can vary with the generator MW output

• Next simplest is multiple generators at a bus. Obviously

they need to be regulating the bus to the same voltage

magnitude

• From a power flow solution perspective, it is similar to a single

generator, with limits being the total of the individual units

• Options for allocation of vars among generators; this can affect

the transient stability results

5

Generator Volt/Reactive Control

6

Case is Aggieland37_

Gen_VoltVar

Generator Volt/Reactive Control

• Next complication is generators at a single bus

regulating a remote bus; usually this is the high side of

their generator step-up (GSU) transformer

• When multiple generators regulate a single point their exciters

need to have a dual input

• This can be implemented in the power flow for the generators

at bus j regulating the voltage at bus k by changing the bus j

voltage constraint equation to be

(however, this does create a zero on the diagonal of the

Jacobian)

• Helps with power system voltage stability 7

, 0k k setV V

Generator Volt/Reactive Control

• The next complication is to have the generators at

multiple buses doing coordinated voltage control

• Controlled bus may or may not be one of the terminal buses

• There must be an a priori decision about how much

reactive power is supplied by each bus; example

allocations are a fixed percentage or placing all

generators at the same place in their regulation range

• Implemented by designating one bus as the master; this

bus models the voltage constraint

• All other buses are treated as PQ, with the equation

including a percent of the total reactive power output of

all the controlling bus generators 8

Remote and Coordinated Var Control Example

9

GIGEM69

KYLE69

KYLE138

WEB138

WEB69

BONFIRE69

FISH69

RING69

TREE69

CENTURY69

REVEILLE69MAROON69

SPIRIT69

YELL69

RELLIS69

WHITE138

RELLIS138

BUSH69

MSC69

RUDDER69

HULLABALOO138

REED69

REED138

AGGIE138 AGGIE345

16%A

MVA

33%A

MVA

78%A

MVA

78%A

MVA

18%A

MVA

55%A

MVA

14%A

MVA

54%A

MVA

60%A

MVA

16%A

MVA

49%A

MVA

49%A

MVA

45%A

MVA

50%A

MVA

49%A

MVA

49%A

MVA

35%A

MVA

A

MVA

57%A

MVA

45%A

MVA

A

MVA

72%A

MVA

75%A

MVA

33%A

MVA

68%A

MVA

33%A

MVA

39%A

MVA

68%A

MVA

68%A

MVA

22%A

MVA

A

MVA

19%A

MVA

52%A

MVA

57%A

MVA

39%A

MVA

63%A

MVA

70%A

MVA

70%A

MVA

0.97 pu

0.945 pu0.98 pu

0.96 pu

0.982 pu

0.97 pu

0.950 pu

0.972 pu0.97 pu

0.98 pu

1.000 pu

1.01 pu

0.993 pu

0.992 pu

0.975 pu0.98 pu

0.96 pu

0.96 pu 0.95 pu

0.981 pu

0.976 pu0.96 pu

1.01 pu1.03 pu

PLUM138

1.01 pu

14%A

MVA

0.97 pu

61%A

MVA

34 MW

0 Mvar

59 MW

17 Mvar

20 MW

8 Mvar

100 MW

30 Mvar

61 MW 17 Mvar

59 MW

6 Mvar

69 MW

0 Mvar

93 MW

58 Mvar

58 MW

17 Mvar

36 MW

24 Mvar

96 MW

20 Mvar

93 MW

65 Mvar 82 MW

27 Mvar

0.0 Mvar

35 MW

11 Mvar

25 MW

10 Mvar

38 MW 10 Mvar

22 MW

0 Mvar

0.0 Mvar

0.0 Mvar

0.0 Mvar

0.0 Mvar

0.0 Mvar

0.0 Mvar

31 MW

13 Mvar

49 MW

17 Mvar

deg 0

tap1.0875

tap1.0000

tap1.0213tap1.0213

3.4 Mvar

52.8 Mvar

pu 1.031

pu 0.993 10.0 Mvar

20.4 Mvar

39.2 Mvar

95%A

MVA

Each oval

corresponds to a

power flow area

with the size

proportional to

the area’s

generation

Model Complexity Examples

• A recent 76,000 bus Eastern Interconnect (EI) power

flow model has voltage magnitudes controlled at about

19,000 buses (by Gens, LTCs, switched shunts) 94%

regulate their own terminals with about 1100 doing

remote regulation. Of this group 572 are regulated by

two or more devices, 277 by three or more, 12 by eight

or more, and three by 12 devices!

• It also has 27,622 transformers with 98 phase shifters

• Impedance correction tables are used for 351, including about

2/3 of the phase shifters; tables can change the impedance by

more than two times

10

PV Bus Voltage Droop

• Traditionally the PV bus approach considered either 1)

on control at setpoint or 2) at a limit

• Increasingly this is no longer the case, particularly for

wind and solar. Rather regulation has a droop

11

PV Bus Voltage Droop

• This actually allows for multiple generators to regulate

a single remote bus using different characteristics

12

B2

RegBus

Generators are

all configured to

regulate the

RegBus

B3

B1

A2

A3

A1

“Arriving

Branches”

PV Droop Implementation

• PowerWorld just implemented this using a voltage

droop control object

13

B7Flat Example with PV Deadband

14

Case is B7Flat_PVDroop

Research opportunity with the synthetic models to discuss

the impact of deadbands on, say, voltage stability

Example of Hourly Voltage Variation Over Time

15

Power Flow Topology Processing

• Commercial power flow software must have

algorithms to determine the number of asynchronous,

interconnected systems in the model

• These separate systems are known as Islands

• In large system models such as the Eastern Interconnect it is

common to have multiple islands in the base case (one recent

EI model had nine islands)

• Islands can also form unexpectedly as a result of

contingencies

• Power can be transferred between islands using dc lines

• Each island must have a slack bus

16

Power Flow Topology Processing

• Anytime a status change occurs the power flow

must perform topology processing to determine

whether there are either 1) new islands or 2) islands

have merged

• Determination is needed to determine whether the

island is “viable.” That is, could it truly function as

an independent system, or should the buses just be

marked as dead

• A quite common occurrence is when a single load or

generator is isolated; in the case of a load it can be

immediately killed; generators are more tricky

17

Topology Processing Algorithm

• Since topology processing is performed often, it must

be quick (order n ln(n))!

• Simple, yet quick topology processing algoritm

• Set all buses as being in their own island (equal to bus

number)

• Set ChangeInIslandStatus true

• While ChangeInIslandStatus Do

• Go through all the in-service lines, setting the islands for each of the

buses to be the smaller island number; if the island numbers are

different set ChangeInIslandStatus true

• Determine which islands are viable, assigning a slack bus as

necessary

18

Example of Island Formation

19

Top Area Cost

Left Area Cost Right Area Cost slack

1.00 pu

1.01 pu

1.04 pu1.04 pu

1.04 pu

0.99 pu1.05 pu

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

62 MW

61 MW

44 MW 42 MW 31 MW 31 MW

38 MW

37 MW

80 MW 78 MW

32 MW

33 MW

14 MW

38 MW

39 MW 20 MW 21 MW

42 MW

41 MW

A

MVA

21 MW 20 MW

8078 $/h

4652 $/h 4189 $/h

Case Hourly Cost 16919 $/h

Bus 1 Bus 3 Bus 4

Bus 2 Bus 5

Bus 6 Bus 7

MW106

MW171

MW200 MW198

110 MW

40 Mvar

80 MW 30 Mvar

130 MW 40 Mvar

40 MW

20 Mvar

MW 94

200 MW

0 Mvar200 MW

0 Mvar

AGC ON

AGC ON

AGC ON

AGC ON

AGC ON

80%A

MVA

Splitting large systems requires a careful consideration

of the flow on the island tie-lines as they are opened

Bus Branch versus Node Breaker

• Due to a variety of issues during the 1970’s and 1980’s

the real-time operations and planning stages of power

systems adopted different modeling approaches

20

PlanningUse simplified bus/branch model

PC approach

Use of files

Stand-alone applications

Real-Time OperationsUse detailed node/breaker model

EMS system as a set of integrated applications and processes

Real-time operating system

Real-time databases

Entire data sets and software tools developed around

these two distinct power system models

Circuit Breakers and Disconnects

• Circuit breakers are devices that are designed to clear

fault current, which can be many times normal

operating current

• AC circuit breakers take advantage of the current going

through zero twice per cycle

• Transmission faults can usually be cleared in less than three

cycles

• Disconnects cannot clear fault current, and usually not

normal current. They provide a visual indication the

line is open. Can be manual or motorized.

• In the power flow they have essentially no impedance;

concept of a zero branch reactance (ZBR)21

Google View of a 345 kV Substation

22

Substation Configurations

• Several different substation breaker/disconnect

configurations are common:

• Single bus: simple but a fault

any where requires taking out the

entire substation; also doing breaker

or disconnect maintenance requires

taking out the associated line

23Source: http://www.skm-eleksys.com/2011/09/substation-bus-schemes.html

Substation Configurations, cont.

• Main and Transfer Bus:

Now the breakers can be taken

out for maintenance without

taking out a line, but protection

is more difficult, and a fault

on one line will take out at least two

• Double Bus Breaker:

Now each line is fully protected

when a breaker is out, so high

reliability, but more costly

24Source: http://www.skm-eleksys.com/2011/09/substation-bus-schemes.html

Ring Bus, Breaker and Half

• As the name implies with a ring

bus the breakers form a ring;

number of breakers is same as

number of devices; any breaker can

be removed for maintenance

• The breaker and half has two buses

and uses three breakers for two

devices; both breakers and buses

can be removed for maintenance

25Source: http://www.skm-eleksys.com/2011/09/substation-bus-schemes.html

• EMS Model

– Used for real-time operations

– Called full topology model

– Has node-breaker detail

• Planning Model

– Used for off-line analysis

– Called consolidated model

by PowerWorld

– Has bus/branch detail

EMS and Planning Models

50 MW

20 Mvar

-30 MW

-18 Mvar

-40 MW

-10 Mvar

10 MW

3 Mvar10 MW

5 Mvar

-30 MW

-18 Mvar

-40 MW

-10 Mvar

10 MW

3 Mvar

10 MW

5 Mvar

26

Node-Breaker Consolidation

• One approach to modeling systems with large numbers

of ZBRs (zero branch reactances, such as from circuit

breakers) is to just assume a small reactance and solve

– This results in lots of buses and branches, resulting in a much

larger problem

– This can cause numerical problems in the solution

• The alterative is to consolidate the nodes that are

connected by ZBRs into a smaller number of buses

– After solution all nodes have the same voltage; use logic to

determine the device flows

27

Node-Breaker Example

28

Case name is FT_11Node. PowerWorld consolidates

nodes (buses) into super buses; available in the Model

Explorer: Solution, Details, Superbuses

Node-Breaker Example

Note there is ambiguity on how much power is flowing

in each device in the ring bus (assuming each device

really has essentially no impedance)29