ECE 530 – Analysis Techniques for Large-Scale Electrical Systems Prof. Hao Zhu Special thanks to Dr.…

ECE 530 – Analysis Techniques for Large-Scale Electrical Systems

Prof. Hao ZhuSpecial thanks to Dr. Kai Van Horn

Dept. of Electrical and Computer EngineeringUniversity of Illinois at Urbana-Champaign

[email protected]

11/4/20151

Lecture 18: DF Applications in Power System Operations

Sensitivity Analysis

• System description and notation• Motivation for the sensitivity analysis• Derivations of (linearized) flow sensitivity• Definitions of the various distribution

factors• Analysis of the distribution factors• Distribution factor applications

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Distribution Factors

• Various additional distribution factors may be defined – power transfer distribution factor (PTDF)– line outage distribution factor (LODF)– line closure distribution factor (LCDF)– outage transfer distribution factor (OTDF)

• These factors may be derived from the ISFs making judicious use of the superposition principle

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UTC Revisited

• We can now revisit the uncommitted transfer capability (UTC) calculation using PTDFs and LODFs

• Recall trying to determine maximum transfer between two areas (or buses in our example)

• For base case maximums are quickly determined with PTDFs

4

, w

0max0m n w

0

f fu min

UTC Revisited

• For the contingencies we use

• Then as before

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( )

( ) ( )1

, ( )kw

max 0 k 0k

m n kw0

f f d fu min

( ) (1), , ,,0

m n m n m nu min u u

Five Bus Example

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2, 3,w t f 42 , 34 , 67 , 118 , 33 , 100 T0

f 150 , 400 , 150 , 150 , 150 , 1,000 Tmax

Line 1

Line 2

Line 3

Line 6

Line 5

Line 4slack

1.050 pu

42 MW

67 MW

100 MW

118 MW

1.040 pu

1.042 pu

A

MVA

A

MVA

A

MVA

1.042 pu

A

MVA

1.044 pu

MW200

258 MW

MW118

260 MW

100 MW

MW100

A

MVA

One Two

Three

Four

Five

34 MW

33 MW

Five Bus Example

2,2

150 42 400 34 150 67 150 118 150 33, , , ,

0.2727 0.1818 0.0909 0.7273 0.0909

44.0

w

0max0

w0

f fu min

min

Therefore, for the base case

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Five Bus Example

• For the contingency case corresponding to the outage of the line 2

The limiting value is line 4

Hence the UTC is limited by the contingency to 23.0

2( )

( ) 2 ( )2(1)

2,3 2( )w

max 0 0

w0

f f d fu min

( ) 2 ( )

22( )

150 118 0.4 340.8

max 0 0

w

f f d f

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Contingency Considerations

• Traditionally contingencies consisted of single element failures (N-1), though utilities have long considered multiple element contingencies–Some can be quite complex

• N-2 involves considering all double element contingencies

• N-1-1 is used to describe contingencies in which a single element contingency occurs, the system is re-dispatched, then a second contingency occurs–The number of contingencies considered following the first

contingency can be quite large, coming close to N-2

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Additional Comments

• Distribution factors are defined as small signal sensitivities, but in practice, they are also used for simulating large disturbance cases

• Distribution factors are widely applied in the operation of electricity markets where the rapid evaluation of the impacts of each transaction on the line flows is required

• Applications to actual system show that the distribution factors provide satisfactory results in terms of accuracy

• For multiple applications that require fast turn around time, distribution factors are used very widely, particularly, in the market environment

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Power System Operational Reliability

• The goal of power system operations is to economically maintain power system reliability

• Recall that a power system is said to be operationally reliable if it can tolerate the outage of a small number of components without jeopardizing continued operation–The “N-1” reliability criterion is an example of

the codification of this principle• To maintain operational reliability, operators

rely extensively on distribution factor (DF)-based tools

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Common DF applications

• In a system that is operationally reliable, total generation matches total demand (plus losses) around-the-clock and no equipment is overloaded

• Power system operators must also ensure that so-called “credible” outages do not result in equipment overloads

• Two main tools are used to achieve these aims:–Real-time contingency analysis (RTCA)–Security-constrained economic dispatch (SCED)

• Both of these tools are based on the DFs derived in previous lectures

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Real-Time Contingency Analysis

• Real-time contingency analysis is the process of assessing the impacts on the loading of the system of the set of “credible” contingencies

• Two flavors of RTCA:– AC RTCA: repeatedly solve the AC power flow

• More accurate than DC RTCA• Captures voltage impacts of outages• More computationally intensive than DC RTCA

– DC RTCA: use DFs to compute contingency impacts directly• Can quickly assess the approximate impacts of a large number of

potential contingencies• Computed flow impacts are invariant to system operating point---may

lead to highly erroneous results in heavily loaded systems (see “DC Power Flow Revisited” by Stott, Jardim, and Alsac)

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DC RTCA• DC RTCA uses injection shift factors (ISFs) and line outage

distribution factors (LODFs) to directly compute the impacts of all “credible” contingencies, i.e., those on the contingency list

14Potential Contingency

Overloads

Contingency List

ISFsLODFs

?

line l ISFs

line k ISFsline l LODF

w.r.t. line k

line l thermal limit

bus injection vector

3-Bus DFs

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• Same reactance on all lines, bus 1 is slack bus

• ISFs given by:

• LODFs given by:

bus 1 bus 2

bus 3

line 1

line 2line 3

$ $$

10 MW limit

3-Bus Basic Economic Dispatch

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bus 1 bus 2

bus 3

line 1

line 2line 3

10 MW limit

$ $$

15 MW

15 MW

f3=10 MW

f1=5 MW

f2=5 MW

• generator at bus 1 is most economic and thus serves all of the bus 3 load

• line 1 is loaded at 5 MW, or 50% of its thermal limit

0 MW

3-Bus Impact of Line 3 Outage on Dispatch Reliability

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bus 1 bus 2

bus 3

line 1

line 2line 3

10 MW limit

$ $$

15 MW

15 MW

f3=10 MW

f1=5 MW

f2=5 MW

• Suppose we must consider the potential outage of line 3

• Recall the LODFs are:

• Line 1 is 150% loaded: – the original dispatch is not

operationally reliable – signals need for additional constraint

in SCED• LODFs enable incorporation of post-

outage system behavior into pre-outage dispatch

f1=15 MW>10

proportion of line 3 flow that will flow line 1 in event of line 3 outage

Green indicates flow with line 3 outaged

Blue indicates flow without outage

Purple indicates dispatch/load

0 MW

f3=0 MW f3=15 MW

The Real-Time SCED

• RTCA results used to dispatch the system via the SCED such that it can tolerate equipment failures and remain without overloads

• SCED objective is to minimize generator cost subject to:– power balance (sum of generation equals load plus losses)– network flow limits (formulated using ISFs)– reliability constraints (formulated using ISFs and LODFs)

• enforce N-1 criterion in dispatch• e.g. the flow on line 1 w.r.t. the outage of line 3 in the previous

example• SCED solution also used to compute LMPs

– LMP computation also depends on DFs!

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3-Bus SCED w/o Network Constraints

Bus 2 Bus 1

Bus 3

Total Cost

0 MW

0 MW

180 MWMW

10.00 $/MWh

60 MW 60 MW

60 MW

60 MW120 MW

120 MW

10.00 $/MWh

10.00 $/MWh

180 MW120%

120%

0 MWMW

1800 $/hr

Line from Bus 1 to Bus 3 is over-loaded; all buses have same marginal cost

Gen 1’scost is $10 per MWh

Gen 2’scost is $12 per MWh

PowerWorld Case: B3LP 19

3-Bus SCED w/ Network Constraints

Bus 2 Bus 1

Bus 3

Total Cost

60 MW

0 MW

180 MWMW

12.00 $/MWh

20 MW 20 MW

80 MW

80 MW100 MW

100 MW

10.00 $/MWh

14.01 $/MWh

120 MW 80% 100%

80% 100%

0 MWMW

1921 $/hr

Line from 1 to 3 is no longer overloaded, but nowthe marginal cost of electricity at 3 is $14 / MWh 20

Other DFs

• The recent San Diego blackout (2011) reiterated the need for DFs that deal with more than just active power flows and equipment overloads

• Reliability issues can also arise if a tripped transmission facility cannot be reclosed due to a large phase angle

• These large phase angles are the result of how the system is loaded and could be mitigated via the SCED

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San Diego Blackout

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1) Large MW transfers AZ-CA

2) Hassayamp-North Gila (H-NG) Line trips (500 kV line at ~75% loading)

3) System operator anticipates relieving overloads due to H-NG trip by reclosing H-NG line

4) Reclosure fails due to large phase angle, downstream overloads trip eventually causing SD system to blackout

The Need For New Tools

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• The system operator had no systematic means of determining the impacts of redispatch on the H-NG angle at the time of the blackout

Line Outage Angle Factors

• The line outage angle factor (LOAF), like the LODF, can can be used to compute the approximate impact of an outage on a relevant quantity (the voltage angle across a line, in this case)

• The LOAF can be used to both monitor line outage angles, as well as to select appropriate redispatch actions (manual and via the SCED) so as to mitigate large outage angles

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Summary

• DFs are critically important to maintaining operational reliability in real-time operations–Used in RTCA and SCED

• DFs allow system operators to quickly compute the impacts on flows, voltage angles, etc. of tens of thousands of potential contingencies

• Power flow sensitivity analysis is a powerful tool in a power engineer’s toolbox!

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