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Security assessment: decision support tools for power system operators

James D. McCalley, jdm@iastate.edu

Iowa State University, Ames, Iowa

September 5, 2000

© Iowa State University. All rights reserved.

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Overview

Security-related decisions

Current approach and what’s wrong with it

Security assessment using probabilistic risk

Illustrations

Risk-based decision-making

Cumulative risk assessment

Conclusions

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On-line Operator How to constrain the Operating rules,assessment economic operation to on-line assessment,(min-hours) maintain the normal state ? and $$$$

Security-related decisions

Time-frame Decision maker Decision Basis for decision

Operational Analyst What should be the Minimum operating

planning operating rules ? criteria, reliability,

(hrs-months) and $$$$

Planning Analyst How to reinforce/maintain Reliability criteria

(months-years) the transmission system ? for system design,

and $$$$

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Decision-Drivers Security

Overloadsecurity

Voltage Security

Dynamic Security

Trans- former Overload

Line Overload

Low Voltage

Unstable Voltage

Transient(early-swing)instability

Oscillatory (damping)instability

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Number of operating studies for determining security limitsNational Grid Company, UK

1985: 3/quarter

1990: 120/week

2000: 1300/week

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Bus 1 500

Bus 1 230

Bus 1 115

Bus 2 500Bus 2 500

Bus2 230Bus2 230

Bus 2 115Bus 2 115

110%

Imports Operator’s view Operator’s view at 2:10 pm, at 2:10 pm, 8/12/998/12/99

200 MW flow

94%

93%

0.95 pu volts

A Stressed A Stressed SystemSystem

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Simulation Simulation Results of a Results of a Preventive ActionPreventive Action

Bus 1 500Bus 1 500

Bus 1 230Bus 1 230

Bus 1 115Bus 1 115

Bus 2 500Bus 2 500

Bus2 230Bus2 230

Bus 2 115Bus 2 115

103%

Imports

0 MW flow

101%

104%

0.91 pu volts

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Power system “states” and actions

Normal (secure)

Emergency

Restorative

Extreme emergency.Separation, cascading

delivery pointinterruption,

load shedding

Alert,Not secure

Off-economic dispatch

Controlled loadcurtailment

Transmission loading reliefprocedures

Other actions(e.g. switching)

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Model current conditions

Select contingencies

Compute post-contingency performance

Determine if alert(the action-trigger)

Identify possible actions

Select action

Assessment and decision today

Determine if alert(the action-trigger)

Identify possible actions

Select action

Perform assessment

a-priori

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What is wrong with this approach?

#2The decision is driven by the most severe credible contingency

#1Assessment is made of the past but the decision is made for the future.

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What is wrong with this approach?

#1Assessment is made of the past but the decision is made for the future.

• actions can come too late

• un-quantified future uncertainties requires large margin

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Actions can come too late;Un-quantified uncertainties require large margin

Line flowContingency-based flow limit

Time

MW

Select action

Assess Action trigger

Identifyaction set

Based on the previous condition

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What is wrong with this approach?

#2The decision is driven by the most severe credible contingency

• inaccurate assessment and consequently an inconsistent action trigger• selection of less effective actions

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4

3 2

1

5

1

2

3

4

5

6 7

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Five-bus test system for illustrating concepts

Loss of cct 1 overloads cct 2

Loss of cct 6 overloads cct 7

Loss of cct 5 createslow voltage at bus 4.

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A

B

C D

E

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What causes the inconsistency?Assumption that all contingencies in selected set are of equal probability

Ignoring risk contribution from problems that are not most constraining

Discrete quantification of severity

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What do we do then?

Model a forecasted future

using probabilistic modeling of uncertainties

and assess it with

quantitative evaluation of contingency severity for each possible condition

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Forecast the future load and transactions

forecasted line flow95% confidence limitsactual line flow

Time

MW Loading

Select action

Assess Action trigger

Identifyaction set

(Based on future Conditions)

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On-line risk-based assessment

∑∑ ×=i j

jtiftjtift XESevXXEXSevRisk ),()|Pr()Pr()|( ,,,,

Uncertainty inoutage conditions

Uncertainty in operating conditions Severity

function

Forecasted operating conditions for future time t

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Possible near-future operating cdts (bus injections)

Selected near-futurecontingency states

Determine low voltageseverity for each bus

Determine overloadseverity for each circuit

Determine voltage instability severity for the system

MM

Forecasted operating

conditions Determine cascadingseverity for each circuit

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• Xt,f is forecasted severity measures: flows, voltages, loadability

• Xt,j is small deviation from forecasted value due to variation (or uncertainty) in parameters k:

kk

XXX ftjt Δ

∂∂

+= ,,

Then, the pdf on Xt+1 can be obtained as:

),(~)|Pr( ,,,

T

ftftjt k

XC

k

XXNormalXX ⎥⎦

⎤⎢⎣

⎡∂∂

⎥⎦

⎤⎢⎣

⎡∂∂

C is the covariance matrix for the vector of uncertain parameters k

Uncertainty in operating conditions...

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Severity modeling

LOLP, EUE, Cost of re-dispatch, as indices for use in security-related decision-making, each pre-suppose adecision and are therefore inappropriate.

It’s modeling should NOT depend on a pre-supposed decision as this constrains the decision space, which is the space of investigation.

Re-dispatch

Loa

d cu

rtai

lmen

t

Trans

miss

ion

load

ing

relie

f

Identified by CIGRE TF38.02.21 Task Force asmost difficult problem in probabilistic security assessment.

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Severity modeling: essential features

Definition: Severity is an unavoidable consequence of a specified condition.

It provides a quantitative evaluation of what would happen to the power system in the specified condition.

One uses it, together with probability of the condition, to decide whether to re-dispatch, call for TLR, or interrupt load.

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Severity modeling

Economic quantification is attractive but difficult and can give a false sense of precision.

Essential features• Simple.• Reasonable reflection of relative severity between outcomes to enable calculation of a composite index. • Increase continuously as the performance indicator (e.g., flow, voltage, loading margin, cascaded lines) gets worse.• Interpretable in physical and deterministic terms.

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Voltage in per unit

Severity

Flow as % of rating

10090

1

Severity

0.950.92

1

OVERLOAD

Severity

MW loading margin

1100 100

1

Severity

Number of cascaded circuits

1 2 3 4 5 …

654321

Severity functions...

Because all severity functions evaluate to 1.0 at the deterministic threshold, a risk level R may be roughly thought of as the expectationOf the number of violations in the next hour.

100

LOW VOLTAGE

CASCADINGNote: non-convergenceat any level of cascading evaluates to 100.

VOLTAGEINSTABILITY

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))},(CasNum()),(VCMargin(

)),(Voltage()),(Flow({

)|Pr()Pr()|(

,1,1

,1,1

,1

jtiCasjtiVC

bjtibb

cjticc

i jtjtit

XESevXESev

XESevXESev

XXEXSevRisk

++

++

+

++

+

×=

∑∑

∑∑Decomposability

The above expresses system risk.

Interchanging summations allows us to obtain:• What incurs risk: total risk for a single component (bus or branch risk) or a set of them (regional risk)• What causes risk:

system, regional, or component risk for a specific contingency system, regional, or component risk for a specific problem type

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Decision-making by RBOPF

Traditional OPF:

Minimize: generation cost

Subject to:

Power flow equations

Generation limits

Branch flow & bus voltage constraints

Other security constraints

A variation:

Minimize: a(generation cost) + b(total system risk)

Subject to:

Power flow equations

Generation limits

Regional risk constraints

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Cumulative risk assessment

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Final CommentsThe “secure” and “alert” states

only differ in terms of how insecure they are, and we need a measurable

index to reflect this.

Risk is a computable quantity thatcan be used to integrate security with

economics in formal decision-making algorithms.