THE USES AND MISUSES OF OPF IN CONGESTION

MANAGEMENTpresentation by

George Gross

University of Illinois at Urbana-Champaign

Seminar “Electric Utilities Restructuring”

Institut d’Electricité Montefiore

Université de Liège

December 8, 1999© Copyright George Gross, 1999

OUTLINE

Review of OPF applications in the vertically integrated

utility environment

Review of congestion management in the two paradigms of

unbundled market structures

Pool based

Bilateral Trading

OPF application to competitive markets

Role of the central decision making authority and impacts

on generators

THE BASIC OPF PROBLEM

Nature: optimization of the static power systems for a fixed

point in time

Objective: optimization of a specified metric (e.g. loss

minimization, production cost minimization, ATC maximization)

Constraints: all physical, operational and policy limitations for

the generation and delivery of electricity in a bulk power

system

Decision: optimal policy for selected objective and associated

sensitivity information with direct economic interpretation

OPF PROBLEM CHARACTERISTICS

Nonlinear model of the static power system

Representation of constraints

Representation of contingencies

Incorporation of relevant economic information

Central decision making authority determines optimal

policy

OPF PROBLEM FORMULATION

u = vector of m control variables

x = vector of n state variables

f : m x n is the objective function

g : m x n n is the equality constraints function

h : m x n q is the inequality constraints function

s.t.

min

0xuh

0xug

xuf

),(

),(

),(

ECONOMIC SIGNALS IN THE OPF SOLUTION

For equality constraints the dual variables are

interpreted as the nodal real power or nodal reactive

power prices at each bus

For inequality constraints the dual variables are

interpreted as the sensitivity of the objective function

to a change in the constraint limit

MARKET STRUCTURE PARADIGMS

Pool model

Bilateral model

THE POOL MODEL

The Pool is the sole buyer and seller of electricity

The Pool uses the offers of the suppliers and the bids

of the demanders to determine the set of successful

bidders whose offers and bids are accepted

The Pool determines the “optimum” by solving a

centralized economic dispatch model taking into

account the network constraints

Seller 1

POOL

Seller M Seller i

Buyer N Buyer j Buyer 1

MWh MWh MWh

MWhMWhMWh

.$

.

. . .. . .

. . .

$

$$

$ $

.

THE POOL MODEL

Buyer NBuyer N

CONGESTION MANAGEMENT IN THE POOL MODEL

The Pool model considers explicitly the impacts of the

transmission network constraints

The Pool model assumes implicitly the commitment of

generators which are bidding to supply power

The determination of the economic optimum is done

with the explicit consideration of congestion

THE BILATERAL TRADING MODEL

Players arrange the purchase and sale transactions

among themselves

Each schedule coordinator (SC) and each power

exchange (PX) are responsible for ensuring

supply/demand balance

The independent system operator (ISO) has the role to

facilitate the undertaking of as many of the

contemplated transactions as possible subject to

ensuring that no system security and physical

constraints are violated

... ...

Load aggregator

End userESP

IGO

Scheduling Coordinator

...

Power Exchange

Ancillary Services Market

D I S T R I B U T I O N (W I R E S)D I S T R I B U T I O N (W I R E S)

GG GG GG GG GG GG GG GGGGGGGGGG

BILATERAL TRADING

Bilateral Transactions

BILATERAL TRADING CONGESTION MANAGEMENT

If all contemplated transactions can be undertaken

without causing any limit violations under postulated

contingencies, the system is judged to be capable of

accommodating these transactions and no CM is

needed

On the other hand, the presence of any violation

causes transmission congestion and steps must be

taken by the IGO to re-dispatch the system to remove

the congestion

Objective function: re-dispatch costs

Decision variables are incremental / decremental

adjustments to the generator outputs and decremental

adjustments to the loads

Constraints

transmission constraints

maximum/minimum incremental/decremental

amounts bid

OPF solution: optimal re-dispatch in generation/load

increment/decrement at participating buses

BILATERAL TRADING MODEL CONGESTION MANAGEMENT

ROLE OF OPF IN THE OLD REGIME

The OPF was originally developed for the vertically

integrated utility (VIU) structure

In the VIU, the central decision maker is the utility that

operates and controls the generation and transmission

plants and has the obligation to serve load

The OPF solution makes sense in the VIU environment

KEY DIFFERENCES IN THE ROLE OF OPF IN THE POOL MODEL

The decision maker and the players are no longer the

same entity

The cost is the price that the Pool has to pay to

competitive supply resources

The demand at each bus may be a decision variable

and as such is not fixed

The demand is expressed in the terms of willingness

to pay

The objective is maximize benefits minus costs

OPF STRUCTURAL CHARACTERISTICS

there exists a continuum of “optimum”

solutions which results in effectively the same

cost within a specified tolerance

the choice of an optimum solution has a great

degree of arbitrariness

The “flatness” of solution

x1 x2 f(x1 ) - f(x2 ) <

OPF STRUCTURAL CHARACTERISTICS

Different solution approaches can lead to different optima

Sensitivity of the solution to the initial point point:

different initial points can lead to solutions that are

equally “good”

Solution may be proved to be unique only if the objective

function is convex; in case of multiple minimum solutions

OPF can fail in finding the “true” solution

Solution may not exist

In VIU one may favor one generating unit or another

but all units are owned by the same entity and so it is

purely an internal problem

In competitive markets bias for or against a given

generator may result in the generator’s success or

failure

IMPLICATIONS UNDER DIFFERENT MARKET STRUCTURE

Different optima correspond to different dual variables

nodal prices may be widely different even when the

“optimal’ solutions are close

market signals may not be reliable

IMPLICATIONS

The central decision-making authority has many

degrees of freedom in specifying the OPF model

The definition of the model has a deep impact on

the optimum and on the dual variables.

The major areas under the discretion of the

central authority include:

the inclusion/exclusion of specific constraints

the definition of the set of contingency to be

applied

algorithm choice and parameters

DISCRETION OF CENTRAL AUTHORITY

DISCRETION OF CENTRAL AUTHORITY

OPFIGO

hnconstraint set

contingencyset

algorithmicdetails

feasible

dual variables

yes

no

solution

NUMERICAL RESULTS OF OPF APPLICATIONS TO POOL MODEL

The objective is to maximize benefits minus costs

the loads are assumed to have fixed benefits

each generator submits a different price offer curve

in effect, the objective is to minimize generation

costs incurred by the Pool operator

Numerical studies are used to study anomalous results

with OPF and the impacts of the discretion of the Pool

operator

ANOMALIES IN OPF RESULTS

Power flows from a node with higher nodal price to a

node with a lower nodal price

Nodal price differences between buses at ends of lines

without limit violations

IEEE 30-BUS TEST SYSTEM

1 2

3 4

86 7

5

9

15 18

14

1213

16 17

19

11

10 20

24

2321

22

26

25

27

28

2930

2.40 MW0.90 MVAR

10.60 MW1.90 MVAR

3.50 MW2.30 MVAR

11.20 MVAR17.50 MW

8.70 MW6.70 MVAR

5.80 MW2.00 MVAR

0.70 MVAR2.20 MW

22.80 MW10.90 MVAR

30.00 MVAR30.00 MW

2.40 MW1.20 MVAR

1.80 MVAR3.50 MW 5.80 MVAR

9.00 MW

3.20 MW1.60 MVAR

11.20 MW7.50 MVAR

12.70 MVAR21.70 MW

6.20 MW1.60 MVAR

8.20 MW2.50 MVAR

3.20 MW0.90 MVAR

3.40 MVAR9.50 MW1.60 MVAR

7.60 MW

EXAMPLES: OPF APPLICATION

IEEE 30-bus system

All line MVA limits are enforced

Additional 8 MVA limit on line joining buses 15 and 23

Unexpected results of OPF solution

power flows from higher to lower priced nodes

flows on lines without limit violation

OPF POWER FLOWS

congested linespower flows from lower to higher nodal pricespower flows from higher to lower nodal prices

IEEE 30-bus system with the standard line flow limits and an 8 MVA flow limit on line 15-23

1 2

3 4

86 7

5

9

15 18

14

1213

16 17

19

11

10 20

24

2321

22

26

25

27

28

2930

18=4.129

15=4.135

19=4.106

1=3.668 2=3.694

3=3.768

10=3.938

22=3.870 24=3.961

25=4.466

28=4.5426=3.770

21=3.988

4=3.786

EXAMPLE: OPF APPLICATION

Real power losses on lines are neglected

Key focus: line flows on lines without limit violations

LINE FLOWS ON LINES WITHOUT LIMIT VIOLATIONS

1 2

3 4

86 7

5

9

15 18

14

1213

16 17

19

11

10 20

24

23

2122

26

25

27

28

2930

2=3.489

3=3.541 4=3.550

10=4.501

22=3.975

21=5.046

IEEE 30-bus system with

standard line flow limits

and an 8 MVA flow limit on line 15-23; real losses neglected

congested linespower flows from lower to higher nodal pricespower flows from higher to lower nodal prices

IMPACTS OF DISCRETION OF CENTRAL AUTHORITY

Nature of discretion

consideration of line flows limits

specification of different voltage profiles

Illustration of the volatility of dual variables

impacts of nodal prices

allocation of generation levels among suppliers

EXAMPLE: LINE FLOWS LIMITS

Base case: no line limits considered

Case C1: limits of 20, 15 and 10 MVA on lines 1-2,

12-13 and 25-27, respectively

Case C2: limits of 20, 20 and 8 MVA on lines 1-3,

21-22 and 27-28 , respectively

Case C3: limits of 15, 15 and 10 MVA on lines 3-4,

12-13 and 15-23, respectively

EXAMPLE: LINE FLOW LIMITS

0.940.950.960.970.980.99

11.011.021.031.041.051.06

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

bus

bu

s vo

ltag

e

BC C1 C2 C3

OPTIMUM AND NODAL PRICE IMPACTS

1.5

2

2.5

3

3.5

4

4.5

5

5.5

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

bus

no

dal

pri

ces

[$/M

Wh

]

BC C1 C2 C3

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

C1 C2 C3

% c

han

ge

in o

bje

ctiv

e

GENERATION LEVEL IMPACTS

0 5 10 15 20 25 30 35 40 45 50 55 60 65

1

2

13

22

23

27

ge

ne

rato

r at

bu

s n

o.

generator real power [MW]

C3

C2

C1

BC

-35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55

1

2

13

22

23

27

gene

rato

r b

us

generator level variation [%]

C3

C2

C1

EXAMPLE: VOLTAGE PROFILE SPECIFICATION

No line power flow limits

Base case: 0.95 Vi 1.05 p.u. for each bus i

Case A: fixed voltage equal to 1.0 p.u. at buses 3,4 and

10, and 0.95 Vi 1.05 p.u. for all other buses

Case B: 0.98 Vi 1.02 p.u. for each bus i

Case C: 0.98 Vj 0.99 p.u. for j = 10,11,14,20 and 26,

and 0.95 Vi 1.05 p.u. for all other buses

case D: fixed voltages at 0.98 at buses 9, 19 and 21, and

0.95 Vi 1.05 p.u. for all other buses

VOLTAGE PROFILE CASES

0.940.950.960.970.980.99

11.011.021.031.041.051.06

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

bus

bu

s vo

ltag

e

BC A B C D

OPTIMUM AND NODAL PRICE IMPACTS

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

bus

no

da

l pri

ce

s [

$/M

W h

r]

BC A B C D

52

0.00

0.50

1.00

1.50

2.00

2.50

A B C D

case

% c

han

ge

in o

bje

ctiv

e

GENERATION LEVEL IMPACTS

0 10 20 30 40 50 60 70 80 90

1

2

13

22

23

27

ge

ne

rato

r at

bu

s n

o.

generator real power [MW]

D

C

B

A

BC

-85 -70 -55 -40 -25 -10 5 20 35 50 65 80 95 110 125

1

2

13

22

23

27

gen

erat

or

bu

s

generation level variation [%]

D

C

B

A

CONCLUDING REMARKS

The OPF tool is applicable in a central decision making

environment The discretion of the central decision making authority

in OPF applications in unbundled electricity markets has

broad economic impacts, which are especially

significant for generators The flat nature of the objective function, particularly in

the neighborhood of the optimum, implies a great

degree of arbitrariness in the choice of the optimum An improved understanding of the anomalous results

and more effective application of OPF in unbundled

markets are necessary for the OPF to gain acceptance