1. THE USES AND MISUSES OF OPF IN CONGESTION MANAGEMENT
presentation 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. MARKET STRUCTURE PARADIGMS
Pool model
Bilateral model

8. 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

9. . . . . . . . . . . THE POOL MODEL $ $ $ $ $ $ MWh MWh MWh POOL MWh
Seller 1
Seller i
Seller M
MWh
MWh
MWh $ $ $
POOL
MWh
MWh
MWh $ $ $ . . . . . .
Buyer N
Buyer 1
Buyer j
Buyer N

10. 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

11. 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

12. Bilateral Transactions Scheduling Coordinator
BILATERAL TRADING
ESP
Load aggregator
End user
D I S T R I B U T I O N (W I R E S)
IGO
Bilateral Transactions
Power Exchange
Ancillary Services Market
Scheduling Coordinator
...
...
... G G G G G G G G G G G G G G G G G G G G G G G G

13. 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

14. BILATERAL TRADING MODEL CONGESTION MANAGEMENT
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

15. 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

16. 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

17. OPF STRUCTURAL CHARACTERISTICS
The “flatness” of solution x1 x2
 f(x1 ) - f(x2 )  < 
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

18. 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

19. IMPLICATIONS UNDER DIFFERENT MARKET STRUCTURE
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

20. IMPLICATIONS 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

21. DISCRETION OF CENTRAL AUTHORITY
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

22. DISCRETION OF CENTRAL AUTHORITYhn
constraint set
dual variables
yes
OPF
solution
contingencyset
IGO
feasible
algorithmic
details no

23. 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

24. 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

25. IEEE 30-BUS TEST SYSTEM 1 2 3 4 8 6 7 5 9 15 18 14 12 13 16 17 19 11 10 20 24 23 21 22 26 25 27 28 29 30
2.40 MW
0.90 MVAR
10.60 MW
1.90 MVAR
3.50 MW
2.30 MVAR
11.20 MVAR
17.50 MW
8.70 MW
6.70 MVAR
5.80 MW
2.00 MVAR
0.70 MVAR
2.20 MW
22.80 MW
10.90 MVAR
30.00 MVAR
30.00 MW
1.20 MVAR
1.80 MVAR
5.80 MVAR
9.00 MW
3.20 MW
1.60 MVAR
11.20 MW
7.50 MVAR
12.70 MVAR
21.70 MW
6.20 MW
8.20 MW
2.50 MVAR
3.40 MVAR
9.50 MW
7.60 MW

26. 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

27. OPF POWER FLOWS
l1=3.668
l2=3.694
l15=4.135
l 18=4.129 1 2 15 18
l 3=3.768 14 19
l19=4.106
l28=4.542 3 4
l4=3.786
l6=3.770 28 13 8 5 12 6 7 9 11
l10=3.938 16 17 10 20
l22=3.870
l24=3.961 26 23
l21=3.988 21
l25=4.466 25 22 24
IEEE 30-bus system with the standard line flow limits and an 8 MVA flow limit on line 15-23 27 29 30
congested lines
power flows from lower to higher nodal prices
power flows from higher to lower nodal prices

28. EXAMPLE: OPF APPLICATION
Real power losses on lines are neglected
Key focus: line flows on lines without limit violations

29. LINE FLOWS ON LINES WITHOUT LIMIT VIOLATIONS1 2 15 18 14 19
l3=3.541 3 4
l4=3.550 28 13 8 5 12 6 7 9 11
l10=4.501 16 17 10 20
l22=3.975 26
l21=5.046 23 21 25 22 24
IEEE 30-bus system with
standard line flow limits
and an 8 MVA flow limit on line 15-23; real losses neglected 27 29 30
congested lines
power flows from lower to higher nodal prices
power flows from higher to lower nodal prices

30. 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

31. EXAMPLE: LINE FLOWS LIMITS
Base case: no line limits considered
Case C1: limits of 20, 15 and 10 MVA on lines 1-2, and 25-27, respectively
Case C2: limits of 20, 20 and 8 MVA on lines 1-3, and , respectively
Case C3: limits of 15, 15 and 10 MVA on lines 3-4, and 15-23, respectively

32. EXAMPLE: LINE FLOW LIMITS

33. OPTIMUM AND NODAL PRICE IMPACTS

34. GENERATION LEVEL IMPACTS

35. 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  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

36. VOLTAGE PROFILE CASES

37. OPTIMUM AND NODAL PRICE IMPACTS

38. GENERATION LEVEL IMPACTS

39. 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