A O L P AOLP - - PowerPoint PPT Presentation

A O L P AOLP E G

F A O

Prakash Ranganathan, Assistant Professor Electrical Engineering, University of North Dakota, Grand Forks, ND, 58202 Kendall Nygard, Professor Department of Computer Science, North Dakota State University, Fargo, ND 58102

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A Smart Agent Oriented Linear Programming Model in Electric grid

Arizona Blackout - 2011

The massive power blackout that caused some 5 million people in Arizona, California and Mexico to lose electricity was apparently triggered by one person in Arizona. An Arizona Public Service Company worker "removed a piece

• f monitoring equipment," which set off a chain reaction

across the region, according to the Associated press [*]. The outage appears to be related to a procedure an Arizona Public Service (APS) employee was carrying out in the North Gila substation, which is located northeast of

• Yuma. Operating and protection protocols typically would

have isolated the resulting outage to the Yuma area. The reason that did not occur in this case is mostly blamed due to lack of automated programs in place and rely heavy on man power, although the investigation into the event is under way. Our approach addresses such events through agent based LP programs such as the (AOLP) architecture discussed below. Reference: *News release, San Diego Gas & Electric Co., IEEE Spectrum, Sept 9 2011, and www.npr.org, EPEC 2012_K_Nygard_Ranganathan 2 "Whether it was human error or some malfunction of equipment, we don't know,“ Bose, Professor of EE at Washington State University said. "Usually in these cases it is a bit of both. “Automated software program or appropriate situational awareness would have alerted the system ahead.

Objective

To show how large linear programming (LP) models can be effective by decomposing into smaller sub problems. Such models prove to be more powerful as decision making tool both economically and computationally. Dantzig-Wolfe decomposition is an optimization technique for solving large scale, block structured, linear programming (LP) problems. Problems from many different fields such as production planning, resource allocation may be formulated as LP problems.

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Agents running Linear Programming (LP) models

(Classifying problems that has special structure as Master and Sub problems)

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• Fig. 2. LP as agents
• Fig. 3. Local microgrid with PMU‐PDC

integration as part of WAMS (Work in progress and in preliminary stages)

Dantzig-Wolfe Structure

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• Fig. 4: DW structure

IEEE 14 bus test system

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• Fig. 5. IEEE 14 bus with 5 Generators and 11 loads

Flow balance constraints

0; 1 1; ; ; ; ; ∈ 0,1 1; ; ; ; ; ∈ 0,1

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Flow balance constraints (Contd.)

Node 2: ; Node 3: ; Node 4: 47;

: 7, 9 , 1

Node 5: 7.6; Other constraints: 1; 1 ; 1; 1; 1; 1; 1; 0;

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Node 6: ; 51 Node 7: 0; Node 8: ; Node 9: 0; Node 10: 0; Node 11: 0; Node 12: 0; Node 13: 0; Node 14: 0;

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Flow balance constraints (Contd.)

Constraints that restrict flow

• nly in one direction

1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1;

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Lower and Upper bounds: Transmission lines

; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

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(Where, UB – Upper bound of capacity of arc and LB – Lower bound)

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Lower and Upper bounds: Transmission lines (Contd.,)

; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

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(Where, UB – Upper bound of capacity of arc and LB – Lower bound)

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Linking Constraints (Master Constraints)

88; 38.3; 60; 25; 13.8; ∑ ;

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Optimization: Objective and Constraints

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• Adding convexity constraint

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Duals and New columns

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DW Decomposition Algorithm

{ Initialization } Choose initial subsets of bus variables such as x1,x2,x3,x4. while true do { Master problem } Solve the restricted master problem. W := duals of coupling constraints k : = duals of the kth convexity constraint {Other bus constraints as Sub problems} for k=1,. . . ,K do Plug W and k into sub‐problem k Solve sub‐problem k if (Zj‐C) >=0 then // termination condition Add proposal xk to the restricted master k to the restricted master end if end for if No proposals generated (i.e., Z=0) then Stop: optimal end if end while

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Load demand

L1(2) L2(3) L3(5) L4(4) L5(6) L6(11) L7(10) L8(9) L9(12) L10(13) L11(14) Supply G1 (1) 5.55 11.7 7.14 14.47 7.15 7.16 7.52 8.11 7.424 7.67 8.21 88 G2 (2) 1 6.15 6.34 9.92 6.35 6.36 6.72 7.31 6.624 6.87 7.41 60 G3 (3) 6.15 1 12.79 8.53 15.88 15.89 16.25 16.84 16.15 16.4 16.9 60 G4 (8) 11.92 10.53 9.34 2.0 3.31 3.3 2.94 2.35 3.58 3.83 3.33 25 G5 (6) 6.35 15.88 0.01 7.35 1 0.01 0.37 0.96 0.274 0.44 0.98 25 21.7 94.2 7.6 47 11.2 3.5 9 29.5 6 13.5 14.8 258 EPEC 2012_K_Nygard_Ranganathan 18

Results for IEEE 14 bus system

(preliminary results) Approach run time Variables Z Direct LP 8ms 400 Z=0.007 (Failure rate) Dantzig Wolfe 1ms 400 Z=0.007 (Failure rate) Direct LP 10ms 400 Z=1.89 (repair rate) Dantzig Wolfe 0.5ms 400 Z=1.89 (repair rate)

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Table 1: Simulation carried in AMPL with 170 Constraints

Column Generation

> trillions of Variables

Variables that were never considered

Restricted Master Problem (RMP)

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Conclusion

• The paper show that, if a reasonable block structure

can be found, the decomposition method is worth

• trying. Dantzig‐Wolfe decomposition will not rival

mainstream techniques as an optimization method for all LP problems.

• We believe that Dantzig‐Wolfe decomposition has

some niche areas of application: certain large scale classes of primal block angular structured problems, and in particular where the context demands rapid results using parallel optimization, or near optimal solutions with a guaranteed quality is possible.

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