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  1. 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 EPEC 2012_K_Nygard_Ranganathan 1 A Smart Agent Oriented Linear Programming Model in Electric grid

  2. 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 of 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., "Whether it was human error or some malfunction of IEEE Spectrum, Sept 9 2011, and www.npr.org, 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. EPEC 2012_K_Nygard_Ranganathan 2

  3. 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. EPEC 2012_K_Nygard_Ranganathan 3

  4. Agents running Linear Programming (LP) models (Classifying problems that has special structure as Master and Sub problems) Fig. 2. LP as agents Fig. 3. Local microgrid with PMU ‐ PDC integration as part of WAMS (Work in progress and in preliminary stages) EPEC 2012_K_Nygard_Ranganathan 4

  5. Dantzig-Wolfe Structure Fig. 4: DW structure EPEC 2012_K_Nygard_Ranganathan 5

  6. IEEE 14 bus test system Fig. 5. IEEE 14 bus with 5 Generators and 11 loads 6 EPEC 2012_K_Nygard_Ranganathan

  7. Flow balance constraints �� �� �� �� � � � �� � � �� � 0; ����� 1� � �� � � �� � 1; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� ��� � �� ∈ 0,1 � �� � � �� � 1; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� ��� � �� ∈ �0,1� 7 EPEC 2012_K_Nygard_Ranganathan

  8. Flow balance constraints (Contd.) Node 2: �� �� �� �� � � �� � � �� � � � �� � � �� � � �� � � �� � � �� ; Node 3: �� �� �� �� � � � �� � � �� � � �� ; Node 4: �� �� �� �� � � �� � � � �� � � �� � � �� � 47; ����: ����� 7, 9 ��� ��� ����������, �� ���� ��� ��� �� ������ 1 Node 5: �� �� �� �� � � �� � � � �� � � �� � � �� � 7.6; � �� � � �� � 1; Other constraints: � �� � � �� � 1 ; � �� � � �� � 1; � �� � � �� � 1; � �� � � �� � 1; � �� � � �� � 1; � �� � � �� � 1; �� �� �� �� � � �� � � �� � � � �� � � �� � � �� � � �� � 0; 8 EPEC 2012_K_Nygard_Ranganathan

  9. Flow balance constraints (Contd.) 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; 9 EPEC 2012_K_Nygard_Ranganathan

  10. Constraints that restrict flow only in one direction � �� � � �� � 1; � ���� � � ���� � 1 ; � ���� � � ���� � 1 ; � �� � � �� � 1 ; � �� � � �� � 1 ; � �� � � �� � 1 ; � �� � � �� � 1 ; � ���� � � ���� � 1 ; � ���� � � ���� � 1 ; � ����� � � ����� � 1 ; � ���� � � ���� � 1 ; � ����� � � ����� � 1 ; � ����� � � ����� � 1 ; � ���� � � ���� � 1 ; � ���� � � ���� � 1 ; � ����� � � ����� � 1 ; 10 EPEC 2012_K_Nygard_Ranganathan

  11. Lower and Upper bounds: Transmission lines � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � �� � �� � �� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ���� � �� � ���� ; � ����� � �� � ����� ; � ����� � �� � ����� ; � ����� � �� � ����� ; � ����� � �� � ����� ; (Where, UB – Upper bound of capacity of arc and LB – Lower bound) 11 EPEC 2012_K_Nygard_Ranganathan

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