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IEEE TRANSACTIONS ON POWER SYSTEMS 1
Decentralized Multi-Area Dynamic Economic
Dispatch Using Modified Generalized
Benders Decomposition
Zhigang Li, Student Member, IEEE, Wenchuan Wu, Senior Member, IEEE, Boming Zhang, Fellow, IEEE, and
Bin Wang
Abstract—Fluctuations in wind power in geographically dis-
tributed areas are typically complementary, and therefore a
coordinated multi-area dynamic economic dispatch may enable
greater wind power penetration in interconnected power systems.
Here we describe a decentralized approach based on a modified
generalized Benders decomposition in which locally optimal cost
function of each area is introduced. The technique exhibits rapid
convergence and does not require parameter tuning. It is suitable
for multi-area interconnected systems with a hierarchical control
architecture. Comparative numerical simulations demonstrate
that the performance of our method is favorable in terms of
accuracy, convergence and computational efficiency. A case study
on a real power system is also carried out to demonstrate the
potential of this technique to increase wind power penetration.
Index Terms—Decentralized optimization, dynamic economic
dispatch, generalized Benders decomposition, multi-area power
systems.
NOMENCLATURE
1) Indices and Sets:
Index of area.
Index of tie-line bus.
Index of iteration time.
Index of scheduling time period.
Index of tie-line.
A Index set of areas.
Index set of feasibility cuts of area .
Index set of optimality cuts of area .
Index set of tie-lines with starting nodes belonging
to area .
Index set of tie-lines with ending nodes belonging
to area .
Manuscript received August 04, 2014; revised November 02, 2014, De-
cember 23, 2014, and February 01, 2015; accepted February 01, 2015. This
work was supported in part by the National Key Basic Research Program
of China (2013CB228205), in part by the National Science Foundation of
China (51177080, 51190105), and in part by New Century Excellent Talents in
University (NCET-11-0281). Paper no. TPWRS-01056-2014.
The authors are with the Department of Electrical Engineering, Tsinghua Uni-
versity, Beijing 100084, China (e- mail: wuwench@tsinghua.edu.cn).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRS.2015.2399474
2) Input Parameters and Functions:
Coefficient matrix/vector/scalar of
generation cost in area .
Generation cost in area during time period
.
Vector of bus loads in area during time
period .
Vector of upper/lower capacity limits of
internal lines in area during time period .
Sensitivity coefficient matrix of network
security constraints area during time
period .
Coefficient matrix relating the equivalent
injected power at boundary buses and at
internal buses in area .
Vector of upper/lower capacity limits of
tie-lines during time period .
Coefficient matrix relating the equivalent
internal injected power at boundary buses of
area and tie-line flows.
Vector of maximum/minimum generated
output of units in area during period .
Upward/downward spinning reserve
requirement in area during time period .
Vector of maximum upward/downward
ramping rates of units in area during time
period .
Coefficient matrix relating the equivalent
external injections in area and the
equivalent internal injections in area .
Total number of periods in the dispatch time
horizon.
Auxiliary variable.
Locally optimal cost of a separated
subproblem in area .
3) Decision Variables:
Vector of the power flow at tie-lines during time
period .
Vector of generated output of units in area during
time period .
Vector of equivalent external injected power at
boundary buses in area during period .
Vector of equivalent internal injected power at
boundary buses in area during period .
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