| dc.description.abstract | For over half a century, Power Flow (PF) and its optimized version, Optimal Power Flow
(OPF), has become one of the most important and widely used tools in power system
planning, operational planning, and operation/control. The solution to the PF problem
is carried out extensively for various power system activities and is essential for both offline
applications, such as planning and stability studies and online applications, including
security monitoring and contingency analysis, optimal power flow, to name a few. In comparison,
OPF seeks to optimize the operation and planning of electric power generation,
transmission, and distribution networks subject to various system constraints and control
limits. Different PF/OPF techniques have been proposed, each with its own unique
formulation, solution methodology, advantages, and drawbacks. Motivated by the growing
inclusion of distributed energy resources, such as highly variable renewable generating
resources; and further, by the speed and convergence limitations of existing tools, this
research focuses on developing simple, accurate, fast; yet, computationally efficient tools
for operation and planning of electric power systems. This thesis introduces a radically
new generalized direction in power system problem formulations and proposes a novel
Graph Theory-based optimization algorithm for solving the PF/OPF problem, that is also
suitable for transmission, distribution, and hybrid AC/DC power systems.
To start, a novel algorithm is developed for a power flow solution based on maximumflow
formulation, titled “Flow-Augmentation PF.” Modeling of power system components
for the proposed network-flow formulation is presented, followed by s-t flow modeling. The
proposed method formulates a power flow problem as a network-flow problem and solves
it by using a maximum-flow algorithm, inspired by the push-relabel max-flow technique.
In contrast to previously established methods in the literature, the proposed methodology
relies on transforming the power system configuration and topology into an efficient analytical
form (matrices and arrays). The solution methodology of the proposed PF algorithm
is discussed in detail. The methodology includes a discussion on the algorithm correctness,
termination, and computational complexity. The developed Flow-Augmentation method
solves the power flow problem using matrix-vector multiplication in its most abstract form, and further, the developed method is independent of system parameters and network configuration.
The proposed algorithm captures the full system model and handles any system
configuration without resorting to special treatment. The presented algorithm is computationally
efficient and compares favorably with current methods, in terms of execution time
and accuracy.
Second, a new generalized PF/OPF framework based on the minimum-cost flow network
model is introduced. The proposed formulation seeks to find the network-flow distribution
that optimizes a stated objective function, such as generator costs or gas emissions,
system losses, or any other indices. The solution of the PF problem is obtained by using
a proposed modified version of the minimum-cost flow model, termed MinLoss-Flow
PF algorithm. This algorithm builds upon the models developed in the above-mentioned
maximum-flow-based method, in terms of system component modeling and graph formulation.
The developed MinLoss-Flow PF focuses on finding the minimum system losses
that satisfy both the technical and engineering constraints. As such, the generalized mathematical
formulation, based on cost flow calculation and its properties, is developed. The
MinLoss-Flow PF method is fully discussed and validated against well-known methods
used for transmission and distribution systems.
Third, this thesis presents a sequential network-flow graph-based method for a steadystate
power flow solution in hybrid AC/DC multi-terminal power systems. The proposed
method is a unique and novel one, which differs from other established methods that involve
the use of modified versions of classical power flow methods. The proposed method
formulates the hybrid AC/DC power flow problem as a maximum network-flow problem
and solves it, using a max-flow-based algorithm. The proposed flow-augmentation power
flow algorithm solves the AC and DC sides sequentially while employing the detailed converter
model, including the converter transformer, filter, and the converter loss parameters
for converter power loss calculations. The proposed method is validated using standard
hybrid 5-bus and CIGR´E-B4-DC systems.
The performance of the novel graph-based PF/OPF tools is validated using several
benchmark networks of different sizes, topologies, and parameters. Many case studies
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were conducted and compared with the most commonly used techniques for transmission,
distribution, and hybrid AC/DC systems. The proposed algorithm is also validated and
compared with the results obtained from two commercial software packages, PSS/E and
PSCAD. The proposed formulation is computationally efficient, as it is based on matrixvector
multiplication, and is also scalable, considering the formulation works as a graphbased
method, which, inherently, allows for parallel computation for added computational
speed. This proves to be a strong advantage for the proposed method, as a significant
reduction in computational time is observed, as a result. Test results show significant
computational gains of about 70% when compared with the Newton-Raphson on the IEEE
118-bus system, and a value less than 50% reduction compared with the Newton-Raphson
method applied to hybrid AC/DC system. The results also show that the proposed algorithm
takes less than 1.4% of the execution time required by the Backward-Forward-Sweep
method on the 69-bus. The developed graph-based PF/OPF algorithms are coded in GNU
OCTAVE environment and the simulation results are presented to validate the effectiveness
of the proposed techniques. | en |
