Matching Items (2)
Filtering by
- All Subjects: Holomorphic Embedding
- Creators: Undrill, John
Description
Power flow calculation plays a significant role in power system studies and operation. To ensure the reliable prediction of system states during planning studies and in the operating environment, a reliable power flow algorithm is desired. However, the traditional power flow methods (such as the Gauss Seidel method and the Newton-Raphson method) are not guaranteed to obtain a converged solution when the system is heavily loaded.
This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution.
By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail.
With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER.
This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution.
By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail.
With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER.
ContributorsLi, Yuting (Author) / Tylavsky, Daniel J (Thesis advisor) / Undrill, John (Committee member) / Vittal, Vijay (Committee member) / Arizona State University (Publisher)
Created2015
Description
For a (N+1)-bus power system, possibly 2N solutions exists. One of these solutions
is known as the high-voltage (HV) solution or operable solution. The rest of the solutions
are the low-voltage (LV), or large-angle, solutions.
In this report, a recently developed non-iterative algorithm for solving the power-
flow (PF) problem using the holomorphic embedding (HE) method is shown as
being capable of finding the HV solution, while avoiding converging to LV solutions
nearby which is a drawback to all other iterative solutions. The HE method provides a
novel non-iterative procedure to solve the PF problems by eliminating the
non-convergence and initial-estimate dependency issues appeared in the traditional
iterative methods. The detailed implementation of the HE method is discussed in the
report.
While published work focuses mainly on finding the HV PF solution, modified
holomorphically embedded formulations are proposed in this report to find the
LV/large-angle solutions of the PF problem. It is theoretically proven that the proposed
method is guaranteed to find a total number of 2N solutions to the PF problem
and if no solution exists, the algorithm is guaranteed to indicate such by the oscillations
in the maximal analytic continuation of the coefficients of the voltage power series
obtained.
After presenting the derivation of the LV/large-angle formulations for both PQ
and PV buses, numerical tests on the five-, seven- and 14-bus systems are conducted
to find all the solutions of the system of nonlinear PF equations for those systems using
the proposed HE method.
After completing the derivation to find all the PF solutions using the HE method, it
is shown that the proposed HE method can be used to find only the of interest PF solutions
(i.e. type-1 PF solutions with one positive real-part eigenvalue in the Jacobian
matrix), with a proper algorithm developed. The closet unstable equilibrium point
(UEP), one of the type-1 UEP’s, can be obtained by the proposed HE method with
limited dynamic models included.
The numerical performance as well as the robustness of the proposed HE method is
investigated and presented by implementing the algorithm on the problematic cases and
large-scale power system.
is known as the high-voltage (HV) solution or operable solution. The rest of the solutions
are the low-voltage (LV), or large-angle, solutions.
In this report, a recently developed non-iterative algorithm for solving the power-
flow (PF) problem using the holomorphic embedding (HE) method is shown as
being capable of finding the HV solution, while avoiding converging to LV solutions
nearby which is a drawback to all other iterative solutions. The HE method provides a
novel non-iterative procedure to solve the PF problems by eliminating the
non-convergence and initial-estimate dependency issues appeared in the traditional
iterative methods. The detailed implementation of the HE method is discussed in the
report.
While published work focuses mainly on finding the HV PF solution, modified
holomorphically embedded formulations are proposed in this report to find the
LV/large-angle solutions of the PF problem. It is theoretically proven that the proposed
method is guaranteed to find a total number of 2N solutions to the PF problem
and if no solution exists, the algorithm is guaranteed to indicate such by the oscillations
in the maximal analytic continuation of the coefficients of the voltage power series
obtained.
After presenting the derivation of the LV/large-angle formulations for both PQ
and PV buses, numerical tests on the five-, seven- and 14-bus systems are conducted
to find all the solutions of the system of nonlinear PF equations for those systems using
the proposed HE method.
After completing the derivation to find all the PF solutions using the HE method, it
is shown that the proposed HE method can be used to find only the of interest PF solutions
(i.e. type-1 PF solutions with one positive real-part eigenvalue in the Jacobian
matrix), with a proper algorithm developed. The closet unstable equilibrium point
(UEP), one of the type-1 UEP’s, can be obtained by the proposed HE method with
limited dynamic models included.
The numerical performance as well as the robustness of the proposed HE method is
investigated and presented by implementing the algorithm on the problematic cases and
large-scale power system.
ContributorsMine, Yō (Author) / Tylavsky, Daniel (Thesis advisor) / Armbruster, Dieter (Committee member) / Holbert, Keith E. (Committee member) / Sankar, Lalitha (Committee member) / Vittal, Vijay (Committee member) / Undrill, John (Committee member) / Arizona State University (Publisher)
Created2015