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- All Subjects: POWER SYSTEM
- 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
Ensuring reliable operation of large power systems subjected to multiple outages is a challenging task because of the combinatorial nature of the problem. Traditional methods of steady-state security assessment in power systems involve contingency analysis based on AC or DC power flows. However, power flow based contingency analysis is not fast enough to evaluate all contingencies for real-time operations. Therefore, real-time contingency analysis (RTCA) only evaluates a subset of the contingencies (called the contingency list), and hence might miss critical contingencies that lead to cascading failures.This dissertation proposes a new graph-theoretic approach, called the feasibility test (FT) algorithm, for analyzing whether a contingency will create a saturated or over-loaded cut-set in a meshed power network; a cut-set denotes a set of lines which if tripped separates the network into two disjoint islands. A novel feature of the proposed approach is that it lowers the solution time significantly making the approach viable for an exhaustive real-time evaluation of the system. Detecting saturated cut-sets in the power system is important because they represent the vulnerable bottlenecks in the network. The robustness of the FT algorithm is demonstrated on a 17,000+ bus model of the Western Interconnection (WI).
Following the detection of post-contingency cut-set saturation, a two-component methodology is proposed to enhance the reliability of large power systems during a series of outages. The first component combines the proposed FT algorithm with RTCA to create an integrated corrective action (iCA), whose goal is to secure the power system against post-contingency cut-set saturation as well as critical branch overloads. The second component only employs the results of the FT to create a relaxed corrective action (rCA) that quickly secures the system against saturated cut-sets.
The first component is more comprehensive than the second, but the latter is computationally more efficient. The effectiveness of the two components is evaluated based upon the number of cascade triggering contingencies alleviated, and the computation time. Analysis of different case-studies on the IEEE 118-bus and 2000-bus synthetic Texas systems indicate that the proposed two-component methodology enhances the scope and speed of power system security assessment during multiple outages.
ContributorsSen Biswas, Reetam (Author) / Pal, Anamitra (Thesis advisor) / Vittal, Vijay (Committee member) / Undrill, John (Committee member) / Wu, Meng (Committee member) / Zhang, Yingchen (Committee member) / Arizona State University (Publisher)
Created2021