A Novel Forbidden-Region-Based Stability Criterion in Modified SequenceDomain for AC Grid-Converter System
Abstract: A novel forbidden-region-based criterion (N-FRBC) is proposed in modified sequence-domain for AC grid-converter system. Compared with the forbiddenregion-based criterion (FRBC) in dq-domain, the number of constraint condition is re-duced due to the mirror frequency symmetry of the impedance matrix in modified sequence-domain. In addition, the improved forbidden region decreases the conservatism of the FRBC. Simulation and experimental results verify the effectiveness and correctness of proposed N-FRBC in studying the stability issues of the AC grid-converter system. Existing system: As the AC grid-converter system is a kind of the multiple inputs and multiple output (MIMO) cascade system in dq-domain, the classical stability analysis method is the generalized Nyquist criterion (GNC). In addition, some estimatedcriterions of stability without calculating eigenvalues of the impedance ratio matrix also play an important role in identifying the stability of the MIMO cascade system, such as singularity values criterion (SVC), norm criterion (NC) and FRBC.
The con-servatism of criterion is an important standard for evaluating these estimated-criterions. The less conservatism implies the less error in analyzed results compared with the real critical stability condition. In the existing estimatedcriterions, the FRBC has less conservatism and is simpler than SVC and NC. Proposed system: Therefore, a N-FRBC based on impedance matrix in modified sequence-domain is proposed in this letter. Firstly, due to the mirror frequency symmetry of the impedance matrix in modified sequence-domain, the constraint conditions of the FRBC are reduced from two to one. Then, the improved for-bidden region decreases the conservatism of the FRBC. As a result, the proposed N-FRBC is more accurate to estimate real critical stability condition of the AC grid-converter system than the FRBC in dq-domain. Advantages: It is caused by the linear trans-formation between the dq-domain and the modified se-quence-domain, and is satisfied in whole frequency range. It implies that the frequency response of Lnn in positive frequency can be calculated by the frequency response of Lpp in corresponding negative frequency. Moreover, the off-diagonal elements Lpn and Lnp also satisfy the mirror frequency symmetry. As the eigenvalues of the impedance ratio matrix in modified sequence-domain are same as, the simulation results of the GNC are matched well in different impedance domains. Thus, the FRBC in modified sequence-domain. Disadvantages: In addition, some estimated-criterions of stability without calculating eigenvalues of the impedance ratio matrix also play an important role in identifying the stability of the MIMO cascade system, such as singularity values criterion (SVC) , norm criterion (NC) and FRBC. The con-servatism of criterion is an important standard for evaluating these estimated-criterions. The less conservatism implies the less error in analyzed results compared with the real critical stability condition. In the existing estimatedcriterions, the FRBC has less conservatism and is simpler than SVC and NC.
Modules: Singularity values criterion: Recently years, many stability criterions based on im-pedance ratio matrix in dqdomain have been presented to investigate the stability of AC grid-converter systems. As the AC grid-converter system is a kind of the multiple input and multiple output (MIMO) cascade system in dq-domain, the classical stability analysis method is the generalized Nyquist criterion (GNC) . In addition, some estimated-criterions of stability without calculating eigenvalues of the impedance ratio matrix also play an important role in identifying the stability of the MIMO cascade system, such as singularity values criterion (SVC), norm criterion (NC) and FRBC . The con-servatism of criterion is an important standard for evaluating these estimated-criterions. The less conservatism implies the less error in analyzed results compared with the real critical stability condition. In the existing estimatedcriterions, the FRBC has less conservatism and is simpler than SVC and NC. N-FRBC Based on Improved Forbidden Region: Although some eigenvalues may locate in the forbidden region, the curves of eigenvalues may not encircle the point. In fact, if one Eigen value locates at the region on the imaginary axis, the curves of eigenvalues must encircle the point. Therefore, in the s plane, shows that the improved forbidden region is decreased as one radial line on the imaginary axis that decreases the conservatism of the FRBC. For a MIMO system, one supplemental sufficient condition to guarantee that eigenvalues do not locate at the region on imaginary axis, which satisfies. Influential Factor Identification: According to, the stability prediction of the FRBC mainly depends on the change of real parts of eigenvalues. It neglects the impact of the imaginary parts. It causes the larger conservatism. However, some parameters have larger influence on the imaginary parts of the eigenvalues. Their influence laws on the stability may not be reflected correctly by using FRBC. For example, when the number of energized electric trains is 3, it can be seen that the Nyquist curves do not encircle the point with increasing Kpc. However, as the real parts of eigenvalues always locate in the forbidden region under different Kpc, the analysis results of the FRBC shown in
indicate that increasing Kpc cannot enhance the stability of the system. Obviously, the larger conservatism of the FRBC causes the wrong conclusion. Fig. 9(c) presents the analysis results by the N-FRBC. The magnitude curves of Condition 2 will be satisfied, which indicates that increasing Kpc will make the railway trainnetwork system stable. The analysis results of the N-FRBC are in a good agreement with that of the GNC.